Chemistry and Distribution of Daughter Species in the Circumstellar Envelopes of O-Rich AGB Stars

Context. Thanks to the advent of Herschel and ALMA, new high-quality observations of molecules present in the circumstellar envelopes of asymptotic giant branch (AGB) stars are being reported that reveal large differences from the existing chemical models. New molecular data and more comprehensive models of the chemistry in circumstellar envelopes are now available.
Aims: The aims are to determine and study the important formation and destruction pathways in the envelopes of O-rich AGB stars and to provide more reliable predictions of abundances, column densities, and radial distributions for potentially detectable species with physical conditions applicable to the envelope surrounding IK Tau.
Methods: We use a large gas-phase chemical model of an AGB envelope including the effects of CO and N2 self-shielding in a spherical geometry and a newly compiled list of inner-circumstellar envelope parent species derived from detailed modeling and observations. We trace the dominant chemistry in the expanding envelope and investigate the chemistry as a probe for the physics of the AGB phase by studying variations of abundances with mass-loss rates and expansion velocities.
Results: We find a pattern of daughter molecules forming from the photodissociation products of parent species with contributions from ion-neutral abstraction and dissociative recombination. The chemistry in the outer zones differs from that in traditional PDRs in that photoionization of daughter species plays a significant role. With the proper treatment of self-shielding, the N → N2 and C+→ CO transitions are shifted outward by factors of 7 and 2, respectively, compared with earlier models. An upper limit on the abundance of CH4 as a parent species of (≲2.5 × 10-6 with respect to H2) is found for IK Tau, and several potentially observable molecules with relatively simple chemical links to other parent species are determined. The assumed stellar mass-loss rate, in particular, has an impact on the calculated abundances of cations and the peak-abundance radius of both cations and neutrals: as the mass-loss rate increases, the peak abundance of cations generally decreases and the peak-abundance radius of all species moves outwards. The effects of varying the envelope expansion velocity and cosmic-ray ionization rate are not as significant.

Sparse multi-carrier index keying OFDM with index separation over correlated sub-carriers

In this paper, we propose a sparse multi-carrier index keying (MCIK) method for orthogonal frequency division multiplexing (OFDM) system, which uses the indices of sparse sub-carriers to transmit the data, and improve the performance
of signal detection in highly correlated sub-carriers. Although a receiver is able to exploit a power gain with precoding in OFDM, the sensitivity of the signal detection is usually high as the orthogonality is not retained in highly dispersive
environments. To overcome this, we focus on developing the trade-off between the sparsity of the MCIK, correlation, and performances, analyzing the average probability of the error propagation imposed by incorrect index detection over highly correlated sub-carriers. In asymptotic cases, we are able to see how sparsity of MCIK should be designed in order to perform superior to the classical OFDM system. Based on this feature, sparse MCIK based OFDM is a better choice for low detection errors in highly correlated sub-carriers.

Dual-Hop Cognitive Amplify-and-Forward Relaying Networks over η− μ Fading Channels

This paper presents a thorough performance analysis of dual-hop cognitive amplify-and-forward (AF) relaying networks under spectrum-sharing mechanism over independent non-identically distributed (i.n.i.d.) 􀀀 fading channels. In order to guarantee the quality-of-service (QoS) of primary networks, both maximum tolerable peak interference power Q at the primary users (PUs) and maximum allowable transmit power P at secondary users (SUs) are considered to constrain transmit power at the cognitive transmitters. For integer-valued fading parameters, a closed-form lower bound for the outage probability (OP) of the considered networks is obtained. Moreover, assuming arbitrary-valued fading parameters, the lower bound in integral form for the OP is derived. In order to obtain further insights on the OP performance, asymptotic expressions for the OP at high SNRs are derived, from which the diversity/coding gains and the diversity-multiplexing gain tradeoff (DMT) of the secondary network can be readily deduced. It is shown that the diversity gain and also the DMT are solely determined by the fading parameters of the secondary network whereas the primary network only affects the coding gain. The derived results include several others available in previously published works as special cases, such as those for Nakagami-m fading channels. In addition, performance evaluation results have been obtained by Monte Carlo computer simulations which have verified the accuracy of the theoretical analysis.

