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In this paper we study the cover time of the simple random walk on the giant component of supercritical $d$-dimensional random geometric graphs on $n$ vertices. We show that the cover time undergoes a jump at the connectivity threshold radius $r_c$: with $r_g$ denoting the threshold for having a giant component, we show that if the radius $r$ satisfies $(1+\eps)r_g \le r \le (1-\eps)r_c$ for $\eps > 0$ arbitrarily small, the cover time of the giant component is asymptotically almost surely $\Theta(n \log^2 n$). On the other hand, we show that for $r \ge (1+\eps)r_c$, the cover time of the graph is asymptotically almost surely $\Theta(n \log n)$ (which was known for $d=2$ only for a radius larger by a constant factor)., Comment: 28 pages

Most MOOC platforms either use simple schemes for aggregating peer grades, e.g., taking the mean or the median, or apply methodologies that increase students' workload considerably, such as calibrated peer review. To reduce the error between the instructor and students' aggregated scores in the simple schemes, without requiring demanding grading calibration phases, some proposals compute specific weights to compute a weighted aggregation of the peer grades. In this work, and in contrast to most previous studies, we analyse the use of students' engagement and performance measures to compute personalized weights and study the validity of the aggregated scores produced by these common functions, mean and median, together with two other from the information retrieval field, namely the geometric and harmonic means. To test this procedure we have analysed data from a MOOC about Philosophy. The course had 1059 students registered, and 91 participated in a peer review process that consisted in writing an essay and rating three of their peers using a rubric. We calculated and compared the aggregation scores obtained using weighted and non-weighted versions. Our results show that the validity of the aggregated scores and their correlation with the instructors grades can be improved in relation to peer grading, when using the median and weights are computed according to students' performance in chapter tests.

This paper explores the practical approach to portfolio selection methods for investments. The study delves into portfolio theory, discussing concepts such as expected return, variance, asset correlation, and opportunity sets. It also presents the efficient frontier and its application in the Markowitz model, which employs mean-variance optimization techniques. An alternative approach based on the mean-semivariance model is introduced. This model accounts for the skewness and kurtosis of the asset return distribution, providing a more comprehensive view of risk and return. The study also addresses the practical implementation of these models, including the use of genetic algorithms to optimize portfolio selection. Additionally, transaction costs and integer constraints in portfolio optimization are considered, demonstrating the applicability of the Markowitz model. -- Este documento explorar la aproximaci\'on pr\'actica a los m\'etodos de selecci\'on de portafolios para inversiones. El estudio profundiza en la teor\'ia de los portafolios, discutiendo conceptos como el rendimiento esperado, la varianza, la correlaci\'on entre activos y los conjuntos de oportunidades. Tambi\'en presenta la frontera eficiente y su aplicaci\'on en el modelo de Markowitz, que utiliza t\'ecnicas de optimizaci\'on media-varianza. Se introduce un enfoque alternativo basado en el modelo media-semivarianza. Este modelo tiene en cuenta la asimetr\'ia y la curtosis de la distribuci\'on de retornos de los activos, proporcionando una visi\'on m\'as completa de riesgo y rendimiento. El estudio tambi\'en aborda la implementaci\'on pr\'actica de estos modelos, incluyendo el uso de algoritmos gen\'eticos para optimizar la selecci\'on de portafolios. Adem\'as, se consideran los costos de transacci\'on y las restricciones enteras en la optimizaci\'on del portafolio., Comment: 78 pages, in Spanish

The manipulation of low-energy matter properties such as superconductivity, ferromagnetism and ferroelectricity via cavity quantum electrodynamics engineering has been suggested as a way to enhance these many-body collective phenomena. In this work, we investigate the effective interactions between low-energy matter excitations induced by the off-resonant coupling with cavity electromagnetic modes. We extend previous work by going beyond the dipole approximation accounting for the full polarization and magnetization densities of matter. We further include the often neglected diamagnetic interaction and, for the cavity, we consider general linear absorbing media with possibly non-local and non-reciprocal response. We demonstrate that, even in this general scenario, the effective cavity-induced interactions between the matter degrees of freedom are of electrostatic and magnetostatic nature. This confirms the necessity of a multimode description for cavity engineering of matter systems where the low-energy assumption holds. Our findings provide a theoretical framework for studying the influence of general optical environments on extended low-energy matter excitations.

Majorana bound states (MBSs) located at the ends of a hybrid superconductor-semiconductor nanowire are only true zero modes if their characteristic localization length is much smaller than the nanowire length, $\xi_M\ll L$. Otherwise, their wave function overlap gives rise to a finite energy splitting that shows a characteristic oscillatory pattern $\sim e^{-2L/\xi_M}\cos(k_F L)$ versus external parameters that modify the Fermi momentum $k_F$. Detecting such "Majorana oscillations", measurable through low-bias conductance, has been proposed as a strategy for Majorana detection in pristine nanowires. Here we discuss how this detection scheme does not work in full-shell hybrid nanowires, an alternative design to partial-shell nanowires in which a superconductor shell fully wraps the semiconductor core. Using microscopic models, we provide both numerical simulations for Al/InAs hybrids as well as analytical approximations in terms of general nanowire parameters. We find that Majorana oscillations with flux in full-shell nanowires are absent in a wide portion of parameter space. This absence is not a signature of non-overlapping left- and right-end MBSs, but a consequence of the Majorana oscillation period being systematically larger than the flux window of odd Little-Parks lobes where Majorana zero-energy peaks are predicted to appear. Our results demonstrate that split near-zero modes or individual zero-energy crossings should not be dismissed as trivial even if they are found not to oscillate with flux., Comment: 15 pages, 9 figures. Final version

