Niche partitioning is a major component in understanding community ecology and how different species divide limited environmental resources, enabling them to coexist. Temporal niche partitioning has been widely studied in a broad sense, such as in species that forage on similar nutritional sources dividing activity along diurnal and nocturnal classifications. Here, we approach this temporal niche partitioning with higher resolution to investigate partitioning between species within the same broad temporal and foraging niche. Two species of diurnal orb-weaving spiders (Araneae: Araneidae), Verrucosa arenata and Micrathena gracilis, both construct their orbs in spatially similar locations throughout the understory of deciduous forests in the morning, forage on flying insects throughout the day, and retreat in the evening. However, despite consisting of what appear to be roughly similar total lengths of adhesive silk in the capture spiral, overall orb structure is starkly different: V. arenata orbs are relatively large in diameter and sparse with capture threads; M. gracilis orbs, condensed in diameter and tightly coiled. What other differences might distinguish foraging strategy within this same niche? With extensive observation in their natural environment, we have found that these two species employ two distinct strategies by modulating behavior and orb structure: V. arenata construct orbs earlier in the day, resulting in a longer foraging period. However, V. arenata webs are more likely to be destroyed during the day such that there is a higher variance in foraging duration in V. arenata. We also found that V. arenata actively capture and consume more large prey and that M. gracilis more passively capture and consume small prey more reliably. These data suggest that these species have evolved different foraging strategies with V. arenata being risk-prone and M. gracilis being risk-averse. This study provides a more nuanced analysis of niche partitioning between species occupying otherwise similar temporal, habitat, and foraging niches.

Os processos de decisão de Markov (Markov Decision Process - MDP) têm sido usados para resolução de problemas de tomada de decisão sequencial. Existem problemas em que lidar com os riscos do ambiente para obter um resultado confiável é mais importante do que maximizar o retorno médio esperado. MDPs que lidam com esse tipo de problemas são chamados de processos de decisão de Markov sensíveis a risco (Risk-Sensitive Markov Decision Process - RSMDP). Dentre as diversas variações de RSMDP, estão os trabalhos baseados em utilidade exponencial que utilizam um fator de risco, o qual modela a atitude a risco do agente e que pode ser propensa ou aversa. Os algoritmos existentes na literatura para resolver esse tipo de RSMDPs são ineficientes se comparados a outros algoritmos de MDP. Neste projeto, é apresentada uma solução que pode ser usada em problemas maiores, tanto por executar cálculos apenas em estados relevantes para atingir um conjunto de estados meta partindo de um estado inicial, quanto por permitir processamento de números com expoentes muito elevados para os ambientes computacionais atuais. Os experimentos realizados evidenciam que (i) o algoritmo proposto é mais eficiente, se comparado aos algoritmos estado-da-arte para RSMDPs; e (ii) o uso da técnica LogSumExp permite resolver o problema de trabalhar com expoentes muito elevados em RSMDPs. / Markov Decision Process (MDP) has been used very efficiently to solve sequential decision-making problems. There are problems where dealing with environmental risks to get a reliable result is more important than maximizing the expected average return. MDPs that deal with this type of problem are called risk-sensitive Markov decision processes (RSMDP). Among the several variations of RSMDP are the works based on exponential utility that use a risk factor, which models the agent\'s risk attitude that can be prone or averse. The algorithms in the literature to solve this type of RSMDPs are inefficient when compared to other MDP algorithms. In this project, a solution is presented that can be used in larger problems, either by performing calculations only in relevant states to reach a set of meta states starting from an initial state, or by allowing the processing of numbers with very high exponents for the current computational environments. The experiments show that (i) the proposed algorithm is more efficient when compared to state-of-the-art algorithms for RSMDPs; and (ii) the LogSumExp technique solves the problem of working with very large exponents in RSMDPs

