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This paper presents results for the innermost stable circular orbit in a Kerr-like spacetime. The metric employed is an approximation that combines the Kerr metric with the Erez-Rosen metric, expanded in a Taylor series. Consequently, this spacetime incorporates three relativistic multipole moments: mass, spin, and quadrupole moment. Our derivation builds upon the analysis conducted by Chandrasekhar for the Kerr metric. Utilizing the Euler-Lagrange method and Hamiltonian dynamics, we define an effective potential for the radial coordinate. This equation can be used to measure the mass quadrupole through observational methods, as it yields a quadratic polynomial for the quadrupole moment. As anticipated, the limiting cases of this equation correspond to the established cases of Kerr and Schwarzschild spacetimes.

The pressing demand for offshore wind energy has driven a significant increase in the size of wind turbines, as exemplified by the proposed 22MW turbine in the IEA Task 55 REFWIND. In addition, today it is common to see offshore farms with 100 or 150 turbines. The combination of turbines of increasing sizes in populated farms facilitates energy production but can lead to non-negligible aerodynamic noise emissions, which can be heard underwater. This paper quantifies the underwater aerodynamic noise footprint of three large offshore turbines (5MW, 10MW, and 22MW) and farms composed of these types of turbines. By comparing the underwater noise spectra with audiograms of marine animals, we confirm that the noise emissions of large offshore farms will soon pose an environmental problem. The proposed methodology allows wind turbine designers to predict and mitigate the impact of noise while promoting sustainable energy.

Feature extraction techniques are crucial in medical image classification; however, classical feature extractors in addition to traditional machine learning classifiers often exhibit significant limitations in providing sufficient discriminative information for complex image sets. While Convolutional Neural Networks (CNNs) and Vision Transformer (ViT) have shown promise in feature extraction, they are prone to overfitting due to the inherent characteristics of medical imaging data, including small sample sizes or high intra-class variance. In this work, the Medical Image Attention-based Feature Extractor (MIAFEx) is proposed, a novel method that employs a learnable refinement mechanism to enhance the classification token within the Transformer encoder architecture. This mechanism adjusts the token based on learned weights, improving the extraction of salient features and enhancing the model's adaptability to the challenges presented by medical imaging data. The MIAFEx output features quality is compared against classical feature extractors using traditional and hybrid classifiers. Also, the performance of these features is compared against modern CNN and ViT models in classification tasks, demonstrating its superiority in accuracy and robustness across multiple complex classification medical imaging datasets. This advantage is particularly pronounced in scenarios with limited training data, where traditional and modern models often struggle to generalize effectively. The source code of this proposal can be found at https://github.com/Oscar-RamosS/Medical-Image-Attention-based-Feature-Extractor-MIAFEx, Comment: In preparation for Journal Submission

Traditional implicit generative models are capable of learning highly complex data distributions. However, their training involves distinguishing real data from synthetically generated data using adversarial discriminators, which can lead to unstable training dynamics and mode dropping issues. In this work, we build on the \textit{invariant statistical loss} (ISL) method introduced in \cite{de2024training}, and extend it to handle heavy-tailed and multivariate data distributions. The data generated by many real-world phenomena can only be properly characterised using heavy-tailed probability distributions, and traditional implicit methods struggle to effectively capture their asymptotic behavior. To address this problem, we introduce a generator trained with ISL, that uses input noise from a generalised Pareto distribution (GPD). We refer to this generative scheme as Pareto-ISL for conciseness. Our experiments demonstrate that Pareto-ISL accurately models the tails of the distributions while still effectively capturing their central characteristics. The original ISL function was conceived for 1D data sets. When the actual data is $n$-dimensional, a straightforward extension of the method was obtained by targeting the $n$ marginal distributions of the data. This approach is computationally infeasible and ineffective in high-dimensional spaces. To overcome this, we extend the 1D approach using random projections and define a new loss function suited for multivariate data, keeping problems tractable by adjusting the number of projections. We assess its performance in multidimensional generative modeling and explore its potential as a pretraining technique for generative adversarial networks (GANs) to prevent mode collapse, reporting promising results and highlighting its robustness across various hyperparameter settings.

