On the duration of negative surplus

Doutoramento em Matemática

Feasibility study and flow scheduling optimization of a multi-product pipeline system

The first goal of this study is to analyse a real-world multiproduct onshore pipeline system in order to verify its hydraulic configuration and operational feasibility by constructing a simulation model step by step from its elementary building blocks that permits to copy the operation of the real system as precisely as possible. The second goal is to develop this simulation model into a user-friendly tool that one could use to find an “optimal” or “best” product batch schedule for a one year time period. Such a batch schedule could change dynamically as perturbations occur during operation that influence the behaviour of the entire system. The result of the simulation, the ‘best’ batch schedule is the one that minimizes the operational costs in the system. The costs involved in the simulation are inventory costs, interface costs, pumping costs, and penalty costs assigned to any unforeseen situations. The key factor to determine the performance of the simulation model is the way time is represented. In our model an event based discrete time representation is selected as most appropriate for our purposes. This means that the time horizon is divided into intervals of unequal lengths based on events that change the state of the system. These events are the arrival/departure of the tanker ships, the openings and closures of loading/unloading valves of storage tanks at both terminals, and the arrivals/departures of trains/trucks at the Delivery Terminal. In the feasibility study we analyse the system’s operational performance with different Head Terminal storage capacity configurations. For these alternative configurations we evaluated the effect of different tanker ship delay magnitudes on the number of critical events and product interfaces generated, on the duration of pipeline stoppages, the satisfaction of the product demand and on the operative costs. Based on the results and the bottlenecks identified, we propose modifications in the original setup.

Keeping Variables within Bounds: Using Information between Observations

This research develops an econometric framework to analyze time series processes with bounds. The framework is general enough that it can incorporate several different kinds of bounding information that constrain continuous-time stochastic processes between discretely-sampled observations. It applies to situations in which the process is known to remain within an interval between observations, by way of either a known constraint or through the observation of extreme realizations of the process. The main statistical technique employs the theory of maximum likelihood estimation. This approach leads to the development of the asymptotic distribution theory for the estimation of the parameters in bounded diffusion models. The results of this analysis present several implications for empirical research. The advantages are realized in the form of efficiency gains, bias reduction and in the flexibility of model specification. A bias arises in the presence of bounding information that is ignored, while it is mitigated within this framework. An efficiency gain arises, in the sense that the statistical methods make use of conditioning information, as revealed by the bounds. Further, the specification of an econometric model can be uncoupled from the restriction to the bounds, leaving the researcher free to model the process near the bound in a way that avoids bias from misspecification. One byproduct of the improvements in model specification is that the more precise model estimation exposes other sources of misspecification. Some processes reveal themselves to be unlikely candidates for a given diffusion model, once the observations are analyzed in combination with the bounding information. A closer inspection of the theoretical foundation behind diffusion models leads to a more general specification of the model. This approach is used to produce a set of algorithms to make the model computationally feasible and more widely applicable. Finally, the modeling framework is applied to a series of interest rates, which, for several years, have been constrained by the lower bound of zero. The estimates from a series of diffusion models suggest a substantial difference in estimation results between models that ignore bounds and the framework that takes bounding information into consideration.

Essays in Financial Econometrics

The first paper sheds light on the informational content of high frequency data and daily data. I assess the economic value of the two family models comparing their performance in forecasting asset volatility through the Value at Risk metric. In running the comparison this paper introduces two key assumptions: jumps in prices and leverage effect in volatility dynamics. Findings suggest that high frequency data models do not exhibit a superior performance over daily data models. In the second paper, building on Majewski et al. (2015), I propose an affine-discrete time model, labeled VARG-J, which is characterized by a multifactor volatility specification. In the VARG-J model volatility experiences periods of extreme movements through a jump factor modeled as an Autoregressive Gamma Zero process. The estimation under historical measure is done by quasi-maximum likelihood and the Extended Kalman Filter. This strategy allows to filter out both volatility factors introducing a measurement equation that relates the Realized Volatility to latent volatility. The risk premia parameters are calibrated using call options written on S&P500 Index. The results clearly illustrate the important contribution of the jump factor in the pricing performance of options and the economic significance of the volatility jump risk premia. In the third paper, I analyze whether there is empirical evidence of contagion at the bank level, measuring the direction and the size of contagion transmission between European markets. In order to understand and quantify the contagion transmission on banking market, I estimate the econometric model by Aït-Sahalia et al. (2015) in which contagion is defined as the within and between countries transmission of shocks and asset returns are directly modeled as a Hawkes jump diffusion process. The empirical analysis indicates that there is a clear evidence of contagion from Greece to European countries as well as self-contagion in all countries.

