The probability distribution of worldwide forest areas

This paper analyses the probability distribution of worldwide forest areas. We find moderate support for a Pareto-type distribution (power law) using FAO data from 1990 to 2015. Power laws are common features of many complex systems in nature. A power law is a plausible model for the world probability distribution of forest areas in all examined years, although the log-normal distribution is a plausible alternative model that cannot be rejected. The random growth of forest areas could generate a power law or log-normal distribution. We study the change in forest coverage using parametric and non-parametric methods. We identified a slight convergence of forest areas over the time reviewed; however, random forest area growth cannot be rejected for most of the distribution of forest areas. Therefore, our results give support to theoretical models of stochastic forest growth

Optimal Stopping of Gauss-Markov processes

Mención Internacional en el título de doctorIn this thesis we contribute to the optimal stopping theory literature, in the time-inhomogeneous framework, by solving Optimal Stopping Problems (OSPs) related to Gauss–Markov (GM) processes, both when they are non-degenerated, and when they are pinned to a deterministic value at a terminal time. For pinned processes, we bypassed the challenge of their explosive drifts by equating them to a time-space-transformed Brownian Motion (BM). For each OSP, we characterized the free-boundary equation as the unique solution of a type-two Volterra integral equation. The value functions were, then, expressed as an integral of the OSBs. We used a solution methodology in the spirit of Peskir (2005). That is, a direct, probabilistic approach that harvests sufficient smoothness of the value function and the Optimal Stopping Boundary (OSB) to solve the associated free-boundary problem by using an extended Itô’s lemma. In doing so, we proved the Lipschitz continuity of the OSB away from the horizon. This result extends the technique in De Angelis and Stabile (2019) and blueprints a methodology to obtain similar smoothness on other OSPs. Another highly customizable technique was the one we employed to obtain the OSB’s boundedness. By comparing the non-degenerated GM process and the Gauss Markov Bridge (GMB) with a BM and a Brownian Bridge (BB), respectively, we found bounds for the OSBs of the former two processes from those of the latter two. Two different fixed-point algorithms were presented and implemented to solve the freeboundary equation. One based on backward induction (see Section 3.4) and one based on the Picard iteration method (see Sections 2.5, 4.6, and 5.6). With the aid of these algorithms, we illustrated the geometry of the OSB for different forms of the processes’ drift and volatility (see Figures 2.1, 3.1, 4.1–4.3, and 5.2). It is worth mentioning the statistical inference study we perform on the OSB in the BB case (see Section 3.4), as this is not a typical subject addressed in optimal stopping theory, and it is potentially extensible to tackle more general settings where likelihood theory is worked out. Indeed, the methodology consists in using the asymptotic normality of the BB volatility’s maximum-likelihood estimate to extend, by using the delta method, such property to the OSB plugin estimator. This allowed us to provide (point-wise) confidence curves for the OSB. We also offer a financial perspective of our work in Chapters 2 and 3, by linking the OSPs to the problem of optimally exercising American options. Remarkably, in Section 3.5, we show the competitiveness of the BB model against the geometric BM in this regard, when the option is written on IBM’s and Apple’s stocks, and in the presence of the pinning-at-the-strike effect. In addition, the confidence curves computed in Section 3.4 provide traders with a mechanism to introduce a risk-preference element.Programa de Doctorado en Ingeniería Matemática por la Universidad Carlos III de MadridPresidente: Franciso de Asís Torres Ruiz.- Secretaria: Rosa Elvira Lillo Rodríguez.- Vocal: Tiziano De Angeli

Learning and recognition by a dynamical system with a plastic velocity field

Learning is a mechanism intrinsic to all sentient biological systems. Despite the diverse range of paradigms that exist, it appears that an artificial system has yet to be developed that can emulate learning with a comparable degree of accuracy or efficiency to the human brain. With the development of new approaches comes the opportunity to reduce this disparity in performance. A model presented by Janson and Marsden [arXiv:1107.0674 (2011)] (Memory foam model) redefines the critical features that an intelligent system should demonstrate. Rather than focussing on the topological constraints of the rigid neuron structure, the emphasis is placed on the on-line, unsupervised, classification, retention and recognition of stimuli. In contrast to traditional AI approaches, the system s memory is not plagued by spurious attractors or the curse of dimensionality. The ability to continuously learn, whilst simultaneously recognising aspects of a stimuli ensures that this model more closely embodies the operations occurring in the brain than many other AI approaches. Here we consider the pertinent deficiencies of classical artificial learning models before introducing and developing this memory foam self-shaping system. As this model is relatively new, its limitations are not yet apparent. These must be established by testing the model in various complex environments. Here we consider its ability to learn and recognize the RGB colours composing cartoons as observed via a web-camera. The self-shaping vector field of the system is shown to adjust its composition to reflect the distribution of three-dimensional inputs. The model builds a memory of its experiences and is shown to recognize unfamiliar colours by locating the most appropriate class with which to associate a stimuli. In addition, we discuss a method to map a three-dimensional RGB input onto a line spectrum of colours. The corresponding reduction of the models dimensions is shown to dramatically improve computational speed, however, the model is then restricted to a much smaller set of representable colours. This models prototype offers a gradient description of recognition, it is evident that a more complex, non-linear alternative may be used to better characterize the classes of the system. It is postulated that non-linear attractors may be utilized to convey the concept of hierarchy that relates the different classes of the system. We relate the dynamics of the van der Pol oscillator to this plastic self-shaping system, first demonstrating the recognition of stimuli with limit cycle trajectories. The location and frequency of each cycle is dependent on the topology of the systems energy potential. For a one-dimensional stimuli the dynamics are restricted to the cycle, the extension of the model to an N dimensional stimuli is approached via the coupling of N oscillators. Here we study systems of up to three mutually coupled oscillators and relate limit cycles, fixed points and quasi-periodic orbits to the recognition of stimuli