Aquaporins play a key role for the regulation of water transport and solute selectivity in biological cells and tissues. Due to their unique properties, during the last years aquaporins (AQPs) have attracted increasing interest for their use in the development of biomimetic membranes for water filtration. Motivated by this fascinating application, and the need for reliable methodologies to rationalize the design of AQPs or other biomimetic molecules with targeted filtration properties, we conduct in this work an all-round analysis of their structural features to provide crucial insights into the key determinants of functionality of these relevant biomolecules. Particularly, we analyze -- on a selected set of experimentally-resolved AQP structures -- the composition and peculiarities of their NPA and Selectivity Filter (SF) motifs, the overall structural and sequence similarities between them, their pore shape and the residue-level pore-lining composition. Then, AQPs' pore structural and physico-chemical descriptors are put into correlation with available data on experimental permeation rate, within the context of a pore-level QSAR modeling. The approach, presented here as a methodological proof of concept, enables the identification of key -- potentially novel -- features related to water permeability, which could contribute to a deeper residue-level understanding of AQP filtering properties. Potential beneficiary areas include the rational design of optimized AQP-based biomimetic membranes and research into the molecular mechanisms underlying AQP-related diseases.

Particle-producing targets in high-energy research facilities are often made from refractory metals, and they typically require dedicated cooling systems due to the challenging thermomechanical conditions they experience. However, direct contact of water with target blocks can induce erosion, corrosion, and embrittlement, especially of tungsten (W). One approach to overcoming this problem is cladding the blocks with tantalum (Ta). Unfortunately, Ta generates high decay heat when irradiated, raising safety concerns in the event of a loss-of-cooling accident. This study explored the capacity of niobium (Nb) and its alloys to form diffusion bonds with W and TZM (a molybdenum alloy with titanium and zirconium). This is because the Beam Dump Facility (BDF), a planned new fixed-target installation in CERN's North Area, uses these target materials. The bonding quality of pure Nb, Nb1Zr, and C103 (a Nb alloy with 10% hafnium and 1% titanium) with TZM and W obtained using hot isostatic pressing (HIP) was evaluated. The effects of different HIP temperatures and the introduction of a Ta interlayer were examined. Optical microscopy indicated promising bonding interfaces, which were further characterized using tensile tests and thermal-diffusivity measurements. Their performance under high-energy beam impact was validated using thermomechanical simulations. C103 exhibited higher interface strengths and safety factors than Ta2.5W, positioning it as a potential alternative cladding material for the BDF production target. The findings highlight the viability of Nb-based materials, particularly C103, for improving operational safety and efficiency in fixed-target physics experiments; however, considerations regarding the long half-life of 94Nb require further attention.

The Beam Dump Facility (BDF) is a planned fixed-target installation in CERN's North Area, set to start operating in 2031. A proton beam of 400 GeV/c will be delivered in 1 s pulses of 4e13 protons every 7.2 s, amounting to 4e19 protons on target (PoT) per year, with an average thermal power deposition of 305 kW. The experiment requires high-Z and high-density materials and involves challenging thermomechanical conditions; hence, a water-cooled refractory metal core is proposed. To prevent corrosion and erosion, the target materials - tungsten and a molybdenum-based alloy, TZM-, are clad with a tantalum alloy using hot isostatic pressing. To verify the reliability of the target design and manufacturing process, a reduced-scale prototype target was manufactured and irradiated with 2.4e16 PoT in 2018. This paper presents the findings of the post-irradiation examination (PIE) conducted 2.5 years later. The PIE consisted of non-destructive and destructive activities, including film imaging, microscopy, metrology, ultrasonic testing, microstructural analysis, and mechanical and thermal characterization. No irradiation effects resulting from thermal stresses, such as geometrical changes or cracks in the cladding, were observed, and it was determined that the bonding between the core and cladding materials was robust. Moreover, no changes were detected in the microstructures or mechanical properties of the bulk materials. In conclusion, the robustness of the target baseline design and manufacturing process was confirmed, validating its suitability for operating under the desired conditions. Nonetheless, the observed brittleness of sintered tungsten indicates a potential area for improvement to enhance the lifetime of the BDF target. Overall, the examinations provided valuable insights into the performance of the prototype and indicated potential refinements for the future BDF target complex.