Cooperative Beamforming and User Selection for Improving the Security of Relay-aided Systems

A relay network in which a source wishes to convey a confidential message to a legitimate destination with the assistance of trusted relays is considered. In particular, cooperative beamforming and user selection techniques are applied to protect the confidential message. The secrecy rate (SR) and secrecy outage probability (SOP) of the network are investigated first, and a tight upper bound for the SR and an exact formula for the SOP are derived. Next, asymptotic approximations for the SR and SOP in the high signal-to-noise ratio (SNR) regime are derived for two different schemes: i) cooperative beamforming and ii) multiuser selection. Further, a new concept of cooperative diversity gain, namely, adapted cooperative diversity gain (ACDG), which can be used to evaluate security level of a cooperative relaying network, is investigated. It is shown that the ACDG of cooperative beamforming is equal to the conventional cooperative diversity gain of traditional multiple-input single-output networks, while the ACDG of the multiuser scenario is equal to that of traditional single-input multiple-output networks.

Spitzer infrared spectrograph point source classification in the Small Magellanic Cloud

The Magellanic Clouds are uniquely placed to study the stellar contribution to dust emission. Individual stars can be resolved in these systems even in the mid-infrared, and they are close enough to allow detection of infrared excess caused by dust. We have searched the Spitzer Space Telescope data archive for all Infrared Spectrograph (IRS) staring-mode observations of the Small Magellanic Cloud (SMC) and found that 209 Infrared Array Camera (IRAC) point sources within the footprint of the Surveying the Agents of Galaxy Evolution in the Small Magellanic Cloud (SAGE-SMC) Spitzer Legacy programme were targeted, within a total of 311 staring-mode observations. We classify these point sources using a decision tree method of object classification, based on infrared spectral features, continuum and spectral energy distribution shape, bolometric luminosity, cluster membership and variability information. We find 58 asymptotic giant branch (AGB) stars, 51 young stellar objects, 4 post-AGB objects, 22 red supergiants, 27 stars (of which 23 are dusty OB stars), 24 planetary nebulae (PNe), 10 Wolf-Rayet stars, 3 H II regions, 3 R Coronae Borealis stars, 1 Blue Supergiant and 6 other objects, including 2 foreground AGB stars. We use these classifications to evaluate the success of photometric classification methods reported in the literature.

Secure Switch-and-Stay Combining (SSSC) for Cognitive Relay Networks

In this paper, we study a two-phase underlay cognitive relay network, where there exists an eavesdropper who can overhear the message. The secure data transmission from the secondary source to secondary destination is assisted by two decode-and-forward (DF) relays. Although the traditional opportunistic relaying technique can choose one relay to provide the best secure performance, it needs to continuously have the channel state information (CSI) of both relays, and may result in a high relay switching rate. To overcome these limitations, a secure switch-and-stay combining (SSSC) protocol is proposed where only one out of the two relays is activated to assist the secure data transmission, and the secure relay switching occurs when the relay cannot support the secure communication any longer. This security switching is assisted by either instantaneous or statistical eavesdropping CSI. For these two cases, we study the system secure performance of SSSC protocol, by deriving the analytical secrecy outage probability as well as an asymptotic expression for the high main-to-eavesdropper ratio (MER) region. We show that SSSC can substantially reduce the system complexity while achieving or approaching the full diversity order of opportunistic relaying in the presence of the instantaneous or statistical eavesdropping CSI.

I/Q imbalance in AF dual-hop relaying: Performance analysis in Nakagami-m fading

We analyze the performance of amplify-and-forward dual-hop relaying systems in the presence of in-phase and quadrature-phase imbalance (IQI) at the relay node. In particular, an exact analytical expression for and tight lower bounds on the outage probability are derived over independent, non-identically distributed Nakagami-m fading channels. Moreover, tractable upper and lower bounds on the ergodic capacity are presented at arbitrary signal-to-noise ratios (SNRs). Some special cases of practical interest (e.g., Rayleigh and Nakagami-0.5 fading) are also studied. An asymptotic analysis is performed in the high SNR regime, where we observe that IQI results in a ceiling effect on the signal-to-interference-plus-noise ratio (SINR), which depends only on the level of I/Q impairments, i.e., the joint image rejection ratio. Finally, the optimal I/Q amplitude and phase mismatch parameters are provided for maximizing the SINR ceiling, thus improving the system performance. An interesting observation is that, under a fixed total phase mismatch constraint, it is optimal to have the same level of transmitter (TX) and receiver (RX) phase mismatch at the relay node, while the optimal values for the TX and RX amplitude mismatch should be inversely proportional to each other.