In this paper, we study how the Koopman operator framework can be combined with kernel methods to effectively control nonlinear dynamical systems. While kernel methods have typically large computational requirements, we show how random subspaces (Nystr\"om approximation) can be used to achieve huge computational savings while preserving accuracy. Our main technical contribution is deriving theoretical guarantees on the effect of the Nystr\"om approximation. More precisely, we study the linear quadratic regulator problem, showing that the approximated Riccati operator converges at the rate $m^{-1/2}$, and the regulator objective, for the associated solution of the optimal control problem, converges at the rate $m^{-1}$, where $m$ is the random subspace size. Theoretical findings are complemented by numerical experiments corroborating our results.

Although metaheuristics have been widely recognized as efficient techniques to solve real-world optimization problems, implementing them from scratch remains difficult for domain-specific experts without programming skills. In this scenario, metaheuristic optimization frameworks are a practical alternative as they provide a variety of algorithms composed of customized elements, as well as experimental support. Recently, many engineering problems require to optimize multiple or even many objectives, increasing the interest in appropriate metaheuristic algorithms and frameworks that might integrate new specific requirements while maintaining the generality and reusability principles they were conceived for. Based on this idea, this paper introduces JCLEC-MO, a Java framework for both multi- and many-objective optimization that enables engineers to apply, or adapt, a great number of multi-objective algorithms with little coding effort. A case study is developed and explained to show how JCLEC-MO can be used to address many-objective engineering problems, often requiring the inclusion of domain-specific elements, and to analyze experimental outcomes by means of conveniently connected R utilities., Comment: 41 pages, 5 figures, journal paper

The full information about the interaction between a quantum emitter and an arbitrary electromagnetic environment is encoded in the so-called spectral density. We present an approach for describing such interaction in any coupling regime, providing a Lindblad-like master equation for the emitter dynamics when coupled to a general nanophotonic structure. Our framework is based on the splitting of the spectral density into two terms. On the one hand, a spectral density responsible for the non-Markovian and strong-coupling-based dynamics of the quantum emitter. On the other hand, a residual spectral density including the remaining weak-coupling terms. The former is treated nonperturbatively with a collection of lossy interacting discrete modes whose parameters are determined by a fit to the original spectral density in a frequency region encompassing the quantum emitter transition frequencies. The latter is treated perturbatively under a Markovian approximation. We illustrate the power and validity of our approach through numerical simulations in three different setups, thus offering a variety of scenarios for a full test, including the ultra-strong coupling regime.

In recent years, interest in expanding from 2D to 3D systems has grown in the magnetism community, from exploring new geometries to broadening the knowledge on the magnetic textures present in thick samples, and with this arise the need for new characterization techniques, in particular tomographic imaging. Here, we present a new tomographic technique based on Fourier transform holography, a lensless imaging technique that uses a known reference in the sample to retrieve the object of interest from its diffraction pattern in one single step of calculation, overcoming the phase problem inherent to reciprocal-space-based techniques. Moreover, by exploiting the phase contrast instead of the absorption contrast, thicker samples can be investigated. We obtain a 3D full-vectorial image of a 800 nm-thick extended Fe/Gd multilayer in a 5$\mu$m-diameter circular field of view with a resolution of approximately 80 nm. The 3D image reveals worm-like domains with magnetization pointing mostly out of plane near the surface of the sample but that falls in-plane near the substrate. Since the FTH setup is fairly simple, it allows modifying the sample environment. Therefore, this technique could enable in particular a 3D view of the magnetic configuration's response to an external magnetic field., Comment: 11 pages, 8 figures

Robotic cloth manipulation is a relevant challenging problem for autonomous robotic systems. Highly deformable objects as textile items can adopt multiple configurations and shapes during their manipulation. Hence, robots should not only understand the current cloth configuration but also be able to predict the future possible behaviors of the cloth. This paper addresses the problem of indirectly controlling the configuration of certain points of a textile object, by applying actions on other parts of the object through the use of a Model Predictive Control (MPC) strategy, which also allows to foresee the behavior of indirectly controlled points. The designed controller finds the optimal control signals to attain the desired future target configuration. The explored scenario in this paper considers tracking a reference trajectory with the lower corners of a square piece of cloth by grasping its upper corners. To do so, we propose and validate a linear cloth model that allows solving the MPC-related optimization problem in real time. Reinforcement Learning (RL) techniques are used to learn the optimal parameters of the proposed cloth model and also to tune the resulting MPC. After obtaining accurate tracking results in simulation, the full control scheme was implemented and executed in a real robot, obtaining accurate tracking even in adverse conditions. While total observed errors reach the 5 cm mark, for a 30x30 cm cloth, an analysis shows the MPC contributes less than 30% to that value.