Satellite-based platforms are currently the only feasible way of achieving intercontinental range for quantum communication, enabling thus the future global quantum internet. Recent demonstrations by the Chinese spacecraft Micius have spurred an international space race and enormous interest in the development of both scientific and commercial systems. Research efforts so far have concentrated upon in-orbit demonstrations involving a single satellite and one or two ground stations. Ultimately satellite quantum key distribution should enable secure network communication between multiple nodes, which requires efficient scheduling of communication with the set of ground stations. Here we present a study of how satellite quantum key distribution can service many ground stations taking into account realistic constraints such as geography, operational hours, and most importantly, weather conditions. The objective is to maximise the number of keys a set of ground stations located in the United Kingdom could share while simultaneously reflecting the communication needs of each node and its relevance in the network. The problem is formulated as a mixed-integer linear optimisation program and solved to a desired optimality gap using a state of the art solver. The approach is presented using a simulation run throughout six years to investigate the total number of keys that can be sent to ground stations.

The paper presents engineering models, optimization algorithms and design results from a Multidisciplinary Design Optimization (MDO) research in the framework of ESA's PRESTIGE PhD program. The application focuses on the conceptual design of classical unmanned Expendable Launch Vehicles, and results are presented from sensitivity studies and validation tests on European launchers (Ariane-5 ECA and VEGA). Relatively simple models and a mixed global/local optimization approach allow obtaining reasonable results with limited computational effort. A critical analysis of the results also leads to the identification of the most critical modeling aspects to be improved to allow for early preliminary design applications. Nomenclature α = engine mixture ratio ε = nozzle expansion ratio θ = pitch angle ψ = yaw angle µ = mean value σ = standard deviation A e = nozzle exhaust area AoA = total angle of attack a = orbit semiaxiscore boosters configuration CpL = cost per launch e = orbit eccentricity GTOW = gross take-off weight i = orbit inclination I sp = specific impulse, nominal conditions (i.e. nozzle optimal expansion) 2 I sp,vac = specific impulse in vacuum I sp,sea = specific impulse at sea level L/D = length over diameter ratio LSP = launch success probability MR = Engine mixture ratio M = Mach number M prop = Propellant mass (usable propellant only) M dry = Dry mass = inert mass + unused propellants mass N s = number of stages N bs = number of booster sets N b,j = number of boosters for j-th boosters set n ax = axial acceleration p cc = chamber pressure PL = payload PLSF = payload scaling factor q dyn = dynamic pressure q heat = heat flux SET = single engine type configuration (i.e. same engine type for all stages) T nom = total thrust, nominal conditions (i.e. nozzle optimal expansion) T ,vac = total thrust in vacuum T sea = total thrust at sea level

In this paper, the well known stagewise additive modeling using a multiclass exponential (SAMME) boosting algorithm is extended to address problems where there exists a natural order in the targets using a cost-sensitive approach. The proposed ensemble model uses an extreme learning machine (ELM) model as a base classifier (with the Gaussian kernel and the additional regularization parameter). The closed form of the derived weighted least squares problem is provided, and it is employed to estimate analytically the parameters connecting the hidden layer to the output layer at each iteration of the boosting algorithm. Compared to the state-of-the-art boosting algorithms, in particular those using ELM as base classifier, the suggested technique does not require the generation of a new training dataset at each iteration. The adoption of the weighted least squares formulation of the problem has been presented as an unbiased and alternative approach to the already existing ELM boosting techniques. Moreover, the addition of a cost model for weighting the patterns, according to the order of the targets, enables the classifier to tackle ordinal regression problems further. The proposed method has been validated by an experimental study by comparing it with already existing ensemble methods and ELM techniques for ordinal regression, showing competitive results.

This paper presents an approach to propagate sets of initial conditions and model parameters through dynamical systems. It is assumed that the dynamics is dependent on a number of model parameters and that the state of the system evolves from some initial conditions. Both model parameters and initial conditions vary within a set Ω. The paper presents an approach to approximate the set Ω with a polynomial expansion and to propagate, under some regularity assumptions, the polynomial representation through the dynamical system. The approach is based on a generalised polynomial algebra that replaces algebraic operators between real numbers with operators between polynomials. The paper first introduces the concept of generalised polynomial algebra and its use to propagate sets through dynamical systems. Then it analyses, both theoretically and experimentally, its time complexity and compares it against the time complexity of a non-intrusive counterpart.

Ordinal regression (OR) is an important branch of supervised learning in between the multiclass classification and regression. In this paper, the traditional classification scheme of neural network is adapted to learn ordinal ranks. The model proposed imposes monotonicity constraints on the weights connecting the hidden layer with the output layer. To do so, the weights are transcribed using padding variables. This reformulation leads to the so-called inequality constrained least squares (ICLS) problem. Its numerical solution can be obtained by several iterative methods, for example, trust region or line search algorithms. In this proposal, the optimum is determined analytically according to the closed-form solution of the ICLS problem estimated from the Karush-Kuhn-Tucker conditions. Furthermore, following the guidelines of the extreme learning machine framework, the weights connecting the input and the hidden layers are randomly generated, so the final model estimates all its parameters without iterative tuning. The model proposed achieves competitive performance compared with the state-of-the-art neural networks methods for OR.

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