Multiuser relaying over mixed RF/FSO links

A multiuser dual-hop relaying system over mixed radio frequency/free-space optical (RF/FSO) links is investigated. Specifically, the system consists of m single-antenna sources, a relay node equipped with n≥ m receive antennas and a single photo-aperture transmitter, and one destination equipped with a single photo-detector. RF links are used for the simultaneous data transmission from multiple sources to the relay. The relay operates under the decode-and-forward protocol and utilizes the popular V-BLAST technique by successively decoding each user's transmitted stream. Two common norm-based orderings are adopted, i.e., the streams are decoded in an ascending or a descending order. After V-BLAST, the relay retransmits the decoded information to the destination via a point-to-point FSO link in m consecutive timeslots. Analytical expressions for the end-to-end outage probability and average symbol error probability of each user are derived, while closed-form asymptotic expressions are also presented. Capitalizing on the derived results, some engineering insights are manifested, such as the coding and diversity gain of each user, the impact of the pointing error displacement on the FSO link and the V-BLAST ordering effectiveness at the relay.

Exploiting Direct Links for Physical Layer Security in Multi-User Multi-Relay Networks

We present two physical layer secure transmission schemes for multi-user multi-relay networks, where the communication from M users to the base station is assisted by direct links and by N decode-and-forward relays. In this network, we consider that a passive eavesdropper exists to overhear the transmitted information, which entails exploiting the advantages of both direct and relay links for physical layer security enhancement. To fulfill this requirement, we investigate two criteria for user and relay selection and examine the achievable secrecy performance. Criterion I performs a joint user and relay selection, while Criterion II performs separate user and relay selections, with a lower implementation complexity. We derive a tight lower bound on the secrecy outage probability for Criterion I and an accurate analytical expression for the secrecy outage probability for Criterion II. We further derive the asymptotic secrecy outage probabilities at high transmit signal-to-noise ratios and high main-to-eavesdropper ratios for both criteria. We demonstrate that the secrecy diversity order is min (MN, M + N) for Criterion I, and N for Criterion II. Finally, we present numerical and simulation results to validate the proposed analysis, and show the occurrence condition of the secrecy outage probability floor

Intermediate-coupling R -matrix calculations of electron-impact excitation of Fe 5+

For applications to laboratory and astrophysical plasmas, there is a great need for accurate electron-impact excitation data between individual levels in the lower charge-state ions of iron. Recently, we have reported on the first intermediate-coupling R -matrix calculation of electron-impact excitation in Fe 4+ , in which the close-coupling expansion of the target included levels from both ground and excited configurations (Ballance et al 2007 J. Phys. B: At. Mol. Opt. Phys. [/0953-4075/40/23/f01] 40 F327 , 2008 Europhys. News 39 14). In this paper, we present the results of two large intermediate-coupling Dirac R -matrix calculations of electron-impact excitation of Fe 5+ . The results from the two calculations, which differ only in the configuration–interaction expansions of the target, are compared. These comparisons provide some indication of the accuracy of the calculations and the resulting data should be useful in modelling plasmas containing iron.

IQ Imbalance in Multiuser Systems: Channel Estimation and Compensation

In this paper, we consider the uplink of a single-cell multi-user single-input multiple-output (MU-SIMO) system with in-phase and quadrature-phase imbalance (IQI). Particularly, we investigate the effect of receive (RX) IQI on the performance of MU-SIMO systems with large antenna arrays employing maximum-ratio combining (MRC) receivers. In order to study how IQI affects channel estimation, we derive a new channel estimator for the IQI-impaired model and show that the higher the value of signal-to-noise ratio (SNR) the higher the impact of IQI on the spectral efficiency (SE). Moreover, a novel pilot-based joint estimator of the augmented MIMO channel matrix and IQI coefficients is described and then, a low-complexity IQI compensation scheme is proposed which is based on the
IQI coefficients’ estimation and it is independent of the channel gain. The performance of the proposed compensation scheme is analytically evaluated by deriving a tractable approximation of the ergodic SE assuming transmission over Rayleigh fading channels with large-scale fading. Furthermore, we investigate how many MSs should be scheduled in massive multiple-input multiple-output (MIMO) systems with IQI and show that the highest SE loss occurs at the optimal operating point. Finally,
by deriving asymptotic power scaling laws, and proving that the SE loss due to IQI is asymptotically independent of the number of BS antennas, we show that massive MIMO is resilient to the effect of RX IQI.

