Um modelo matemático para o desemprego: controlo ótimo com dados reais de Portugal

During this thesis we study the Calculus of Variations and Optimal Control theory while we present a few examples. After a brief overview of the Portuguese employment market reality we propose a simple Optimal Control model for unemployment and we compare it with previous studies. Despite its inherent simpleness, we claim that the model is more realistic and useful than the ones available in the literature. A case study with real data from Portugal (2004- 2016) supports our claimAo longo desta tese, estudamos a teoria do Cálculo das Variações e do Controlo Óptimo enquanto formulamos e apresentamos alguns exemplos. Depois de uma breve revisão geral da realidade do mercado de trabalho em Portugal, propomos um modelo matemático simples de Controlo Óptimo direccionado para o mercado do desemprego efectuando a comparacão em relação a estudos anteriores. Apesar da simplicidade inerente, afirmamos que o modelo é mais realista e útil do que os disponíveis na literatura. Um caso de estudo com dados reais de Portugal (2004-2016), suporta a nossa afirmaçãoMestrado em Matemática e Aplicaçõe

Stability analysis of drinking epidemic models and investigation of optimal treatment strategy

In this research we investigate a class of drinking epidemic models, namely the SPARS type models. The basic reproduction number is derived, and the system dynamical behaviours are investigated for both drinking free equilibrium and drinking persistent equilibrium. The purpose is to determine the long term optimal treatment method and the optimal short period vaccination strategy for controlling the population of the periodic drinkers and alcoholics

Network based data oriented methods for application driven problems

Networks are amazing. If you think about it, some of them can be found in almost every single aspect of our life from sociological, financial and biological processes to the human body. Even considering entities that are not necessarily connected to each other in a natural sense, can be connected based on real life properties, creating a whole new aspect to express knowledge. A network as a structure implies not only interesting and complex mathematical questions, but the possibility to extract hidden and additional information from real life data. The data that is one of the most valuable resources of this century. The different activities of the society and the underlying processes produces a huge amount of data, which can be available for us due to the technological knowledge and tools we have nowadays. Nevertheless, the data without the contained knowledge does not represent value, thus the main focus in the last decade is to generate or extract information and knowledge from the data. Consequently, data analytics and science, as well as data-driven methodologies have become leading research fields both in scientific and industrial areas. In this dissertation, the author introduces efficient algorithms to solve application oriented optimization and data analysis tasks built on network science based models. The main idea is to connect these problems along graph based approaches, from virus modelling on an existing system through understanding the spreading mechanism of an infection/influence and maximize or minimize the effect, to financial applications, such as fraud detection or cost optimization in a case of employee rostering

Hybrid Evolutionary Routing Optimisation for Wireless Sensor Mesh Networks

Battery powered wireless sensors are widely used in industrial and regulatory monitoring applications. This is primarily due to the ease of installation and the ability to monitor areas that are difficult to access. Additionally, they can be left unattended for long periods of time. However, there are many challenges to successful deployments of wireless sensor networks (WSNs). In this thesis we draw attention to two major challenges. Firstly, with a view to extending network range, modern WSNs use mesh network topologies, where data is sent either directly or by relaying data from node-to-node en route to the central base station. The additional load of relaying other nodes’ data is expensive in terms of energy consumption, and depending on the routes taken some nodes may be heavily loaded. Hence, it is crucial to locate routes that achieve energy efficiency in the network and extend the time before the first node exhausts its battery, thus improving the network lifetime. Secondly, WSNs operate in a dynamic radio environment. With changing conditions, such as modified buildings or the passage of people, links may fail and data will be lost as a consequence. Therefore in addition to finding energy efficient routes, it is important to locate combinations of routes that are robust to the failure of radio links. Dealing with these challenges presents a routing optimisation problem with multiple objectives: find good routes to ensure energy efficiency, extend network lifetime and improve robustness. This is however an NP-hard problem, and thus polynomial time algorithms to solve this problem are unavailable. Therefore we propose hybrid evolutionary approaches to approximate the optimal trade-offs between these objectives. In our approach, we use novel search space pruning methods for network graphs, based on k-shortest paths, partially and edge disjoint paths, and graph reduction to combat the combinatorial explosion in search space size and consequently conduct rapid optimisation. The proposed methods can successfully approximate optimal Pareto fronts. The estimated fronts contain a wide range of robust and energy efficient routes. The fronts typically also include solutions with a network lifetime close to the optimal lifetime if the number of routes per nodes were unconstrained. These methods are demonstrated in a real network deployed at the Victoria & Albert Museum, London, UK.Part of this work was supported by a knowledge transfer partnership (KTP) awarded to the IMC Group Ltd. and the University of Exeter (KTP008748).University of Exeter has provided financial support for the student

Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...