Evaluating tests for convergence of economic series using Monte Carlo methods with an application to real GDP's per head.

Doutoramento em Economia.

Computer Aided Design Algorithmic Technique for Very Large Scale Integrated Circuit Design and Smart Home Embedded System Design

To tackle the challenges at circuit level and system level VLSI and embedded system design, this dissertation proposes various novel algorithms to explore the efficient solutions. At the circuit level, a new reliability-driven minimum cost Steiner routing and layer assignment scheme is proposed, and the first transceiver insertion algorithmic framework for the optical interconnect is proposed. At the system level, a reliability-driven task scheduling scheme for multiprocessor real-time embedded systems, which optimizes system energy consumption under stochastic fault occurrences, is proposed. The embedded system design is also widely used in the smart home area for improving health, wellbeing and quality of life. The proposed scheduling scheme for multiprocessor embedded systems is hence extended to handle the energy consumption scheduling issues for smart homes. The extended scheme can arrange the household appliances for operation to minimize monetary expense of a customer based on the time-varying pricing model.

Volatility transmission between stock and exchange-rate markets: A connectedness analysis

This paper empirically investigates volatility transmission among stock and foreign exchange markets in seven major world economies during the period July 1988 to January 2015. To this end, we first perform a static and dynamic analysis to measure the total volatility connectedness in the entire period (the system-wide approach) using a framework recently proposed by Diebold and Yilmaz (2014). Second, we make use of a dynamic analysis to evaluate the net directional connectedness for each market. To gain further insights, we examine the time-varying behaviour of net pair-wise directional connectedness during the financial turmoil periods experienced in the sample period Our results suggest that slightly more than half of the total variance of the forecast errors is explained by shocks across markets rather than by idiosyncratic shocks. Furthermore, we find that volatility connectedness varies over time, with a surge during periods of increasing economic and financial instability.

Pairs trading in the UK equity market: risk and return

In this paper, we provide the first comprehensive UK evidence on the profitability of the pairs trading strategy. Evidence suggests that the strategy performs well in crisis periods, so we control for both risk and liquidity to assess performance. To evaluate the effect of market frictions on the strategy, we use several estimates of transaction costs. We also present evidence on the performance of the strategy in different economic and market states. Our results show that pairs trading portfolios typically have little exposure to known equity risk factors such as market, size, value, momentum and reversal. However, a model controlling for risk and liquidity explains a far larger proportion of returns. Incorporating different assumptions about bid-ask spreads leads to reductions in performance estimates. When we allow for time-varying risk exposures, conditioned on the contemporaneous equity market return, risk-adjusted returns are generally not significantly different from zero.

The conditional performance of euro bond funds: evidence from Portugal during the debt crisis

This paper evaluates the performance of a survivorship bias-free data set of Portuguese funds investing in Euro-denominated bonds by using conditional models that consider the public information available to investors when the returns are generated. We find that bond funds underperform the market significantly and by an economically relevant magnitude. This underperformance cannot be explained by the expenses they charge. Our findings support the use of conditional performance evaluation models, since we find strong evidence of both time-varying risk and performance, dependent on the slope of the term structure and the inverse relative wealth variables. We also show that survivorship bias has a significant impact on performance estimates. Furthermore, during the European debt crisis, bond fund managers performed significantly better than in non-crisis periods and were able to achieve neutral performance. This improved performance throughout the crisis seems to be related to changes in funds’ investment styles.

Autonomous formation flying: unified control and collision avoidance methods for close manoeuvring spacecraft

