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With the goal of improving spectral efficiency, complex rotation-based precoding and power allocation schemes are developed for two multiple-input multiple-output (MIMO) communication systems, namely, simultaneous wireless information and power transfer (SWIPT) and physical layer multicasting. While the state-of-the-art solutions for these problems use very different approaches, the proposed approach treats them similarly using a general tool and works efficiently for any number of antennas at each node. Through modeling the precoder using complex rotation matrices, objective functions (transmission rates) of the above systems can be formulated and solved in a similar structure. Hence, this approach simplifies signaling design for MIMO systems and can reduce the hardware complexity by having one set of parameters to optimize. Extensive numerical results show that the proposed approach outperforms state-of-the-art solutions for both problems. It increases transmission rates for multicasting and achieves higher rate-energy regions in the SWIPT case. In both cases, the improvement is significant (20%-30%) in practically important settings where the users have one or two antennas. Furthermore, the new precoders are less time-consuming than the existing solutions.

Civil and maritime engineering systems, among others, from bridges to offshore platforms and wind turbines, must be efficiently managed as they are exposed to deterioration mechanisms throughout their operational life, such as fatigue or corrosion. Identifying optimal inspection and maintenance policies demands the solution of a complex sequential decision-making problem under uncertainty, with the main objective of efficiently controlling the risk associated with structural failures. Addressing this complexity, risk-based inspection planning methodologies, supported often by dynamic Bayesian networks, evaluate a set of pre-defined heuristic decision rules to reasonably simplify the decision problem. However, the resulting policies may be compromised by the limited space considered in the definition of the decision rules. Avoiding this limitation, Partially Observable Markov Decision Processes (POMDPs) provide a principled mathematical methodology for stochastic optimal control under uncertain action outcomes and observations, in which the optimal actions are prescribed as a function of the entire, dynamically updated, state probability distribution. In this paper, we combine dynamic Bayesian networks with POMDPs in a joint framework for optimal inspection and maintenance planning, and we provide the formulation for developing both infinite and finite horizon POMDPs in a structural reliability context. The proposed methodology is implemented and tested for the case of a structural component subject to fatigue deterioration, demonstrating the capability of state-of-the-art point-based POMDP solvers for solving the underlying planning optimization problem. Within the numerical experiments, POMDP and heuristic-based policies are thoroughly compared, and results showcase that POMDPs achieve substantially lower costs as compared to their counterparts, even for traditional problem settings.

This work recasts time-dependent optimal control problems governed by partial differential equations in a Dynamic Mode Decomposition with control framework. Indeed, since the numerical solution of such problems requires a lot of computational effort, we rely on this specific data-driven technique, using both solution and desired state measurements to extract the underlying system dynamics. Thus, after the Dynamic Mode Decomposition operators construction, we reconstruct and perform future predictions for all the variables of interest at a lower computational cost with respect to the standard space-time discretized models. We test the methodology in terms of relative reconstruction and prediction errors on a boundary control for a Graetz flow and on a distributed control with Stokes constraints.

In the current work we are concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain $\Omega\subset {\mathbb R}^d$, $d\ge 1$. When $\Omega=[0,1]$, such graphs include the standard Toeplitz graphs and, for $\Omega=[0,1]^d$, the considered class includes $d$-level Toeplitz graphs. In the general case, the underlying sequence of adjacency matrices has a canonical eigenvalue distribution, in the Weyl sense, and it has been shown in the theoretical part of this work that we can associate to it a symbol $\boldsymbol{\mathfrak{f}}$. The knowledge of the symbol and of its basic analytical features provides key information on the eigenvalue structure in terms of localization, spectral gap, clustering, and global distribution. In the present paper, many different applications are discussed and various numerical examples are presented in order to underline the practical use of the developed theory. Tests and applications are mainly obtained from the approximation of differential operators via numerical schemes such as Finite Differences (FDs), Finite Elements (FEs), and Isogeometric Analysis (IgA). Moreover, we show that more applications can be taken into account, since the results presented here can be applied as well to study the spectral properties of adjacency matrices and Laplacian operators of general large graphs and networks, whenever the involved matrices enjoy a uniform local structure.

