Fractional Calculus and the Future of Science

Newton foresaw the limitations of geometry’s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton’s laws. Mandelbrot’s mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton’s macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton’s laws to describe the many guises of complexity, most of which lay beyond Newton’s experience, and many had even eluded Mandelbrot’s powerful intuition. The book’s authors look behind the mathematics and examine what must be true about a phenomenon’s behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding

Variable bit rate video time-series and scene modeling using discrete-time statistically self-similar systems

This thesis investigates the application of discrete-time statistically self-similar (DTSS) systems to modeling of variable bit rate (VBR) video traffic data. The work is motivated by the fact that while VBR video has been characterized as self-similar by various researchers, models based on self-similarity considerations have not been previously studied. Given the relationship between self-similarity and long-range dependence the potential for using DTSS model in applications involving modeling of VBR MPEG video traffic data is presented. This thesis initially explores the characteristic properties of the model and then establishes relationships between the discrete-time self-similar model and fractional order transfer function systems. Using white noise as the input, the modeling approach is presented using least-square fitting technique of the output autocorrelations to the correlations of various VBR video trace sequences. This measure is used to compare the model performance with the performance of other existing models such as Markovian, long-range dependent and M/G/(infinity) . The study shows that using heavy-tailed inputs the output of these models can be used to match both the scene time-series correlations as well as scene density functions. Furthermore, the discrete-time self-similar model is applied to scene classification in VBR MPEG video to provide a demonstration of potential application of discrete-time self-similar models in modeling self-similar and long-range dependent data. Simulation results have shown that the proposed modeling technique is indeed a better approach than several earlier approaches and finds application is areas such as automatic scene classification, estimation of motion intensity and metadata generation for MPEG-7 applications

Timely Classification of Encrypted or ProtocolObfuscated Internet Traffic Using Statistical Methods

