Environmental management and restoration under unified risk and uncertainty using robustified dynamic Orlicz risk

Environmental management and restoration should be designed such that the risk and uncertainty owing to nonlinear stochastic systems can be successfully addressed. We apply the robustified dynamic Orlicz risk to the modeling and analysis of environmental management and restoration to consider both the risk and uncertainty within a unified theory. We focus on the control of a jump-driven hybrid stochastic system that represents macrophyte dynamics. The dynamic programming equation based on the Orlicz risk is first obtained heuristically, from which the associated Hamilton-Jacobi-Bellman (HJB) equation is derived. In the proposed Orlicz risk, the risk aversion of the decision-maker is represented by a power coefficient that resembles a certainty equivalence, whereas the uncertainty aversion is represented by the Kullback-Leibler divergence, in which the risk and uncertainty are handled consistently and separately. The HJB equation includes a new state-dependent discount factor that arises from the uncertainty aversion, which leads to a unique, nonlinear, and nonlocal term. The link between the proposed and classical stochastic control problems is discussed with a focus on control-dependent discount rates. We propose a finite difference method for computing the HJB equation. Finally, the proposed model is applied to an optimal harvesting problem for macrophytes in a brackish lake that contains both growing and drifting populations

Advanced sequential Monte Carlo methods and their applications to sparse sensor network for detection and estimation

The general state space models present a flexible framework for modeling dynamic systems and therefore have vast applications in many disciplines such as engineering, economics, biology, etc. However, optimal estimation problems of non-linear non-Gaussian state space models are analytically intractable in general. Sequential Monte Carlo (SMC) methods become a very popular class of simulation-based methods for the solution of optimal estimation problems. The advantages of SMC methods in comparison with classical filtering methods such as Kalman Filter and Extended Kalman Filter are that they are able to handle non-linear non-Gaussian scenarios without relying on any local linearization techniques. In this thesis, we present an advanced SMC method and the study of its asymptotic behavior. We apply the proposed SMC method in a target tracking problem using different observation models. Specifically, a distributed SMC algorithm is developed for a wireless sensor network (WSN) that incorporates with an informative-sensor detection technique. The novel SMC algorithm is designed to surmount the degeneracy problem by employing a multilevel Markov chain Monte Carlo (MCMC) procedure constructed by engaging drift homotopy and likelihood bridging techniques. The observations are gathered only from the informative sensors, which are sensing useful observations of the nearby moving targets. The detection of those informative sensors, which are typically a small portion of the WSN, is taking place by using a sparsity-aware matrix decomposition technique. Simulation results showcase that our algorithm outperforms current popular tracking algorithms such as bootstrap filter and auxiliary particle filter in many scenarios

A simple estimator for the distribution of random coefficients

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/88065/1/QE49.pd

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

B

Integrating Systems and Economic Models for Security Investments in the Presence of Dynamic Stochastic Shocks

Organizations deploy a number of security measures with differing intensities to protect their company’s information assets. These assets are found in various location within a company, with differing levels of security applied to them. Such measures protect the different aspects of the organization’s information systems, which are typically separated into three different attributes; confidentiality, integrity, and availability. We start by defining a system in terms of its locations, resources and processes to use as an underlying framework for our security model. We then systematically define the time evolution of all the three attributes when subjected to shocks aiming at degrading the system’s capacity. We shock each of the attributes of the system and trace the adjustment of the attributes and policy responses; we undertake this exercise for different types of organizations: a military weapons system operator, a financial firm or bank, a retail organization, and a medical research organization, producing their impulse-response functions to quantify their responses and speed of adjustment. This economic model is validated through various means, including Monte Carlo simulations. We find that organizations, although they react in similar ways to shocks to their attributes over time, and are able quickly to get back to their pre-shock states over time, differ in the intensity of their policy responses which differ depending upon the character of the organization

Numerical simulation of magnetic nanoparticles

We solved the Landau-Lifshitz equations numerically to examine the time development of a system of magnetic particles. Constant or periodical external magnetic field has been applied. First, the system has been studied without dissipation. Local energy excitations (breathers) and chaotic transients have been found. The behaviour of the system and the final configurations can strongly depend on the initial conditions, and the strength of the external field at an earlier time. We observed some sudden switching between two remarkably different states. Series of bifurcations have been found. When a weak Gilbert-damping has been taken into account, interesting behaviour has been found even in the case of one particle as well: bifurcation series and period multiplication leading to chaos. For a system of antiferromagnetically coupled particles, highly nontrivial hysteresis loops have been produced. The dynamics of the magnetization reversal has been investigated and the characteristic time-scale of the reversal has been estimated. For more particles, the energy spectrum and the magnetization of the system exhibits fractal characteristics for increasing system size. Finally, energy have been pumped into the system in addition to the dissipation. For constant field, complicated phase diagrams have been produced. For microwave field, it has been found that the chaotic behaviour crucially depends on the parity of the number of the particles