Os processos de decisão de Markov (Markov Decision Process - MDP) têm sido usados para resolução de problemas de tomada de decisão sequencial. Existem problemas em que lidar com os riscos do ambiente para obter um resultado confiável é mais importante do que maximizar o retorno médio esperado. MDPs que lidam com esse tipo de problemas são chamados de processos de decisão de Markov sensíveis a risco (Risk-Sensitive Markov Decision Process - RSMDP). Dentre as diversas variações de RSMDP, estão os trabalhos baseados em utilidade exponencial que utilizam um fator de risco, o qual modela a atitude a risco do agente e que pode ser propensa ou aversa. Os algoritmos existentes na literatura para resolver esse tipo de RSMDPs são ineficientes se comparados a outros algoritmos de MDP. Neste projeto, é apresentada uma solução que pode ser usada em problemas maiores, tanto por executar cálculos apenas em estados relevantes para atingir um conjunto de estados meta partindo de um estado inicial, quanto por permitir processamento de números com expoentes muito elevados para os ambientes computacionais atuais. Os experimentos realizados evidenciam que (i) o algoritmo proposto é mais eficiente, se comparado aos algoritmos estado-da-arte para RSMDPs; e (ii) o uso da técnica LogSumExp permite resolver o problema de trabalhar com expoentes muito elevados em RSMDPs. / Markov Decision Process (MDP) has been used very efficiently to solve sequential decision-making problems. There are problems where dealing with environmental risks to get a reliable result is more important than maximizing the expected average return. MDPs that deal with this type of problem are called risk-sensitive Markov decision processes (RSMDP). Among the several variations of RSMDP are the works based on exponential utility that use a risk factor, which models the agent\'s risk attitude that can be prone or averse. The algorithms in the literature to solve this type of RSMDPs are inefficient when compared to other MDP algorithms. In this project, a solution is presented that can be used in larger problems, either by performing calculations only in relevant states to reach a set of meta states starting from an initial state, or by allowing the processing of numbers with very high exponents for the current computational environments. The experiments show that (i) the proposed algorithm is more efficient when compared to state-of-the-art algorithms for RSMDPs; and (ii) the LogSumExp technique solves the problem of working with very large exponents in RSMDPs

This thesis presents a comprehensive example framework on how current multiple model state estimation algorithms for jump Markov linear systems can be improved. The possible improvements are categorized as: -Design of multiple model state estimation algorithms using new criteria. -Improvements obtained using existing multiple model state estimation algorithms. In the first category, risk-sensitive estimation is proposed for jump Markov linear systems. Two types of cost functions namely, the instantaneous and cumulative cost functions related with risk-sensitive estimation are examined and for each one, the corresponding multiple model estate estimation algorithm is derived. For the cumulative cost function, the derivation involves the reference probability method where one defines and uses a new probability measure under which the involved processes has independence properties. The performance of the proposed risk-sensitive filters are illustrated and compared with conventional algorithms using simulations. The thesis addresses the second category of improvements by proposing -Two new online transition probability estimation schemes for jump Markov linear systems. -A mixed multiple model state estimation scheme which combines desirable properties of two different multiple model state estimation methods. The two online transition probability estimators proposed use the recursive Kullback-Leibler (RKL) procedure and the maximum likelihood (ML) criteria to derive the corresponding identification schemes. When used in state estimation, these methods result in an average error decrease in the root mean square (RMS) state estimation errors, which is proved using simulation studies. The mixed multiple model estimation procedure which utilizes the analysis of the single Gaussian approximation of Gaussian mixtures in Bayesian filtering, combines IMM (Interacting Multiple Model) filter and GPB2 (2nd Order Generalized Pseudo Bayesian) filter efficiently. The resulting algorithm reaches the performance of GPB2 with less Kalman filters.

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The Autonomic Power System (APS) grand challenge was a multi-disciplinary EPSRC-funded research project that examined novel techniques that would enable the transition between today's and 2050's highly uncertain and complex energy network. Being part of the APS, this thesis reports on the sub-project 'RR2: Avoiding High-Impact Low Probability events'. The goal of RR2 is to develop new algorithms for controlling risk exposure to high-impact low probability (Hi-Lo) events through the provision of appropriate risk-sensitive control strategies. Additionally, RR2 is concerned with new techniques for identifying and modelling risk in future energy networks, in particular, the risk of Hi-Lo events. In this context, this thesis investigates two distinct problems arising from energy risk management. On the one hand, we examine the problem of finding managerial strategies for exercising the operational flexibility of energy assets. We look at this problem from a risk perspective taking into account non-linear risk preferences of energy asset managers. Our main contribution is the development of a risk-sensitive approach to the class of optimal switching problems. By recasting the problem as an iterative optimal stopping problem, we are able to characterise the optimal risk-sensitive switching strategies. As byproduct, we obtain a multiplicative dynamic programming equation for the value function, upon which we propose a numerical algorithm based on least squares Monte Carlo regression. On the other hand, we develop tools to identify and model the risk factors faced by energy asset managers. For this, we consider a class of models consisting of superposition of Gaussian and non-Gaussian Ornstein-Uhlenbeck processes. Our main contribution is the development of a Bayesian methodology based on Markov chain Monte Carlo (MCMC) algorithms to make inference into this class of models. On extensive simulations, we demonstrate the robustness and efficiency of the algorithms to different data features. Furthermore, we construct a diagnostic tool based on Bayesian p-values to check goodness-of-fit of the models on a Bayesian framework. We apply this tool to MCMC results from fitting historical electricity and gas spot price data- sets corresponding to the UK and German energy markets. Our analysis demonstrates that the MCMC-estimated models are able to capture not only long- and short-lived positive price spikes, but also short-lived negative price spikes which are typical of UK gas prices and German electricity prices. Combining together the solutions to the two problems above, we strive to capture the interplay between risk, uncertainty, flexibility and performance in various applications to energy systems. In these applications, which include power stations, energy storage and district energy systems, we consistently show that our risk management methodology offers a tradeoff between maximising average performance and minimising risk, while accounting for the jump dynamics of energy prices. Moreover, the tradeoff is achieved in such way that the benefits in terms of risk reduction outweigh the loss in average performance.