The idea of spacecraft formations, flying in tight configurations with maximum baselines of a few hundred meters in low-Earth orbits, has generated widespread interest over the last several years. Nevertheless, controlling the movement of spacecraft in formation poses difficulties, such as in-orbit high-computing demand and collision avoidance capabilities, which escalate as the number of units in the formation is increased and complicated nonlinear effects are imposed to the dynamics, together with uncertainty which may arise from the lack of knowledge of system parameters. These requirements have led to the need of reliable linear and nonlinear controllers in terms of relative and absolute dynamics. The objective of this thesis is, therefore, to introduce new control methods to allow spacecraft in formation, with circular/elliptical reference orbits, to efficiently execute safe autonomous manoeuvres. These controllers distinguish from the bulk of literature in that they merge guidance laws never applied before to spacecraft formation flying and collision avoidance capacities into a single control strategy. For this purpose, three control schemes are presented: linear optimal regulation, linear optimal estimation and adaptive nonlinear control. In general terms, the proposed control approaches command the dynamical performance of one or several followers with respect to a leader to asymptotically track a time-varying nominal trajectory (TVNT), while the threat of collision between the followers is reduced by repelling accelerations obtained from the collision avoidance scheme during the periods of closest proximity. Linear optimal regulation is achieved through a Riccati-based tracking controller. Within this control strategy, the controller provides guidance and tracking toward a desired TVNT, optimizing fuel consumption by Riccati procedure using a non-infinite cost function defined in terms of the desired TVNT, while repelling accelerations generated from the CAS will ensure evasive actions between the elements of the formation. The relative dynamics model, suitable for circular and eccentric low-Earth reference orbits, is based on the Tschauner and Hempel equations, and includes a control input and a nonlinear term corresponding to the CAS repelling accelerations. Linear optimal estimation is built on the forward-in-time separation principle. This controller encompasses two stages: regulation and estimation. The first stage requires the design of a full state feedback controller using the state vector reconstructed by means of the estimator. The second stage requires the design of an additional dynamical system, the estimator, to obtain the states which cannot be measured in order to approximately reconstruct the full state vector. Then, the separation principle states that an observer built for a known input can also be used to estimate the state of the system and to generate the control input. This allows the design of the observer and the feedback independently, by exploiting the advantages of linear quadratic regulator theory, in order to estimate the states of a dynamical system with model and sensor uncertainty. The relative dynamics is described with the linear system used in the previous controller, with a control input and nonlinearities entering via the repelling accelerations from the CAS during collision avoidance events. Moreover, sensor uncertainty is added to the control process by considering carrier-phase differential GPS (CDGPS) velocity measurement error. An adaptive control law capable of delivering superior closed-loop performance when compared to the certainty-equivalence (CE) adaptive controllers is finally presented. A novel noncertainty-equivalence controller based on the Immersion and Invariance paradigm for close-manoeuvring spacecraft formation flying in both circular and elliptical low-Earth reference orbits is introduced. The proposed control scheme achieves stabilization by immersing the plant dynamics into a target dynamical system (or manifold) that captures the desired dynamical behaviour. They key feature of this methodology is the addition of a new term to the classical certainty-equivalence control approach that, in conjunction with the parameter update law, is designed to achieve adaptive stabilization. This parameter has the ultimate task of shaping the manifold into which the adaptive system is immersed. The performance of the controller is proven stable via a Lyapunov-based analysis and Barbalat’s lemma. In order to evaluate the design of the controllers, test cases based on the physical and orbital features of the Prototype Research Instruments and Space Mission Technology Advancement (PRISMA) are implemented, extending the number of elements in the formation into scenarios with reconfigurations and on-orbit position switching in elliptical low-Earth reference orbits. An extensive analysis and comparison of the performance of the controllers in terms of total Δv and fuel consumption, with and without the effects of the CAS, is presented. These results show that the three proposed controllers allow the followers to asymptotically track the desired nominal trajectory and, additionally, those simulations including CAS show an effective decrease of collision risk during the performance of the manoeuvre.