We present a novel approach to automate and optimize anisotropic p-adaptation in high-order h/p solvers using Reinforcement Learning (RL). The dynamic RL adaptation uses the evolving solution to adjust the high-order polynomials. We develop an offline training approach, decoupled from the main solver, which shows minimal overcost when performing simulations. In addition, we derive an inexpensive RL-based error estimation approach that enables the quantification of local discretization errors. The proposed methodology is agnostic to both the computational mesh and the partial differential equation to be solved. The application of RL to mesh adaptation offers several benefits. It enables automated and adaptive mesh refinement, reducing the need for manual intervention. It optimizes computational resources by dynamically allocating high-order polynomials where necessary and minimizing refinement in stable regions. This leads to computational cost savings while maintaining the accuracy of the solution. Furthermore, RL allows for the exploration of unconventional mesh adaptations, potentially enhancing the accuracy and robustness of simulations. This work extends our original research, offering a more robust, reproducible, and generalizable approach applicable to complex three-dimensional problems. We provide validation for laminar and turbulent cases: circular cylinders, Taylor Green Vortex and a 10MW wind turbine to illustrate the flexibility of the proposed approach., Comment: 38 pages, 18 figures, 5 tables

We develop a torque-pitch control framework using deep reinforcement learning for wind turbines to optimize the generation of wind turbine energy while minimizing operational noise. We employ a double deep Q-learning, coupled to a blade element momentum solver, to enable precise control over wind turbine parameters. In addition to the blade element momentum, we use the wind turbine acoustic model of Brooks Pope and Marcolini. Through training with simple winds, the agent learns optimal control policies that allow efficient control for complex turbulent winds. Our experiments demonstrate that the reinforcement learning is able to find optima at the Pareto front, when maximizing energy while minimizing noise. In addition, the adaptability of the reinforcement learning agent to changing turbulent wind conditions, underscores its efficacy for real-world applications. We validate the methodology using a SWT2.3-93 wind turbine with a rated power of 2.3 MW. We compare the reinforcement learning control to classic controls to show that they are comparable when not taking into account noise emissions. When including a maximum limit of 45 dB to the noise produced (100 meters downwind of the turbine), the extracted yearly energy decreases by 22%. The methodology is flexible and allows for easy tuning of the objectives and constraints through the reward definitions, resulting in a flexible multi-objective optimization framework for wind turbine control. Overall, our findings highlight the potential of RL-based control strategies to improve wind turbine efficiency while mitigating noise pollution, thus advancing sustainable energy generation technologies

In this contribution, the classical tests of general relativity using the Gutsunaev-Manko metric with slow rotation are obtained. This metric represents the spacetime of an object endowed with mass, magnetic dipole moment and angular moment. These tests are the deflection of light, time delay, precession of the periastron and gravitational redshift. We also provide numerical estimations for real magnetars and magnetar candidates from the McGill magnetar catalogue, and for the Sun in the cycles of low activity. Our results find that the magnetic dipole contribution to the deflection of light is significant when compared to the rotation contribution. The magnetic dipole contributions to the periastron precession and the time delay are 3 and 6 orders of magnitude lower than the rotation contribution respectively. For the gravitational redshift, the contribution is negligible within the approximation presented.