This work investigates the effect of double intelligent reflecting surface (IRS) in improving the spectrum efficient of multi-user multiple-input multiple-output (MIMO) network operating in the millimeter wave (mmWave) band. Specifically, we aim to solve a weighted sum rate maximization problem by jointly optimizing the digital precoding at the transmitter and the analog phase shifters at the IRS, subject to the minimum achievable rate constraint. To facilitate the design of an efficient solution, we first reformulate the original problem into a tractable one by exploiting the majorization-minimization (MM) method. Then, a block coordinate descent (BCD) method is proposed to obtain a suboptimal solution, where the precoding matrices and the phase shifters are alternately optimized. Specifically, the digital precoding matrix design problem is solved by the quadratically constrained quadratic programming (QCQP), while the analog phase shift optimization is solved by the Riemannian manifold optimization (RMO). The convergence and computational complexity are analyzed. Finally, simulation results are provided to verify the performance of the proposed design, as well as the effectiveness of double-IRS in improving the spectral efficiency.

We introduce the \textit{generalized join the shortest queue model with retrials} and two infinite capacity orbit queues. Three independent Poisson streams of jobs, namely a \textit{smart}, and two \textit{dedicated} streams, flow into a single server system, which can hold at most one job. Arriving jobs that find the server occupied are routed to the orbits as follows: Blocked jobs from the \textit{smart} stream are routed to the shortest orbit queue, and in case of a tie, they choose an orbit randomly. Blocked jobs from the \textit{dedicated} streams are routed directly to their orbits. Orbiting jobs retry to connect with the server at different retrial rates, i.e., heterogeneous orbit queues. Applications of such a system are found in the modelling of wireless cooperative networks. We are interested in the asymptotic behaviour of the stationary distribution of this model, provided that the system is stable. More precisely, we investigate the conditions under which the tail asymptotic of the minimum orbit queue length is exactly geometric. Moreover, we apply a heuristic asymptotic approach to obtain approximations of the steady-state joint orbit queue-length distribution. Useful numerical examples are presented, and shown that the results obtained through the asymptotic analysis and the heuristic approach agreed.

Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well conditioned problems. In this paper, specialized variants of an interior point-proximal method of multipliers are proposed and analyzed for problems of this class. Computational experience on a variety of problems, namely, multi-period portfolio optimization, classification of data coming from functional Magnetic Resonance Imaging, restoration of images corrupted by Poisson noise, and classification via regularized logistic regression, provides substantial evidence that interior point methods, equipped with suitable linear algebra, can offer a noticeable advantage over first-order approaches.

We develop a rapid and accurate contour method for the solution of time-fractional PDEs. The method inverts the Laplace transform via an optimised stable quadrature rule, suitable for infinite-dimensional operators, whose error decreases like $\exp(-cN/\log(N))$ for $N$ quadrature points. The method is parallisable, avoids having to resolve singularities of the solution as $t\downarrow 0$, and avoids the large memory consumption that can be a challenge for time-stepping methods applied to time-fractional PDEs. The ODEs resulting from quadrature are solved using adaptive sparse spectral methods that converge exponentially with optimal linear complexity. These solutions of ODEs are reused for different times. We provide a complete analysis of our approach for fractional beam equations used to model small-amplitude vibration of viscoelastic materials with a fractional Kelvin-Voigt stress-strain relationship. We calculate the system's energy evolution over time and the surface deformation in cases of both constant and non-constant viscoelastic parameters. An infinite-dimensional ``solve-then-discretise'' approach considerably simplifies the analysis, which studies the generalisation of the numerical range of a quasi-linearisation of a suitable operator pencil. This allows us to build an efficient algorithm with explicit error control. The approach can be readily adapted to other time-fractional PDEs and is not constrained to fractional parameters in the range $0<\nu<1$.

Periodic signals play an important role in daily lives. Although conventional sequential models have shown remarkable success in various fields, they still come short in modeling periodicity; they either collapse, diverge or ignore details. In this paper, we introduce a novel framework inspired by Fourier series to generate periodic signals. We first decompose the given signals into multiple sines and cosines and then conditionally generate periodic signals with the output components. We have shown our model efficacy on three tasks: reconstruction, imputation and conditional generation. Our model outperforms baselines in all tasks and shows more stable and refined results.

High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.