Propagation modelling and resource allocation in mobile radio communications

Over the past years, ray tracing (RT) models popularity has been increasing. From the nineties, RT has been used for field prediction in environment such as indoor and urban environments. Nevertheless, with the advent of new technologies, the channel model has become decidedly more dynamic and to perform RT simulations at each discrete time instant become computationally expensive. In this thesis, a new dynamic ray tracing (DRT) approach is presented in which from a single ray tracing simulation at an initial time t0, through analytical formulas we are able to track the motion of the interaction points. The benefits that this approach bring are that Doppler frequencies and channel prediction can be derived at every time instant, without recurring to multiple RT runs and therefore shortening the computation time. DRT performance was studied on two case studies and the results shows the accuracy and the computational gain that derives from this approach. Another issue that has been addressed in this thesis is the licensed band exhaustion of some frequency bands. To deal with this problem, a novel unselfish spectrum leasing scheme in cognitive radio networks (CRNs) is proposed that offers an energy-efficient solution minimizing the environmental impact of the network. In addition, a network management architecture is introduced and resource allocation is proposed as a constrained sum energy efficiency maximization problem. System simulations demonstrate an increment in the energy efficiency of the primary users’ network compared with previously proposed algorithms.

Utilizing the Internet of Things to promote energy awareness and efficiency at discrete production processes: Practices and methodology