In this contribution, we present a short account of gravitational lenses and how to calculate different properties of its images in the case of having a transparent distribution of matter such as the uniform transparent sphere, isothermal gas sphere, non-singular isothermal gas sphere and a transparent King profile. With the help of XFGLenses software, and numerical methods, different images arising from all of these profiles, and the different caustics and critical curves are shown. The images were consistent with several previous results that are expected for transparent profiles, like having an odd number of images, and reducing the number of images by two when the source passes through the caustic. The curves shown in the caustics where the diamond, the ellipse and the lemniscate-like. For the critical curves, the most common curve was the ellipse, and the lemniscate appeared in the transparent NSIS case, which is consistent with the fact that these curves are common in gravitational lenses.

An study of the equatorial circular motion of photons and massive particles around a rotating compact body like a neutron star is presented. For this goal, we use an approximate Kerr-like metric with mass quadrupole as perturbation. The effect of this deformation on the photon sphere, and the innermost stable circular orbit, is determined via an effective potential. Furthermore, a stability anaysis is shown, where we observed the same behavior of the effective potential for co-rotating and counter-rotating particles. A comparison with the results for the innermost stable circular orbit obtained for the Hartle-Thorne spacetime is also presented.

Implicit generative models have the capability to learn arbitrary complex data distributions. On the downside, training requires telling apart real data from artificially-generated ones using adversarial discriminators, leading to unstable training and mode-dropping issues. As reported by Zahee et al. (2017), even in the one-dimensional (1D) case, training a generative adversarial network (GAN) is challenging and often suboptimal. In this work, we develop a discriminator-free method for training one-dimensional (1D) generative implicit models and subsequently expand this method to accommodate multivariate cases. Our loss function is a discrepancy measure between a suitably chosen transformation of the model samples and a uniform distribution; hence, it is invariant with respect to the true distribution of the data. We first formulate our method for 1D random variables, providing an effective solution for approximate reparameterization of arbitrary complex distributions. Then, we consider the temporal setting (both univariate and multivariate), in which we model the conditional distribution of each sample given the history of the process. We demonstrate through numerical simulations that this new method yields promising results, successfully learning true distributions in a variety of scenarios and mitigating some of the well-known problems that state-of-the-art implicit methods present., Comment: Proceedings of the 27th International Conference on Artificial Intelligence and Statistics (AISTATS) 2024

We propose a reinforcement learning strategy to control wind turbine energy generation by actively changing the rotor speed, the rotor yaw angle and the blade pitch angle. A double deep Q-learning with a prioritized experience replay agent is coupled with a blade element momentum model and is trained to allow control for changing winds. The agent is trained to decide the best control (speed, yaw, pitch) for simple steady winds and is subsequently challenged with real dynamic turbulent winds, showing good performance. The double deep Q- learning is compared with a classic value iteration reinforcement learning control and both strategies outperform a classic PID control in all environments. Furthermore, the reinforcement learning approach is well suited to changing environments including turbulent/gusty winds, showing great adaptability. Finally, we compare all control strategies with real winds and compute the annual energy production. In this case, the double deep Q-learning algorithm also outperforms classic methodologies.

In the present work, the applicability of physics-augmented neural network (PANN) constitutive models for complex electro-elastic finite element analysis is demonstrated. For the investigations, PANN models for electro-elastic material behavior at finite deformations are calibrated to different synthetically generated datasets, including an analytical isotropic potential, a homogenised rank-one laminate, and a homogenised metamaterial with a spherical inclusion. Subsequently, boundary value problems inspired by engineering applications of composite electro-elastic materials are considered. Scenarios with large electrically induced deformations and instabilities are particularly challenging and thus necessitate extensive investigations of the PANN constitutive models in the context of finite element analyses. First of all, an excellent prediction quality of the model is required for very general load cases occurring in the simulation. Furthermore, simulation of large deformations and instabilities poses challenges on the stability of the numerical solver, which is closely related to the constitutive model. In all cases studied, the PANN models yield excellent prediction qualities and a stable numerical behavior even in highly nonlinear scenarios. This can be traced back to the PANN models excellent performance in learning both the first and second derivatives of the ground truth electro-elastic potentials, even though it is only calibrated on the first derivatives. Overall, this work demonstrates the applicability of PANN constitutive models for the efficient and robust simulation of engineering applications of composite electro-elastic materials.