Zipf's Law for Cities and the Double-Pareto-Lognormal Distribution

This dissertation concentrates on the size distribution of cities. From an empirical perspective, it is shown that Zipf's law for cities holds for the upper tail of the distribution and that the overall distribution is the Double-Pareto-Lognormal distribution. From a theoretical perspective, the dissertation builds a dynamic general equilibrium model of random urban growth with endogenous city formation, which explains the empirical finding of a Double-Pareto-Lognormal city size distribution

Complexity in Economic and Social Systems

There is no term that better describes the essential features of human society than complexity. On various levels, from the decision-making processes of individuals, through to the interactions between individuals leading to the spontaneous formation of groups and social hierarchies, up to the collective, herding processes that reshape whole societies, all these features share the property of irreducibility, i.e., they require a holistic, multi-level approach formed by researchers from different disciplines. This Special Issue aims to collect research studies that, by exploiting the latest advances in physics, economics, complex networks, and data science, make a step towards understanding these economic and social systems. The majority of submissions are devoted to financial market analysis and modeling, including the stock and cryptocurrency markets in the COVID-19 pandemic, systemic risk quantification and control, wealth condensation, the innovation-related performance of companies, and more. Looking more at societies, there are papers that deal with regional development, land speculation, and the-fake news-fighting strategies, the issues which are of central interest in contemporary society. On top of this, one of the contributions proposes a new, improved complexity measure

Análise de movimento de corpos deformáveis usando visão computacional

O tema desta tese está inserido no domínio da visão por computador e na área da análise de movimento de corpos deformáveis. O seu interesse tem vindo a aumentar consideravelmente nos últimos tempos devido, sobretudo, ao fracasso das tentativas de utilizar as metodologias normalmente associadas aos corpos rígidos para a análise do movimento não rígido, e também ao elevado número de aplicações que existem para tal análise. O enorme potencial de aplicação existente na área da imagem médica, nomeadamente na segmentação, no emparelhamento e na análise e seguimento do movimento de estruturas, é responsável por grande parte do trabalho realizado neste âmbito. Outras aplicações que podem ser referidas são o seguimento de sistemas articulados, a análise do escoamento de fluidos, do movimento de nuvens para a previsão meteorológica, do comportamento de materiais sob a acção de forças, a análise e reconhecimento de faces, de veículos e de caracteres, etc.Ao contrário do que sucede com os objectos rígidos, a representação da forma de um objecto deformável está fortemente relacionada com a análise e seguimento do seu movimento e, para se desenvolverem técnicas para resolver tais problemas, é necessário utilizar determinadas restrições sobre o movimento/forma o que, consequentemente, individualiza as abordagens desenvolvidas e as torna específicas para determinadas classes de problemas.The theme of this thesis is in the computer vision domain and more specifically in the area of motion analysis of deformable bodies. The interest in this field has risen significantly in the last few years due to the failure of adapting existing rigid-body methods and to the very wide range of potential applications. A strong impulse originated in the area of medical imaging for segmenting, matching and tracking body structures, but other application domains have also contributed, namely the tracking of articulate systems, the analysis of fluids flow, the movement of clouds for weather forecasting, the structural analysis of materials, the recognition of faces, vehicles and characters, etc.Unlike rigid objects, the shape representation of deformable objects is strongly related with the analysis and tracking of its motion and thus, in order to develop suitable approaches and techniques for analysis, certain restrictions and constraints on the shape/motion must be specific to the type of task under consideration

Sequential investment planning for complex oil development projects

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2008.Includes bibliographical references (leaves 86-90).In this thesis, we consider sequential real investment decisions for the development of discovered oil prospects. Following a decision analysis approach, we propose a methodology to explore the upside of a dynamic drilling strategy, where there is a significant uncertainty about the reservoir complexity. We introduce the notion of information lag, whereby the decision-maker receives the information with a certain delay after each drilling is completed. In an illustrative case study, we apply our proposed methodology on a single reservoir to characterize the value of flexibility and to describe the relative impact of the information lags, in the context of an extensive drilling plan. We also provide several extensions of this case study in order to show how this methodology would be extended in a more comprehensive decision framework. Topics include choosing the optimal production capacity, valuing an initial test opportunity, and developing a field with multiple reservoirs. Our results indicate that flexible thinking may be a significant source of value to the projects. However, the incremental value might be over-rated if information lags are not appropriately included in the analysis.by Cevat Onur Aydın.S.M