Exact and numerical solutions for diffusio-reaction equations with convection term

Esta dissertação estuda essencialmente dois problemas: (A) uma classe de equações unidimensionais de reacção-difusão-convecção em meios não uniformes (dependentes do espaço), e (B) um problema elíptico não-linear e paramétrico ligado a fenómenos de capilaridade. A Análise de Perturbação Singular e a dinâmica de Hamilton-Jacobi são utilizadas na obtenção de expressões assimptóticas para a solução (com comportamento de frente) e para a sua velocidade de propagação. Os seguintes três métodos de decomposição, Adomian Decomposition Method (ADM), Decomposition Method based on Infinite Products (DIP), e New Iterative Method (NIM), são apresentados e brevemente comparados. Adicionalmente, condições suficientes para a convergência da solução em série, obtida pelo ADM, e uma aplicação a um problema da Telecomunicações por Fibras Ópticas, envolvendo EDOs não-lineares designadas equações de Raman, são discutidas. Um ponto de vista mais abrangente que unifica os métodos de decomposição referidos é também apresentado. Para subclasses desta EDP são obtidas soluções numa forma explícita, para diferentes tipos de dados e usando uma variante do método de simetrias de Bluman-Cole. Usando Teoria de Pontos Críticos (o teorema usualmente designado mountain pass) e técnicas de truncatura, prova-se a existência de duas soluções não triviais (uma positiva e uma negativa) para o problema elíptico não-linear e paramétrico (B). A existência de uma terceira solução não trivial é demonstrada usando Grupos Críticos e Teoria de Morse.

Metodologias de optimização topológica em cálculo estrutural

A optimização estrutural é uma temática antiga em engenharia. No entanto, com o crescimento do método dos elementos finitos em décadas recentes, dá origem a um crescente número de aplicações. A optimização topológica, especificamente, surge associada a uma fase de definição de domínio efectivo de um processo global de optimização estrutural. Com base neste tipo de optimização, é possível obter a distribuição óptima de material para diversas aplicações e solicitações. Os materiais compósitos e alguns materiais celulares, em particular, encontram-se entre os materiais mais proeminentes dos nossos dias, em termos das suas aplicações e de investigação e desenvolvimento. No entanto, a sua estrutura potencialmente complexa e natureza heterogénea acarretam grandes complexidades, tanto ao nível da previsão das suas propriedades constitutivas quanto na obtenção das distribuições óptimas de constituintes. Procedimentos de homogeneização podem fornecer algumas respostas em ambos os casos. Em particular, a homogeneização por expansão assimptótica pode ser utilizada para determinar propriedades termomecânicas efectivas e globais a partir de volumes representativos, de forma flexível e independente da distribuição de constituintes. Além disso, integra processos de localização e fornece informação detalhada acerca de sensibilidades locais em metodologias de optimização multiescala. A conjugação destas áreas pode conduzir a metodologias de optimização topológica multiescala, nas quais de procede à obtenção não só de estruturas óptimas mas também das distribuições ideais de materiais constituintes. Os problemas associados a estas abordagens tendem, no entanto, a exigir recursos computacionais assinaláveis, criando muitas vezes sérias limitações à exequibilidade da sua resolução. Neste sentido, técnicas de cálculo paralelo e distribuído apresentam-se como uma potencial solução. Ao dividir os problemas por diferentes unidades memória e de processamento, é possível abordar problemas que, de outra forma, seriam proibitivos. O principal foco deste trabalho centra-se na importância do desenvolvimento de procedimentos computacionais para as aplicações referidas. Adicionalmente, estas conduzem a diversas abordagens alternativas na procura simultânea de estruturas e materiais para responder a aplicações termomecânicas. Face ao exposto, tudo isto é integrado numa plataforma computacional de optimização multiobjectivo multiescala em termoelasticidade, desenvolvida e implementada ao longo deste trabalho. Adicionalmente, o trabalho é complementado com a montagem e configuração de um cluster do tipo Beowulf, assim como com o desenvolvimento do código com vista ao cálculo paralelo e distribuído.