Internet traffic classification aims to identify the type of application or protocol that generated a particular packet or stream of packets on the network. Through traffic classification, Internet Service Providers (ISPs), governments, and network administrators can access basic functions and several solutions, including network management, advanced network monitoring, network auditing, and anomaly detection. Traffic classification is essential as it ensures the Quality of Service (QoS) of the network, as well as allowing efficient resource planning. With the increase of encrypted or obfuscated protocol traffic on the Internet and multilayer data encapsulation, some classical classification methods have lost interest from the scientific community. The limitations of traditional classification methods based on port numbers and payload inspection to classify encrypted or obfuscated Internet traffic have led to significant research efforts focused on Machine Learning (ML) based classification approaches using statistical features from the transport layer. In an attempt to increase classification performance, Machine Learning strategies have gained interest from the scientific community and have shown promise in the future of traffic classification, specially to recognize encrypted traffic. However, ML approach also has its own limitations, as some of these methods have a high computational resource consumption, which limits their application when classifying large traffic or realtime flows. Limitations of ML application have led to the investigation of alternative approaches, including featurebased procedures and statistical methods. In this sense, statistical analysis methods, such as distances and divergences, have been used to classify traffic in large flows and in realtime. The main objective of statistical distance is to differentiate flows and find a pattern in traffic characteristics through statistical properties, which enable classification. Divergences are functional expressions often related to information theory, which measure the degree of discrepancy between any two distributions. This thesis focuses on proposing a new methodological approach to classify encrypted or obfuscated Internet traffic based on statistical methods that enable the evaluation of network traffic classification performance, including the use of computational resources in terms of CPU and memory. A set of traffic classifiers based on KullbackLeibler and JensenShannon divergences, and Euclidean, Hellinger, Bhattacharyya, and Wootters distances were proposed. The following are the four main contributions to the advancement of scientific knowledge reported in this thesis. First, an extensive literature review on the classification of encrypted and obfuscated Internet traffic was conducted. The results suggest that portbased and payloadbased methods are becoming obsolete due to the increasing use of traffic encryption and multilayer data encapsulation. MLbased methods are also becoming limited due to their computational complexity. As an alternative, Support Vector Machine (SVM), which is also an ML method, and the KolmogorovSmirnov and Chisquared tests can be used as reference for statistical classification. In parallel, the possibility of using statistical methods for Internet traffic classification has emerged in the literature, with the potential of good results in classification without the need of large computational resources. The potential statistical methods are Euclidean Distance, Hellinger Distance, Bhattacharyya Distance, Wootters Distance, as well as KullbackLeibler (KL) and JensenShannon divergences. Second, we present a proposal and implementation of a classifier based on SVM for P2P multimedia traffic, comparing the results with KolmogorovSmirnov (KS) and Chisquare tests. The results suggest that SVM classification with Linear kernel leads to a better classification performance than KS and Chisquare tests, depending on the value assigned to the Self C parameter. The SVM method with Linear kernel and suitable values for the Self C parameter may be a good choice to identify encrypted P2P multimedia traffic on the Internet. Third, we present a proposal and implementation of two classifiers based on KL Divergence and Euclidean Distance, which are compared to SVM with Linear kernel, configured with the standard Self C parameter, showing a reduced ability to classify flows based solely on packet sizes compared to KL and Euclidean Distance methods. KL and Euclidean methods were able to classify all tested applications, particularly streaming and P2P, where for almost all cases they efficiently identified them with high accuracy, with reduced consumption of computational resources. Based on the obtained results, it can be concluded that KL and Euclidean Distance methods are an alternative to SVM, as these statistical approaches can operate in realtime and do not require retraining every time a new type of traffic emerges. Fourth, we present a proposal and implementation of a set of classifiers for encrypted Internet traffic, based on JensenShannon Divergence and Hellinger, Bhattacharyya, and Wootters Distances, with their respective results compared to those obtained with methods based on Euclidean Distance, KL, KS, and ChiSquare. Additionally, we present a comparative qualitative analysis of the tested methods based on Kappa values and Receiver Operating Characteristic (ROC) curves. The results suggest average accuracy values above 90% for all statistical methods, classified as ”almost perfect reliability” in terms of Kappa values, with the exception of KS. This result indicates that these methods are viable options to classify encrypted Internet traffic, especially Hellinger Distance, which showed the best Kappa values compared to other classifiers. We conclude that the considered statistical methods can be accurate and costeffective in terms of computational resource consumption to classify network traffic. Our approach was based on the classification of Internet network traffic, focusing on statistical distances and divergences. We have shown that it is possible to classify and obtain good results with statistical methods, balancing classification performance and the use of computational resources in terms of CPU and memory. The validation of the proposal supports the argument of this thesis, which proposes the implementation of statistical methods as a viable alternative to Internet traffic classification compared to methods based on port numbers, payload inspection, and ML.A classificação de tráfego Internet visa identificar o tipo de aplicação ou protocolo que gerou um determinado pacote ou fluxo de pacotes na rede. Através da classificação de tráfego, Fornecedores de Serviços de Internet (ISP), governos e administradores de rede podem ter acesso às funções básicas e várias soluções, incluindo gestão da rede, monitoramento avançado de rede, auditoria de rede e deteção de anomalias. Classificar o tráfego é essencial, pois assegura a Qualidade de Serviço (QoS) da rede, além de permitir planear com eficiência o uso de recursos. Com o aumento de tráfego cifrado ou protocolo ofuscado na Internet e do encapsulamento de dados multicamadas, alguns métodos clássicos da classificação perderam interesse de investigação da