A principal component approach to space-based gravitational wave astronomy

The current approach to data analysis for the Laser Interferometry Space Antenna (LISA) depends on the time delay interferometry observables (TDI) which have to be generated before any weak signal detection can be performed. These are linear combinations of the raw data with appropriate time shifts that lead to the cancellation of the laser frequency noises. This is possible because of the multiple occurrences of the same noises in the different raw data. Originally, these observables were manually generated starting with LISA as a simple stationary array and then adjusted to incorporate the antenna's motions. However, none of the observables survived the flexing of the arms in that they did not lead to cancellation with the same structure. The principal component approach is another way of handling these noises that was presented by Romano and Woan which simplified the data analysis by removing the need to create them before the analysis. This method also depends on the multiple occurrences of the same noises but, instead of using them for cancellation, it takes advantage of the correlations that they produce between the different readings. These correlations can be expressed in a noise (data) covariance matrix which occurs in the Bayesian likelihood function when the noises are assumed be Gaussian. Romano and Woan showed that performing an eigendecomposition of this matrix produced two distinct sets of eigenvalues that can be distinguished by the absence of laser frequency noise from one set. The transformation of the raw data using the corresponding eigenvectors also produced data that was free from the laser frequency noises. This result led to the idea that the principal components may actually be time delay interferometry observables since they produced the same outcome, that is, data that are free from laser frequency noise. The aims here were (i) to investigate the connection between the principal components and these observables, (ii) to prove that the data analysis using them is equivalent to that using the traditional observables and (ii) to determine how this method adapts to real LISA especially the flexing of the antenna. For testing the connection between the principal components and the TDI observables a 10x 10 covariance matrix containing integer values was used in order to obtain an algebraic solution for the eigendecomposition. The matrix was generated using fixed unequal arm lengths and stationary noises with equal variances for each noise type. Results confirm that all four Sagnac observables can be generated from the eigenvectors of the principal components. The observables obtained from this method however, are tied to the length of the data and are not general expressions like the traditional observables, for example, the Sagnac observables for two different time stamps were generated from different sets of eigenvectors. It was also possible to generate the frequency domain optimal AET observables from the principal components obtained from the power spectral density matrix. These results indicate that this method is another way of producing the observables therefore analysis using principal components should give the same results as that using the traditional observables. This was proven by fact that the same relative likelihoods (within 0.3%) were obtained from the Bayesian estimates of the signal amplitude of a simple sinusoidal gravitational wave using the principal components and the optimal AET observables. This method fails if the eigenvalues that are free from laser frequency noises are not generated. These are obtained from the covariance matrix and the properties of LISA that are required for its computation are the phase-locking, arm lengths and noise variances. Preliminary results of the effects of these properties on the principal components indicate that only the absence of phase-locking prevented their production. The flexing of the antenna results in time varying arm lengths which will appear in the covariance matrix and, from our toy model investigations, this did not prevent the occurrence of the principal components. The difficulty with flexing, and also non-stationary noises, is that the Toeplitz structure of the matrix will be destroyed which will affect any computation methods that take advantage of this structure. In terms of separating the two sets of data for the analysis, this was not necessary because the laser frequency noises are very large compared to the photodetector noises which resulted in a significant reduction in the data containing them after the matrix inversion. In the frequency domain the power spectral density matrices were block diagonals which simplified the computation of the eigenvalues by allowing them to be done separately for each block. The results in general showed a lack of principal components in the absence of phase-locking except for the zero bin. The major difference with the power spectral density matrix is that the time varying arm lengths and non-stationarity do not show up because of the summation in the Fourier transform.

Distributed Large-scale Mixed-Integer Optimization with Application to Energy and Multi-robot Networks

Several decision and control tasks in cyber-physical networks can be formulated as large- scale optimization problems with coupling constraints. In these "constraint-coupled" problems, each agent is associated to a local decision variable, subject to individual constraints. This thesis explores the use of primal decomposition techniques to develop tailored distributed algorithms for this challenging set-up over graphs. We first develop a distributed scheme for convex problems over random time-varying graphs with non-uniform edge probabilities. The approach is then extended to unknown cost functions estimated online. Subsequently, we consider Mixed-Integer Linear Programs (MILPs), which are of great interest in smart grid control and cooperative robotics. We propose a distributed methodological framework to compute a feasible solution to the original MILP, with guaranteed suboptimality bounds, and extend it to general nonconvex problems. Monte Carlo simulations highlight that the approach represents a substantial breakthrough with respect to the state of the art, thus representing a valuable solution for new toolboxes addressing large-scale MILPs. We then propose a distributed Benders decomposition algorithm for asynchronous unreliable networks. The framework has been then used as starting point to develop distributed methodologies for a microgrid optimal control scenario. We develop an ad-hoc distributed strategy for a stochastic set-up with renewable energy sources, and show a case study with samples generated using Generative Adversarial Networks (GANs). We then introduce a software toolbox named ChoiRbot, based on the novel Robot Operating System 2, and show how it facilitates simulations and experiments in distributed multi-robot scenarios. Finally, we consider a Pickup-and-Delivery Vehicle Routing Problem for which we design a distributed method inspired to the approach of general MILPs, and show the efficacy through simulations and experiments in ChoiRbot with ground and aerial robots.

Active Control of the Acoustic Field in a Vehicle Cabin

In this thesis, a thorough investigation on acoustic noise control systems for realistic automotive scenarios is presented. The thesis is organized in two parts dealing with the main topics treated: Active Noise Control (ANC) systems and Virtual Microphone Technique (VMT), respectively. The technology of ANC allows to increase the driver's/passenger's comfort and safety exploiting the principle of mitigating the disturbing acoustic noise by the superposition of a secondary sound wave of equal amplitude but opposite phase. Performance analyses of both FeedForwrd (FF) and FeedBack (FB) ANC systems, in experimental scenarios, are presented. Since, environmental vibration noises within a car cabin are time-varying, most of the ANC solutions are adaptive. However, in this work, an effective fixed FB ANC system is proposed. Various ANC schemes are considered and compared with each other. In order to find the best possible ANC configuration which optimizes the performance in terms of disturbing noise attenuation, a thorough research of \gls{KPI}, system parameters and experimental setups design, is carried out. In the second part of this thesis, VMT, based on the estimation of specific acoustic channels, is investigated with the aim of generating a quiet acoustic zone around a confined area, e.g., the driver's ears. Performance analysis and comparison of various estimation approaches is presented. Several measurement campaigns were performed in order to acquire a sufficient duration and number of microphone signals in a significant variety of driving scenarios and employed cars. To do this, different experimental setups were designed and their performance compared. Design guidelines are given to obtain good trade-off between accuracy performance and equipment costs. Finally, a preliminary analysis with an innovative approach based on Neural Networks (NNs) to improve the current state of the art in microphone virtualization is proposed.