Optimal alarms systems and its application to financial time series

This thesis focuses on the application of optimal alarm systems to non linear time series models. The most common classes of models in the analysis of real-valued and integer-valued time series are described. The construction of optimal alarm systems is covered and its applications explored. Considering models with conditional heteroscedasticity, particular attention is given to the Fractionally Integrated Asymmetric Power ARCH, FIAPARCH(p; d; q) model and an optimal alarm system is implemented, following both classical and Bayesian methodologies. Taking into consideration the particular characteristics of the APARCH(p; q) representation for financial time series, the introduction of a possible counterpart for modelling time series of counts is proposed: the INteger-valued Asymmetric Power ARCH, INAPARCH(p; q). The probabilistic properties of the INAPARCH(1; 1) model are comprehensively studied, the conditional maximum likelihood (ML) estimation method is applied and the asymptotic properties of the conditional ML estimator are obtained. The final part of the work consists on the implementation of an optimal alarm system to the INAPARCH(1; 1) model. An application is presented to real data series.

F. G. Teixeira e a comunidade matemática europeia nos séculos XIX-XX

Esta dissertação descreve o processo de integração dos matemáticos portugueses na comunidade matemática internacional no final do século XIX e início do século XX, focando-se na vida e obra do matemático Francisco Gomes Teixeira (1851-1933). Tenciona a ser mais um contributo para o reconhecimento nacional e internacional do matemático Gomes Teixeira analisando a sua obra como matemático e organizador científico em Portugal através de fontes, parcialmente ainda não conhecidas. Para esse efeito analisou-se a evolução histórica que ocorreu no mundo científico daquela época, em particular a formação da comunidade matemática através de iniciativas individuais ou coletivas, muitas vezes acompanhadas pela fundação de revistas e elaboração de manuais que contribuíram para a internacionalização e, de certa forma, para uma estandardização do estudo universitário básico. Em particular foi estudada a situação em Portugal, onde o papel de liderança foi assumido por Gomes Teixeira. Mostra-se como Gomes Teixeira, graças ao seu trabalho, ao seu talento como matemático e à sua atividade como organizador académico, conseguiu reduzir significativamente o isolamento científico de Portugal na área da matemática. Estudou-se em extensão a fundação de revistas científicas em diferentes países, acompanhando a sua evolução desde de revistas nacionais até revistas internacionais. Focando-nos no Jornal de Sciencias Matemáticas e Astronómicas, fundado em 1877 por Gomes Teixeira (mais tarde conhecido internacionalmente como Teixeira’s Journal), acompanhamos detalhadamente a sua transformação de uma revista nacional numa revista internacional, sendo esta transformação comum naquela época à maioria de revistas científicas importantes de outros países como, por exemplo, no caso do Jornal de Crelle, do Jornal de Liouville, ou outros. Estudou-se igualmente o reconhecimento a nível internacional, através de referências estrangeiras, da abordagem original de Gomes Teixeira à Análise Infinitesimal patente nos seus manuais. O interesse de Gomes Teixeira pela teoria das funções analíticas e pelos seus diferentes desenvolvimentos em série manifestou-se no grande número de artigos publicados sobre este tema e encontrou reconhecimento justo pela designação de um teorema que completa resultados de Lagrange e de Laurent como Teorema de Teixeira. Na sua análise do mérito científico de Gomes Teixeira esta dissertação restringiu-se conscientemente nesta área da Análise Matemática, uma vez que um estudo abrangente de toda a obra ultrapassasse o nosso objetivo. Foi também discutido o intenso intercâmbio científico levado a cabo por Gomes Teixeira através de correspondência e troca de publicações ou permuta de revistas com os matemáticos de diferentes países. Esta análise permitiu verificar um aumento da popularidade dos matemáticos portugueses através do incremento do número de artigos publicados no estrangeiro durante quase 30 anos. Uma fonte imprescindível nesta análise foi o Jahrbuch über die Fortschritte der Mathematik, cujas referências (em geral na língua alemã e por isso até agora quase nunca usadas na literatura Portuguesa) documentaram as publicações em quase todas as revistas matemáticas durante os anos da sua existência entre 1868 e 1942. Descreve-se a colaboração de Gomes Teixeira com diferentes organizações internacionais e documenta-se o apreço internacional por parte do mundo académico. Novos documentos traçam o processo de eleição como membro da Academia das Ciências Alemã Leopoldina, sob proposta de Georg Cantor e outros matemáticos alemães. Finalmente, incluí-se uma breve descrição das atividades levadas a cabo na Rússia, em Espanha e na Grécia em prol do processo de internacionalização da comunidade matemática europeia tendo em vista uma melhor contextualização do contributo de Gomes Teixeira para a integração de Portugal neste processo.