Dynamics and steady-state properties of adaptive networks

Tese de doutoramento, Física, Universidade de Lisboa, Faculdade de Ciências, 2013Collective phenomena often arise through structured interactions among a system's constituents. In the subclass of adaptive networks, the interaction structure coevolves with the dynamics it supports, yielding a feedback loop that is common in a variety of complex systems. To understand and steer such systems, modeling their asymptotic regimes is an essential prerequisite. In the particular case of a dynamic equilibrium, each node in the adaptive network experiences a perpetual change in connections and state, while a comprehensive set of measures characterizing the node ensemble are stationary. Furthermore, the dynamic equilibria of a wide class of adaptive networks appear to be unique, as their characteristic measures are insensitive to initial conditions in both state and topology. This work focuses on dynamic equilibria in adaptive networks, and while it does so in the context of two paradigmatic coevolutionary processes, obtained results easily generalize to other dynamics. In the rst part, a low-dimensional framework is elaborated on using the adaptive contact process. A tentative description of the phase diagram and the steady state is obtained, and a parameter region identi ed where asymmetric microscopic dynamics yield a symmetry between node subensembles. This symmetry is accounted for by novel recurrence relations, which predict it for a wide range of adaptive networks. Furthermore, stationary nodeensemble distributions are analytically generated by these relations from one free parameter. Secondly, another analytic framework is put forward that detects and describes dynamic equilibria, while assigning to them general properties that must hold for a variety of adaptive networks. Modeling a single node's evolution in state and connections as a random walk, the ergodic properties of the network process are used to extract node-ensemble statistics from the node's long-term behavior. These statistical measures are composed of a variety of stationary distributions that are related to one another through simple transformations. Applying this fully self-su cient framework, the dynamic equilibria of three di erent avors of the adaptive contact process are subsequently described and compared. Lastly, an asymmetric variant of the coevolutionary voter model is motivated and proposed, and as for the adaptive contact process, a low-dimensional description is given. In a parameter region where a dynamic equilibrium lets the in nite system display perpetual dynamics, this description can be further reduced to a one-dimensional random walk. For nite system sizes, this allows to analytically characterize longevity of the dynamic equilibrium, with results being compared to the symmetric variant of the process. A nontrivial parameter combination is identi ed for which, in the low-dimensional description of the process, the asymmetric coevolutionary model emulates symmetric voter dynamics without topological coevolution. This emerging symmetry is partially con rmed for the full system and subsequently elaborated on. Slightly varying the original asymmetric model, an additional asymptotic regime is shown to occur that coexists with all others and complicates system description.A estrutura das interacções entre os constituintes elementares de um sistema está frequentemente na origem de comportamentos colectivos não triviais. Em redes adaptativas, esta estrutura de interacção evolui a par com a dinâaica que nela assenta, traduzindo uma retroacção que de comum encontrar em vários sistemas complexos. Resultados analíticos sobre os estados assimptóticos destes sistemas são uma peça essencial para a sua compreensão e controlo. O equilíbrio dinâmico de um caso particular de estado assimptótico em que cada nodo da rede adaptativa vai sempre mudando o seu estado e as suas ligações a outros nodos, enquanto que um conjunto de medidas que caracterizam estatisticamente o ensemble dos nodos mantêm valores fixos. Alémm disso, uma classe muito geral de redes adaptativas apresenta equilíbrios dinâmicos que parecem ser únicos, no sentido em que aqueles valores estacionários não dependem das condições iniciais, quer em termos do estados dos nodos quer em termos da topologia da rede.Este trabalho incide no estudo do equilíbrio dinâmiico de redes adaptativas no contexto particular de dois modelos paradigmáticos de coevolação, mas os principais resultados podem ser facilmente generalizados a outros processos. Na primeira parte, revisita-se e desenvolve-se uma abordagem da variante adaptativa do processo de contacto baseada num modelo de baixa dimensão. Obtem-se uma descrição aproximada do diagrama de fases do sistema e do equilíbrio dinâmico, e identifica-se nessa fase uma combinação de parâmetros para a qual a dinâmica microscópica, que de assimétrica nos estados dos nodos, da origem a uma simetria entre os dois subconjuntos de nodos. Esta simetria é explicada através da derivação de relações de recorrência para as distribuições de grau, que a preveêm para uma ampla classe de redes adaptativas. Estas relações permitem também gerar analiticamente as distribuições de grau estacionárias de cada subconjunto de nodos a partir de um parâmetro livre.Na segunda parte, desenvolve-se uma outra abordagem analítica que permite detectar e descrever o equilíbrio dinâmico, a partir de propriedades gerais que se têm que verificar em muitas redes adaptativas. Na base desta abordagem está a descrição do processo estocástico associado à evolução do estado e das ligações de cada nó, e as propriedades ergódicas que permitem obter as estatísticas de ensemble na rede a partir do comportamento a longo termo de um nó. Estas medidas estatísticas podem ser calculadas a partir de várias distribuições estacionárias que se relacionam umas com as outras através de transformações simples. Como aplicação desta abordagem completa, os equilíbrios dinâmicos de três diferentes variantes do processo de contacto adaptativo são descritos e comparados. Finalmente, motiva-se e propõe-se uma variante assimétrica do voter model coevolutivo. A fase activa metastável é tentativamente descrita como uma random walk ao longo de uma variedade lenta, à semelhan ca do que foi feito na literatura para o modelo simétrico, e os resultados para os dois casos são comparados.É identicada uma combinação de parâmetros particular para a qual este modelo assim etrico emula o modelo simétrico em rede fixa, o que é mais um exemplo da simetria emergente prevista pelas relações de recorrência estabelecidas na primeira parte. Considera-se ainda uma outra variante assimétrica, mais complexa, do voter model co-evolutivo, que apresenta um diagrama de fases essencialmente diferente, e cuja descrição se mostra requerer novas abordagens.Fundação para a Ciência e a Tecnologia (FCT, SFRH/BD/45179/2008