El actual contexto de fabricación, con incrementos en los precios de la energía, una creciente preocupación medioambiental y cambios continuos en los comportamientos de los consumidores, fomenta que los responsables prioricen la fabricación respetuosa con el medioambiente. El paradigma del Internet de las Cosas (IoT) promete incrementar la visibilidad y la atención prestada al consumo de energía gracias tanto a sensores como a medidores inteligentes en los niveles de máquina y de línea de producción. En consecuencia es posible y sencillo obtener datos de consumo de energía en tiempo real proveniente de los procesos de fabricación, pero además es posible analizarlos para incrementar su importancia en la toma de decisiones. Esta tesis pretende investigar cómo utilizar la adopción del Internet de las Cosas en el nivel de planta de producción, en procesos discretos, para incrementar la capacidad de uso de la información proveniente tanto de la energía como de la eficiencia energética. Para alcanzar este objetivo general, la investigación se ha dividido en cuatro sub-objetivos y la misma se ha desarrollado a lo largo de cuatro fases principales (en adelante estudios). El primer estudio de esta tesis, que se apoya sobre una revisión bibliográfica comprehensiva y sobre las aportaciones de expertos, define prácticas de gestión de la producción que son energéticamente eficientes y que se apoyan de un modo preeminente en la tecnología IoT. Este primer estudio también detalla los beneficios esperables al adoptar estas prácticas de gestión. Además, propugna un marco de referencia para permitir la integración de los datos que sobre el consumo energético se obtienen en el marco de las plataformas y sistemas de información de la compañía. Esto se lleva a cabo con el objetivo último de remarcar cómo estos datos pueden ser utilizados para apalancar decisiones en los niveles de procesos tanto tácticos como operativos. Segundo, considerando los precios de la energía como variables en el mercado intradiario y la disponibilidad de información detallada sobre el estado de las máquinas desde el punto de vista de consumo energético, el segundo estudio propone un modelo matemático para minimizar los costes del consumo de energía para la programación de asignaciones de una única máquina que deba atender a varios procesos de producción. Este modelo permite la toma de decisiones en el nivel de máquina para determinar los instantes de lanzamiento de cada trabajo de producción, los tiempos muertos, cuándo la máquina debe ser puesta en un estado de apagada, el momento adecuado para rearrancar, y para pararse, etc. Así, este modelo habilita al responsable de producción de implementar el esquema de producción menos costoso para cada turno de producción. En el tercer estudio esta investigación proporciona una metodología para ayudar a los responsables a implementar IoT en el nivel de los sistemas productivos. Se incluye un análisis del estado en que se encuentran los sistemas de gestión de energía y de producción en la factoría, así como también se proporcionan recomendaciones sobre procedimientos para implementar IoT para capturar y analizar los datos de consumo. Esta metodología ha sido validada en un estudio piloto, donde algunos indicadores clave de rendimiento (KPIs) han sido empleados para determinar la eficiencia energética. En el cuarto estudio el objetivo es introducir una vía para obtener visibilidad y relevancia a diferentes niveles de la energía consumida en los procesos de producción. El método propuesto permite que las factorías con procesos de producción discretos puedan determinar la energía consumida, el CO2 emitido o el coste de la energía consumida ya sea en cualquiera de los niveles: operación, producto o la orden de fabricación completa, siempre considerando las diferentes fuentes de energía y las fluctuaciones en los precios de la misma. Los resultados muestran que decisiones y prácticas de gestión para conseguir sistemas de producción energéticamente eficientes son posibles en virtud del Internet de las Cosas. También, con los resultados de esta tesis los responsables de la gestión energética en las compañías pueden plantearse una aproximación a la utilización del IoT desde un punto de vista de la obtención de beneficios, abordando aquellas prácticas de gestión energética que se encuentran más próximas al nivel de madurez de la factoría, a sus objetivos, al tipo de producción que desarrolla, etc. Así mismo esta tesis muestra que es posible obtener reducciones significativas de coste simplemente evitando los períodos de pico diario en el precio de la misma. Además la tesis permite identificar cómo el nivel de monitorización del consumo energético (es decir al nivel de máquina), el intervalo temporal, y el nivel del análisis de los datos son factores determinantes a la hora de localizar oportunidades para mejorar la eficiencia energética. Adicionalmente, la integración de datos de consumo energético en tiempo real con datos de producción (cuando existen altos niveles de estandarización en los procesos productivos y sus datos) es esencial para permitir que las factorías detallen la energía efectivamente consumida, su coste y CO2 emitido durante la producción de un producto o componente. Esto permite obtener una valiosa información a los gestores en el nivel decisor de la factoría así como a los consumidores y reguladores. ABSTRACT In today‘s manufacturing scenario, rising energy prices, increasing ecological awareness, and changing consumer behaviors are driving decision makers to prioritize green manufacturing. The Internet of Things (IoT) paradigm promises to increase the visibility and awareness of energy consumption, thanks to smart sensors and smart meters at the machine and production line level. Consequently, real-time energy consumption data from the manufacturing processes can be easily collected and then analyzed, to improve energy-aware decision-making. This thesis aims to investigate how to utilize the adoption of the Internet of Things at shop floor level to increase energy–awareness and the energy efficiency of discrete production processes. In order to achieve the main research goal, the research is divided into four sub-objectives, and is accomplished during four main phases (i.e., studies). In the first study, by relying on a comprehensive literature review and on experts‘ insights, the thesis defines energy-efficient production management practices that are enhanced and enabled by IoT technology. The first study also explains the benefits that can be obtained by adopting such management practices. Furthermore, it presents a framework to support the integration of gathered energy data into a company‘s information technology tools and platforms, which is done with the ultimate goal of highlighting how operational and tactical decision-making processes could leverage such data in order to improve energy efficiency. Considering the variable energy prices in one day, along with the availability of detailed machine status energy data, the second study proposes a mathematical model to minimize energy consumption costs for single machine production scheduling during production processes. This model works by making decisions at the machine level to determine the launch times for job processing, idle time, when the machine must be shut down, ―turning on‖ time, and ―turning off‖ time. This model enables the operations manager to implement the least expensive production schedule during a production shift. In the third study, the research provides a methodology to help managers implement the IoT at the production system level; it includes an analysis of current energy management and production systems at the factory, and recommends procedures for implementing the IoT to collect and analyze energy data. The methodology has been validated by a pilot study, where energy KPIs have been used to evaluate energy efficiency. In the fourth study, the goal is to introduce a way to achieve multi-level awareness of the energy consumed during production processes. The proposed method enables discrete factories to specify energy consumption, CO2 emissions, and the cost of the energy consumed at operation, production and order levels, while considering energy sources and fluctuations in energy prices. The results show that energy-efficient production management practices and decisions can be enhanced and enabled by the IoT. With the outcomes of the thesis, energy managers can approach the IoT adoption in a benefit-driven way, by addressing energy management practices that are close to the maturity level of the factory, target, production type, etc. The thesis also shows that significant reductions in energy costs can be achieved by avoiding high-energy price periods in a day. Furthermore, the thesis determines the level of monitoring energy consumption (i.e., machine level), the interval time, and the level of energy data analysis, which are all important factors involved in finding opportunities to improve energy efficiency. Eventually, integrating real-time energy data with production data (when there are high levels of production process standardization data) is essential to enable factories to specify the amount and cost of energy consumed, as well as the CO2 emitted while producing a product, providing valuable information to decision makers at the factory level as well as to consumers and regulators.

Discrete Models of Time-Fractional Diffusion in a Potential Well

Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.