comunidade científica. As limitações dos métodos tradicionais da classificação com base no número da porta e na inspeção de carga útil payload para classificar o tráfego de Internet cifrado ou ofuscado levaram a esforços significativos de investigação com foco em abordagens da classificação baseadas em técnicas de Aprendizagem Automática (ML) usando recursos estatísticos da camada de transporte. Na tentativa de aumentar o desempenho da classificação, as estratégias de Aprendizagem Automática ganharam o interesse da comunidade científica e se mostraram promissoras no futuro da classificação de tráfego, principalmente no reconhecimento de tráfego cifrado. No entanto, a abordagem em ML também têm as suas próprias limitações, pois alguns desses métodos possuem um elevado consumo de recursos computacionais, o que limita a sua aplicação para classificação de grandes fluxos de tráfego ou em tempo real. As limitações no âmbito da aplicação de ML levaram à investigação de abordagens alternativas, incluindo procedimentos baseados em características e métodos estatísticos. Neste sentido, os métodos de análise estatística, tais como distâncias e divergências, têm sido utilizados para classificar tráfego em grandes fluxos e em tempo real. A distância estatística possui como objetivo principal diferenciar os fluxos e permite encontrar um padrão nas características de tráfego através de propriedades estatísticas, que possibilitam a classificação. As divergências são expressões funcionais frequentemente relacionadas com a teoria da informação, que mede o grau de discrepância entre duas distribuições quaisquer. Esta tese focase na proposta de uma nova abordagem metodológica para classificação de tráfego cifrado ou ofuscado da Internet com base em métodos estatísticos que possibilite avaliar o desempenho da classificação de tráfego de rede, incluindo a utilização de recursos computacionais, em termos de CPU e memória. Foi proposto um conjunto de classificadores de tráfego baseados nas Divergências de KullbackLeibler e JensenShannon e Distâncias Euclidiana, Hellinger, Bhattacharyya e Wootters. A seguir resumemse os tese. Primeiro, realizámos uma ampla revisão de literatura sobre classificação de tráfego cifrado e ofuscado de Internet. Os resultados sugerem que os métodos baseados em porta e baseados em carga útil estão se tornando obsoletos em função do crescimento da utilização de cifragem de tráfego e encapsulamento de dados multicamada. O tipo de métodos baseados em ML também está se tornando limitado em função da complexidade computacional. Como alternativa, podese utilizar a Máquina de Vetor de Suporte (SVM), que também é um método de ML, e os testes de KolmogorovSmirnov e Quiquadrado como referência de comparação da classificação estatística. Em paralelo, surgiu na literatura a possibilidade de utilização de métodos estatísticos para classificação de tráfego de Internet, com potencial de bons resultados na classificação sem aporte de grandes recursos computacionais. Os métodos estatísticos potenciais são as Distâncias Euclidiana, Hellinger, Bhattacharyya e Wootters, além das Divergências de Kullback–Leibler (KL) e JensenShannon. Segundo, apresentamos uma proposta e implementação de um classificador baseado na Máquina de Vetor de Suporte (SVM) para o tráfego multimédia P2P (PeertoPeer), comparando os resultados com os testes de KolmogorovSmirnov (KS) e Quiquadrado. Os resultados sugerem que a classificação da SVM com kernel Linear conduz a um melhor desempenho da classificação do que os testes KS e Quiquadrado, dependente do valor atribuído ao parâmetro Self C. O método SVM com kernel Linear e com valores adequados para o parâmetro Self C pode ser uma boa escolha para identificar o tráfego Par a Par (P2P) multimédia cifrado na Internet. Terceiro, apresentamos uma proposta e implementação de dois classificadores baseados na Divergência de KullbackLeibler (KL) e na Distância Euclidiana, sendo comparados com a SVM com kernel Linear, configurado para o parâmestro Self C padrão, apresenta reduzida capacidade de classificar fluxos com base apenas nos tamanhos dos pacotes em relação aos métodos KL e Distância Euclidiana. Os métodos KL e Euclidiano foram capazes de classificar todas as aplicações testadas, destacandose streaming e P2P, onde para quase todos os casos foi eficiente identificálas com alta precisão, com reduzido consumo de recursos computacionais.Com base nos resultados obtidos, podese concluir que os métodos KL e Distância Euclidiana são uma alternativa à SVM, porque essas abordagens estatísticas podem operar em tempo real e não precisam de retreinamento cada vez que surge um novo tipo de tráfego. Quarto, apresentamos uma proposta e implementação de um conjunto de classificadores para o tráfego de Internet cifrado, baseados na Divergência de JensenShannon e nas Distâncias de Hellinger, Bhattacharyya e Wootters, sendo os respetivos resultados comparados com os resultados obtidos com os métodos baseados na Distância Euclidiana, KL, KS e Quiquadrado. Além disso, apresentamos uma análise qualitativa comparativa dos métodos testados com base nos valores de Kappa e Curvas Característica de Operação do Receptor (ROC). Os resultados sugerem valores médios de precisão acima de 90% para todos os métodos estatísticos, classificados como “confiabilidade quase perfeita” em valores de Kappa, com exceçãode KS. Esse resultado indica que esses métodos são opções viáveis para a classificação de tráfego cifrado da Internet, em especial a Distância de Hellinger, que apresentou os melhores resultados do valor de Kappa em comparaçãocom os demais classificadores. Concluise que os métodos estatísticos considerados podem ser precisos e económicos em termos de consumo de recursos computacionais para classificar o tráfego da rede. A nossa abordagem baseouse na classificação de tráfego de rede Internet, focando em distâncias e divergências estatísticas. Nós mostramos que é possível classificar e obter bons resultados com métodos estatísticos, equilibrando desempenho de classificação e uso de recursos computacionais em termos de CPU e memória. A validação da proposta sustenta o argumento desta tese, que propõe a implementação de métodos estatísticos como alternativa viável à classificação de tráfego da Internet em relação aos métodos com base no número da porta, na inspeção de carga útil e de ML.Thesis prepared at Instituto de Telecomunicações Delegação da Covilhã and at the Department of Computer Science of the University of Beira Interior, and submitted to the University of Beira Interior for discussion in public session to obtain the Ph.D. Degree in Computer Science and Engineering. This work has been funded by Portuguese FCT/MCTES through national funds and, when applicable, cofunded by EU funds under the project UIDB/50008/2020, and by operation Centro010145FEDER000019 C4 Centro de Competências em Cloud Computing, cofunded by the European Regional Development Fund (ERDF/FEDER) through the Programa Operacional Regional do Centro (Centro 2020). This work has also been funded by CAPES (Brazilian Federal Agency for Support and Evaluation of Graduate Education) within the Ministry of Education of Brazil under a scholarship supported by the International Cooperation Program CAPES/COFECUB Project 9090134/ 2013 at the University of Beira Interior