Learning representations for graph-structured socio-technical systems

The recent widespread use of social media platforms and web services has led to a vast amount of behavioral data that can be used to model socio-technical systems. A significant part of this data can be represented as graphs or networks, which have become the prevalent mathematical framework for studying the structure and the dynamics of complex interacting systems. However, analyzing and understanding these data presents new challenges due to their increasing complexity and diversity. For instance, the characterization of real-world networks includes the need of accounting for their temporal dimension, together with incorporating higher-order interactions beyond the traditional pairwise formalism. The ongoing growth of AI has led to the integration of traditional graph mining techniques with representation learning and low-dimensional embeddings of networks to address current challenges. These methods capture the underlying similarities and geometry of graph-shaped data, generating latent representations that enable the resolution of various tasks, such as link prediction, node classification, and graph clustering. As these techniques gain popularity, there is even a growing concern about their responsible use. In particular, there has been an increased emphasis on addressing the limitations of interpretability in graph representation learning. This thesis contributes to the advancement of knowledge in the field of graph representation learning and has potential applications in a wide range of complex systems domains. We initially focus on forecasting problems related to face-to-face contact networks with time-varying graph embeddings. Then, we study hyperedge prediction and reconstruction with simplicial complex embeddings. Finally, we analyze the problem of interpreting latent dimensions in node embeddings for graphs. The proposed models are extensively evaluated in multiple experimental settings and the results demonstrate their effectiveness and reliability, achieving state-of-the-art performances and providing valuable insights into the properties of the learned representations.

Existence and uniqueness of viscosity solution for Hamilton-Jacobi equation with discontinuous coefficients dependent on time

The main result is a proof of the existence of a unique viscosity solution for Hamilton-Jacobi equation, where the hamiltonian is discontinuous with respect to variable, usually interpreted as the spatial one. Obtained generalized solution is continuous, but not necessarily differentiable.

Distribution-Free Bounds for Serial Correlation Coefficients in Heteroskedastic Symmetric Time Series

We consider the problem of testing whether the observations X1, ..., Xn of a time series are independent with unspecified (possibly nonidentical) distributions symmetric about a common known median. Various bounds on the distributions of serial correlation coefficients are proposed: exponential bounds, Eaton-type bounds, Chebyshev bounds and Berry-Esséen-Zolotarev bounds. The bounds are exact in finite samples, distribution-free and easy to compute. The performance of the bounds is evaluated and compared with traditional serial dependence tests in a simulation experiment. The procedures proposed are applied to U.S. data on interest rates (commercial paper rate).

Use of the statistical properties of the wavelet-transform coefficients for optimization of integration time in Fourier transform spectrometry

We show that an analysis of the mean and variance of discrete wavelet coefficients of coaveraged time-domain interferograms can be used as a specification for determining when to stop coaveraging. We also show that, if a prediction model built in the wavelet domain is used to determine the composition of unknown samples, a stopping criterion for the coaveraging process can be developed with respect to the uncertainty tolerated in the prediction.

Anomalous dependence on the diffusion coefficients of the ionic relaxation time in electrolytes

We show, by using a numerical analysis, that the dynamic toward equilibrium for an electrolytic cell subject to a step-like external electric field is a multirelaxation process when the diffusion coefficients of positive and negative ions are different. By assuming that the diffusion coefficient of positive ions is constant, we observe that the number of involved relaxation processes increases when the diffusion coefficient of the negative ions diminishes. Furthermore, two of the relaxation times depend nonmonotonically on the ratio of the diffusion coefficients. This result is unexpected, because the ionic drift velocity, by means of which the ions move to reach the equilibrium distribution, increases with increasing ionic mobility.

Difference equations with delays depending on time

For linear difference equations with coefficients and delays varying in time, sufficient conditions are given, in the scalar case, the zero solution to be stable. © 1990 Sociedade Brasileira de Matemática.