An investigation of imputation methods for discrete databases and multi-variate time series

When it comes to information sets in real life, often pieces of the whole set may not be available. This problem can find its origin in various reasons, describing therefore different patterns. In the literature, this problem is known as Missing Data. This issue can be fixed in various ways, from not taking into consideration incomplete observations, to guessing what those values originally were, or just ignoring the fact that some values are missing. The methods used to estimate missing data are called Imputation Methods. The work presented in this thesis has two main goals. The first one is to determine whether any kind of interactions exists between Missing Data, Imputation Methods and Supervised Classification algorithms, when they are applied together. For this first problem we consider a scenario in which the databases used are discrete, understanding discrete as that it is assumed that there is no relation between observations. These datasets underwent processes involving different combina- tions of the three components mentioned. The outcome showed that the missing data pattern strongly influences the outcome produced by a classifier. Also, in some of the cases, the complex imputation techniques investigated in the thesis were able to obtain better results than simple ones. The second goal of this work is to propose a new imputation strategy, but this time we constrain the specifications of the previous problem to a special kind of datasets, the multivariate Time Series. We designed new imputation techniques for this particular domain, and combined them with some of the contrasted strategies tested in the pre- vious chapter of this thesis. The time series also were subjected to processes involving missing data and imputation to finally propose an overall better imputation method. In the final chapter of this work, a real-world example is presented, describing a wa- ter quality prediction problem. The databases that characterized this problem had their own original latent values, which provides a real-world benchmark to test the algorithms developed in this thesis.

Polar organic marker compounds in atmospheric aerosols during the LBA-SMOCC 2002 biomass burning experiment in Rondonia, Brazil: sources and source processes, time series, diel variations and size distributions

Measurements of polar organic marker compounds were performed on aerosols that were collected at a pasture site in the Amazon basin (Rondonia, Brazil) using a high-volume dichotomous sampler (HVDS) and a Micro-Orifice Uniform Deposit Impactor (MOUDI) within the framework of the 2002 LBA-SMOCC (Large-Scale Biosphere Atmosphere Experiment in Amazonia - Smoke Aerosols, Clouds, Rainfall, and Climate: Aerosols From Biomass Burning Perturb Global and Regional Climate) campaign. The campaign spanned the late dry season (biomass burning), a transition period, and the onset of the wet season (clean conditions). In the present study a more detailed discussion is presented compared to previous reports on the behavior of selected polar marker compounds, including levoglucosan, malic acid, isoprene secondary organic aerosol (SOA) tracers and tracers for fungal spores. The tracer data are discussed taking into account new insights that recently became available into their stability and/or aerosol formation processes. During all three periods, levoglucosan was the most dominant identified organic species in the PM(2.5) size fraction of the HVDS samples. In the dry period levoglucosan reached concentrations of up to 7.5 mu g m(-3) and exhibited diel variations with a nighttime prevalence. It was closely associated with the PM mass in the size-segregated samples and was mainly present in the fine mode, except during the wet period where it peaked in the coarse mode. Isoprene SOA tracers showed an average concentration of 250 ng m(-3) during the dry period versus 157 ng m(-3) during the transition period and 52 ng m(-3) during the wet period. Malic acid and the 2-methyltetrols exhibited a different size distribution pattern, which is consistent with different aerosol formation processes (i.e., gas-to-particle partitioning in the case of malic acid and heterogeneous formation from gas-phase precursors in the case of the 2-methyltetrols). The 2-methyltetrols were mainly associated with the fine mode during all periods, while malic acid was prevalent in the fine mode only during the dry and transition periods, and dominant in the coarse mode during the wet period. The sum of the fungal spore tracers arabitol, mannitol, and erythritol in the PM(2.5) fraction of the HVDS samples during the dry, transition, and wet periods was, on average, 54 ng m(-3), 34 ng m(-3), and 27 ng m(-3), respectively, and revealed minor day/night variation. The mass size distributions of arabitol and mannitol during all periods showed similar patterns and an association with the coarse mode, consistent with their primary origin. The results show that even under the heavy smoke conditions of the dry period a natural background with contributions from bioaerosols and isoprene SOA can be revealed. The enhancement in isoprene SOA in the dry season is mainly attributed to an increased acidity of the aerosols, increased NO(x) concentrations and a decreased wet deposition.