This paper studies the relationships between three notions of behavioural preorder that have been proposed in the literature: refinement over modal transition systems, and the covariant-contravariant simulation and the partial bisimulation preorders over labelled transition systems. It is shown that there are mutual translations between modal transition systems and labelled transition systems that preserve, and reflect, refinement and the covariant-contravariant simulation preorder. The translations are also shown to preserve the modal properties that can be expressed in the logics that characterize those preorders. A translation from labelled transition systems modulo the partial bisimulation preorder into the same model modulo the covariant-contravariant simulation preorder is also offered, together with some evidence that the former model is less expressive than the latter. In order to gain more insight into the relationships between modal transition systems modulo refinement and labelled transition systems modulo the covariant-contravariant simulation preorder, their connections are also phrased and studied in the context of institutions., Comment: Replaced conference version with the extended paper published in a journal (This update includes a change in the title of the paper)

Covariant-contravariant simulation and conformance simulation are two generalizations of the simple notion of simulation which aim at capturing the fact that it is not always the case that "the larger the number of behaviors, the better". Therefore, they can be considered to be more adequate to express the fact that a system is a correct implementation of some specification. We have previously shown that these two more elaborated notions fit well within the categorical framework developed to study the notion of simulation in a generic way. Now we show that their behaviors have also simple and natural logical characterizations, though more elaborated than those for the plain simulation semantics.

We present a study of the notion of coalgebraic simulation introduced by Hughes and Jacobs. Although in their original paper they allow any functorial order in their definition of coalgebraic simulation, for the simulation relations to have good properties they focus their attention on functors with orders which are strongly stable. This guarantees a so-called "composition-preserving" property from which all the desired good properties follow. We have noticed that the notion of strong stability not only ensures such good properties but also "distinguishes the direction" of the simulation. For example, the classic notion of simulation for labeled transition systems, the relation "p is simulated by q", can be defined as a coalgebraic simulation relation by means of a strongly stable order, whereas the opposite relation, "p simulates q", cannot. Our study was motivated by some interesting classes of simulations that illustrate the application of these results: covariant-contravariant simulations and conformance simulations.

Our concrete objective is to present both ordinary bisimulations and probabilistic bisimulations in a common coalgebraic framework based on multiset bisimulations. For that we show how to relate the underlying powerset and probabilistic distributions functors with the multiset functor by means of adequate natural transformations. This leads us to the general topic that we investigate in the paper: a natural transformation from a functor F to another G transforms F-bisimulations into G-bisimulations but, in general, it is not possible to express G-bisimulations in terms of F-bisimulations. However, they can be characterized by considering Hughes and Jacobs' notion of simulation, taking as the order on the functor F the equivalence induced by the epi-mono decomposition of the natural transformation relating F and G. We also consider the case of alternating probabilistic systems where non-deterministic and probabilistic choices are mixed, although only in a partial way, and extend all these results to categorical simulations.

Our objective is to extend the standard results of preservation and reflection of properties by bisimulations to the coalgebraic setting, as well as to study under what conditions these results hold for simulations. The notion of bisimulation is the classical one, while for simulations we use that proposed by Hughes and Jacobs. As for properties, we start by using a generalization of linear temporal logic to arbitrary coalgebras suggested by Jacobs, and then an extension by Kurtz which includes atomic propositions too.

It has been claimed in I. Arraut, 2023 EPL 144 29003 [arXiv:2311.05652] that General Relativity can generate effects equivalent to dark matter, based on a "new modified symmetry that emerges at galactic scale". We show that (i) the spacetime considered is unphysical, violating energy conditions everywhere; (ii) actually no new symmetry emerges, which results from incorrect definitions of angular momentum, velocity, and arclength in the proposed geometry; (iii) no Tully-Fisher law, or flat rotation curves are obtained either, they simply result from a series of errors in the equations., Comment: 2 pages, no figures. Two minor typos in the text corrected, matches the final published version