A Semigroup Approach to the System with Primary and Secondary Failures

We investigate the solution of a repairable parallel system with primary as well as secondary failures. By using the method of functional analysis, especially, the spectral theory of linear operators and the theory of C0-semigroups, we prove well-posedness of the system and the existence of positive solution of the system. And then we show that the time-dependent solution strongly converges to steady-state solution, thus we obtain the asymptotic stability of the time-dependent solution

Multipath inter-domain policy routing

Dissertação submetida para a obtenção do grau de Doutor em Engenharia Electrotécnica e de ComputadoresRouting can be abstracted to be a path nding problem in a graph that models the network. The problem can be modelled using an algebraic approach that describes the way routes are calculated and ranked. The shortest path problem is the most common form and consists in nding the path with the smallest cost. The inter-domain scenario introduces some new challenges to the routing problem: the routing is performed between independently con gured and managed networks; the ranking of the paths is not based on measurable metrics but on policies; and the forwarding is destination based hop-by-hop. In this thesis we departed from the Border gateway Protocol (BGP) identifying its main problems and elaborating on some ideal characteristics for a routing protocol suited for the inter-domain reality. The main areas and contributions of this work are the following: The current state of the art in algebraic modeling of routing problems is used to provide a list of possible alternative conditions for the correct operation of such protocols. For each condition the consequences in terms of optimality and network restrictions are presented. A routing architecture for the inter-domain scenario is presented. It is proven that it achieves a multipath routing solution in nite time without causing forwarding loops. We discuss its advantages and weaknesses. A tra c-engineering scheme is designed to take advantage of the proposed architecture. It works using only local information and cooperation of remote ASes to minimize congestion in the network with minimal signalling. Finally a general model of a routing protocol based on hierarchical policies is used to study how e cient is the protocol operation when the correctness conditions are met. This results in some conclusions on how the policies should be chosen and applied in order to achieve speci c goals.Portuguese Science and Technology Foundation -(FCT/MCTES)grant SFRH/BD/44476/2008; CTS multi-annual funding project PEst OE/EEI/UI0066/2011; MPSat project PTDC/EEA TEL/099074/2008; OPPORTUNISTICCR project PTDC/EEA-TEL/115981/2009; Fentocells project PTDC/EEA TEL/120666/201

Multipath policy routing in packet switched networks

Dissertação apresentada para obtenção do Grau de Mestre em Engenharia Electrotécnica e de Computadores, pela Universidade Nova de Lisboa, Faculdade de Ciências e TecnologiaNowadays, the continuous operations of large networks, under multiple ownerships, are of tremendous importance and as a result, routing protocols have gained numerous extensions and accumulated complexity. Policy-based routing can be of signi cance for common networks when the cost of transporting a bit is no longer the biggest pressure point. The best path problem is a generalization of the shortest path problem that suits policy based routing. This means that preferences for the paths depend on semantically rich characteristics, in which two di erent paths may have the same preference. However, current policy-based routing models cannot take full advantage of the multiplicity of connections to a given destination and are single path in nature. Therefore multipath can bring several advantages in policy based routing. Designing multipath routing protocols based on policies seem to be a problem of interest. To model routing problems, algebraic structures and graph theory are used. Through variants of classical methods of linear algebra routing problems can be solved. The objective of this dissertation is to devise a multipath policy-based routing protocol using a simple destination-based hop-by-hop protocol with independent forwarding decisions. Networks featuring these characteristics can be more resilient to failures, provide better tra c distribution and maintain a simple forwarding paradigm. The dissertation concludes with the trade-o 's between the exibility of the proposed solution, the amount of multiple paths that can be used simultaneously and the network restrictions that must be applied

VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)

Proceedings of the Workshop on Applications of Distributed System Theory to the Control of Large Space Structures

Two general themes in the control of large space structures are addressed: control theory for distributed parameter systems and distributed control for systems requiring spatially-distributed multipoint sensing and actuation. Topics include modeling and control, stabilization, and estimation and identification

Finite model theory for pseudovarieties and universal algebra: preservation, definability and complexity

We explore new interactions between finite model theory and a number of classical streams of universal algebra and semigroup theory. A key result is an example of a finite algebra whose variety is not finitely axiomatisable in first order logic, but which has first order definable finite membership problem. This algebra witnesses the simultaneous failure of the {\L}os-Tarski Theorem, the SP-preservation theorem and Birkhoff's HSP-preservation theorem at the finite level as well as providing a negative solution to a first order formulation of the long-standing Eilenberg Sch\"utzenberger problem. The example also shows that a pseudovariety without any finite pseudo-identity basis may be finitely axiomatisable in first order logic. Other results include the undecidability of deciding first order definability of the pseudovariety of a finite algebra and a mapping from any fixed template constraint satisfaction problem to a first order equivalent variety membership problem, thereby providing examples of variety membership problems complete in each of the classes $\texttt{L}$, $\texttt{NL}$, $\texttt{Mod}_p(\texttt{L})$, $\texttt{P}$, and infinitely many others (depending on complexity-theoretic assumptions)

Intelligent Monitoring System with High Temperature Distributed Fiberoptic Sensor for Power Plant Combustion Processes

The objective of the proposed work is to develop an intelligent distributed fiber optical sensor system for real-time monitoring of high temperature in a boiler furnace in power plants. Of particular interest is the estimation of spatial and temporal distributions of high temperatures within a boiler furnace, which will be essential in assessing and controlling the mechanisms that form and remove pollutants at the source, such as NOx. The basic approach in developing the proposed sensor system is three fold: (1) development of high temperature distributed fiber optical sensor capable of measuring temperatures greater than 2000 C degree with spatial resolution of less than 1 cm; (2) development of distributed parameter system (DPS) models to map the three-dimensional (3D) temperature distribution for the furnace; and (3) development of an intelligent monitoring system for real-time monitoring of the 3D boiler temperature distribution. Under Task 1, we have set up a dedicated high power, ultrafast laser system for fabricating in-fiber gratings in harsh environment optical fibers, successfully fabricated gratings in single crystal sapphire fibers by the high power laser system, and developed highly sensitive long period gratings (lpg) by electric arc. Under Task 2, relevant mathematical modeling studies of NOx formation in practical combustors have been completed. Studies show that in boiler systems with no swirl, the distributed temperature sensor may provide information sufficient to predict trends of NOx at the boiler exit. Under Task 3, we have investigated a mathematical approach to extrapolation of the temperature distribution within a power plant boiler facility, using a combination of a modified neural network architecture and semigroup theory. Given a set of empirical data with no analytic expression, we first developed an analytic description and then extended that model along a single axis