Exceptional times for the dynamical discrete web

The dynamical discrete web (DyDW), introduced in the recent work of Howitt and Warren, is a system of coalescing simple symmetric one-dimensional random walks which evolve in an extra continuous dynamical time parameter tau. The evolution is by independent updating of the underlying Bernoulli variables indexed by discrete space-time that define the discrete web at any fixed tau. In this paper, we study the existence of exceptional (random) values of tau where the paths of the web do not behave like usual random walks and the Hausdorff dimension of the set of such exceptional tau. Our results are motivated by those about exceptional times for dynamical percolation in high dimension by Haggstrom, Peres and Steif, and in dimension two by Schramm and Steif. The exceptional behavior of the walks in the DyDW is rather different from the situation for the dynamical random walks of Benjamini, Haggstrom, Peres and Steif. For example, we prove that the walk from the origin S(0)(tau) violates the law of the iterated logarithm (LIL) on a set of tau of Hausdorff dimension one. We also discuss how these and other results should extend to the dynamical Brownian web, the natural scaling limit of the DyDW. (C) 2009 Elsevier B.V. All rights reserved.

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

The shoot controls zeatin riboside export from pea roots. Evidence from the branching mutant rms4

The rms4 mutant of pea (Pisum sativum L.) was used in grafting studies and cytokinin analyses of the root xylem sap to provide evidence that, at least for pea, the shoot can modify the import of cytokinins from the root. The rms4 mutation, which confers a phenotype with increased branching in the shoot, causes a very substantial decrease (down to 40-fold less) in the concentration of zeatin riboside (ZR) in the xylem sap of the roots. Results from grafts between wild-type (WT) and rms4 plants indicate that the concentration of cytokinins in the xylem sap of the roots is determined almost entirely by the genotype of the shoot. WT scions normalize the cytokinin concentration in the sap of rms4 mutant roots, whereas mutant scions cause WT roots to behave like those of self-grafted mutant plants. The mechanism whereby rms4 shoots of pea cause a down-regulation in the export of cytokinins from the roots is unknown at this time. However, our data provide evidence that the shoot transmits a signal to the roots and thereby controls processes involved in the regulation of cytokinin biosynthesis in the root.

Real time manufacturing systems simulator

A área da simulação computacional teve um rápido crescimento desde o seu apareciment, sendo actualmente uma das ciências de gestão e de investigação operacional mais utilizadas. O seu princípio baseia-se na replicação da operação de processos ou sistemas ao longo de períodos de tempo, tornando-se assim uma metodologia indispensável para a resolução de variados problemas do mundo real, independentemente da sua complexidade. Das inúmeras áreas de aplicação, nos mais diversos campos, a que mais se destaca é a utilização em sistemas de produção, onde o leque de aplicações disponível é muito vasto. A sua aplicação tem vindo a ser utilizada para solucionar problemas em sistemas de produção, uma vez que permite às empresas ajustar e planear de uma maneira rápida, eficaz e ponderada as suas operações e os seus sistemas, permitindo assim uma rápida adaptação das mesmas às constantes mudanças das necessidades da economia global. As aplicações e packages de simulação têm seguindo as tendências tecnológicas pelo que é notório o recurso a tecnologias orientadas a objectos para o desenvolvimento das mesmas. Este estudo baseou-se, numa primeira fase, na recolha de informação de suporte aos conceitos de modelação e simulação, bem como a respectiva aplicação a sistemas de produção em tempo real. Posteriormente centralizou-se no desenvolvimento de um protótipo de uma aplicação de simulação de ambientes de fabrico em tempo real. O desenvolvimento desta ferramenta teve em vista eventuais fins pedagógicos e uma utilização a nível académico, sendo esta capaz de simular um modelo de um sistema de produção, estando também dotada de animação. Sem deixar de parte a possibilidade de integração de outros módulos ou, até mesmo, em outras plataformas, houve ainda a preocupação acrescida de que a sua implementação recorresse a metodologias de desenvolvimento orientadas a objectos.

Modeling and simulation of population balances for particulate processes

This work focuses on the modeling and numerical approximations of population balance equations (PBEs) for the simulation of different phenomena occurring in process engineering. The population balance equation (PBE) is considered to be a statement of continuity. It tracks the change in particle size distribution as particles are born, die, grow or leave a given control volume. In the population balance models the one independent variable represents the time, the other(s) are property coordinate(s), e.g., the particle volume (size) in the present case. They typically describe the temporal evolution of the number density functions and have been used to model various processes such as granulation, crystallization, polymerization, emulsion and cell dynamics. The semi-discrete high resolution schemes are proposed for solving PBEs modeling one and two-dimensional batch crystallization models. The schemes are discrete in property coordinates but continuous in time. The resulting ordinary differential equations can be solved by any standard ODE solver. To improve the numerical accuracy of the schemes a moving mesh technique is introduced in both one and two-dimensional cases ...

Simulations for modelling of population balance equations of particulate processes using the discrete particle model (DPM)

Magdeburg, Univ., Fak. für Mathematik, Diss., 2009