The 8th International Conference on Time Series and Forecasting

The aim of ITISE 2022 is to create a friendly environment that could lead to the establishment or strengthening of scientific collaborations and exchanges among attendees. Therefore, ITISE 2022 is soliciting high-quality original research papers (including significant works-in-progress) on any aspect time series analysis and forecasting, in order to motivating the generation and use of new knowledge, computational techniques and methods on forecasting in a wide range of fields

Telecommunications Networks

This book guides readers through the basics of rapidly emerging networks to more advanced concepts and future expectations of Telecommunications Networks. It identifies and examines the most pressing research issues in Telecommunications and it contains chapters written by leading researchers, academics and industry professionals. Telecommunications Networks - Current Status and Future Trends covers surveys of recent publications that investigate key areas of interest such as: IMS, eTOM, 3G/4G, optimization problems, modeling, simulation, quality of service, etc. This book, that is suitable for both PhD and master students, is organized into six sections: New Generation Networks, Quality of Services, Sensor Networks, Telecommunications, Traffic Engineering and Routing

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

A Unified Mobility Management Architecture for Interworked Heterogeneous Mobile Networks

The buzzword of this decade has been convergence: the convergence of telecommunications, Internet, entertainment, and information technologies for the seamless provisioning of multimedia services across different network types. Thus the future Next Generation Mobile Network (NGMN) can be envisioned as a group of co-existing heterogeneous mobile data networking technologies sharing a common Internet Protocol (IP) based backbone. In such all-IP based heterogeneous networking environments, ongoing sessions from roaming users are subjected to frequent vertical handoffs across network boundaries. Therefore, ensuring uninterrupted service continuity during session handoffs requires successful mobility and session management mechanisms to be implemented in these participating access networks. Therefore, it is essential for a common interworking framework to be in place for ensuring seamless service continuity over dissimilar networks to enable a potential user to freely roam from one network to another. For the best of our knowledge, the need for a suitable unified mobility and session management framework for the NGMN has not been successfully addressed as yet. This can be seen as the primary motivation of this research. Therefore, the key objectives of this thesis can be stated as: To propose a mobility-aware novel architecture for interworking between heterogeneous mobile data networks To propose a framework for facilitating unified real-time session management (inclusive of session establishment and seamless session handoff) across these different networks. In order to achieve the above goals, an interworking architecture is designed by incorporating the IP Multimedia Subsystem (IMS) as the coupling mediator between dissipate mobile data networking technologies. Subsequently, two different mobility management frameworks are proposed and implemented over the initial interworking architectural design. The first mobility management framework is fully handled by the IMS at the Application Layer. This framework is primarily dependant on the IMS’s default session management protocol, which is the Session Initiation Protocol (SIP). The second framework is a combined method based on SIP and the Mobile IP (MIP) protocols, which is essentially operated at the Network Layer. An analytical model is derived for evaluating the proposed scheme for analyzing the network Quality of Service (QoS) metrics and measures involved in session mobility management for the proposed mobility management frameworks. More precisely, these analyzed QoS metrics include vertical handoff delay, transient packet loss, jitter, and signaling overhead/cost. The results of the QoS analysis indicates that a MIP-SIP based mobility management framework performs better than its predecessor, the Pure-SIP based mobility management method. Also, the analysis results indicate that the QoS performances for the investigated parameters are within acceptable levels for real-time VoIP conversations. An OPNET based simulation platform is also used for modeling the proposed mobility management frameworks. All simulated scenarios prove to be capable of performing successful VoIP session handoffs between dissimilar networks whilst maintaining acceptable QoS levels. Lastly, based on the findings, the contributions made by this thesis can be summarized as: The development of a novel framework for interworked heterogeneous mobile data networks in a NGMN environment. The final design conveniently enables 3G cellular technologies (such as the Universal Mobile Telecommunications Systems (UMTS) or Code Division Multiple Access 2000 (CDMA2000) type systems), Wireless Local Area Networking (WLAN) technologies, and Wireless Metropolitan Area Networking (WMAN) technologies (e.g., Broadband Wireless Access (BWA) systems such as WiMAX) to interwork under a common signaling platform. The introduction of a novel unified/centralized mobility and session management platform by exploiting the IMS as a universal coupling mediator for real-time session negotiation and management. This enables a roaming user to seamlessly handoff sessions between different heterogeneous networks. As secondary outcomes of this thesis, an analytical framework and an OPNET simulation framework are developed for analyzing vertical handoff performance. This OPNET simulation platform is suitable for commercial use