Shorter product life cycles and rapid product obsolescence provide increasing incentives to introduce newproducts to markets more quickly. As a consequence of rapidly changing market conditions, firms focus onimproving their new product development processes to reap the benefits of early market entry. Researchershave analyzed market entry, but have seldom provided quantitative approaches for the product rolloverproblem. This research builds upon the literature by using established optimization methods to examine howfirms can minimize their net loss during the rollover process. Specifically, our work explicitly optimizes thetiming of removal of old products and introduction of new products, the optimal strategy, and the magnitudeof net losses when the market entry approval date of a new product is unknown. In the first paper, we use theconditional value at risk to optimize the net loss and investigate the effect of risk perception of the manageron the rollover process. We compare it to the minimization of the classical expected net loss. We deriveconditions for optimality and unique closed-form solutions for single and dual rollover cases. In the secondpaper, we investigate the rollover problem, but for a time-dependent demand rate for the second producttrying to approximate the Bass Model. Finally, in the third paper, we apply the data-driven optimizationapproach to the product rollover problem where the probability distribution of the approval date is unknown.We rather have historical observations of approval dates. We develop the optimal times of rollover and showthe superiority of the data-driven method over the conditional value at risk in case where it is difficult to guessthe real probability distribution

Les consommateurs d’aujourd’hui ont des goûts très variés et cherchent les produits les plus récents. Avec l’accélération technologique, les cycles de vie des produits se sont raccourcis et donc, de nouveaux produits doivent être introduits au marché plus souvent et progressivement, les anciens doivent y être retirés. L’introduction d’un nouveau produit est une source de croissance et d’avantage concurrentiel. Les directeurs du Marketing et Supply Chain se sont confrontés à la question de savoir comment gérer avec succès le remplacement de leurs produits et d’optimiser les coûts de la chaîne d’approvisionnement associée. Dans une situation idéale, la procédure de rollover est efficace et claire: l’ancien produit est vendu jusqu’à une date prévue où un nouveau produit est introduit. Dans la vie réelle, la situation est moins favorable. Le but de notre travail est d’analyser et de caractériser la politique optimale du rollover avec une date de disponibilitéstochastique pour l’introduction du nouveau produit sur le marché. Pour résoudre le problème d’optimisation,nous utilisons dans notre premier article deux mesures de minimisation: le coût moyen et le coût de la valeurconditionnelle à risque. On obtient des solutions en forme explicite pour les politiques optimales. En outre, nous caractérisons l’influence des paramètres de coûts sur la structure de la politique optimale. Dans cet esprit, nous analysons aussi le comportement de la politique de rollover optimale dans des contextes différents. Dans notre deuxième article, nous examinons le même problème mais avec une demande constante pour le premier produit et une demande linéaire au début puis constante pour le deuxième. Ce modèle est inspiré par la demande de Bass. Dans notre troisième article, la date de disponibilité du nouveau produit existe mais elle est inconnue. La seule information disponible est un ensemble historique d’échantillons qui sont tirés de la vraie distribution. Nous résoudrons le problème avec l’approche data drivenet nous obtenons des formulations tractables. Nous développons aussi des bornes sur le nombre d’échantillons nécessaires pour garantir qu’avec une forte probabilité, le coût n’est pas très loin du vrai coût optimal. / Shorter product life cycles and rapid product obsolescence provide increasing incentives to introduce newproducts to markets more quickly. As a consequence of rapidly changing market conditions, firms focus onimproving their new product development processes to reap the benefits of early market entry. Researchershave analyzed market entry, but have seldom provided quantitative approaches for the product rolloverproblem. This research builds upon the literature by using established optimization methods to examine howfirms can minimize their net loss during the rollover process. Specifically, our work explicitly optimizes thetiming of removal of old products and introduction of new products, the optimal strategy, and the magnitudeof net losses when the market entry approval date of a new product is unknown. In the first paper, we use theconditional value at risk to optimize the net loss and investigate the effect of risk perception of the manageron the rollover process. We compare it to the minimization of the classical expected net loss. We deriveconditions for optimality and unique closed-form solutions for single and dual rollover cases. In the secondpaper, we investigate the rollover problem, but for a time-dependent demand rate for the second producttrying to approximate the Bass Model. Finally, in the third paper, we apply the data-driven optimizationapproach to the product rollover problem where the probability distribution of the approval date is unknown.We rather have historical observations of approval dates. We develop the optimal times of rollover and showthe superiority of the data-driven method over the conditional value at risk in case where it is difficult to guessthe real probability distribution