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In this work we present a unified model for the cosmological dark sector. The theory is based on a simple minimally coupled scalar field whose action only contains a canonical kinetic term and is invariant under transverse diffeomorphisms (TDiff). The model has the same number of free parameters as $\Lambda$CDM. We confront the predictions of the model at the background level with data from Planck 2018 CMB distance priors, Pantheon+ and SH0ES SNIa distance moduli, BAO data points from 6dFGS, BOSS, eBOSS and DES and measurements of the Hubble parameter from cosmic chronometers. The model provides excellent results in the joint fit analysis, showing very strong evidence compared to $\Lambda$CDM in the deviance information criterion (DIC). We also show that the Hubble tension between Planck 2018 and SH0ES measurements can be alleviated in the unified TDiff model although further analysis is still needed., Comment: 17 pages, 8 figures. Final version published in PRD

The enforcement of the unimodularity condition in a gravity theory by means of a Lagrange multiplier leads, in general, to inconsistencies upon quantization. This is so, in particular, when the classic linear splitting of the metric between the background and quantum fields is used. To avoid the need of introducing such a Lagrange multiplier while using the classic linear splitting, we carry out the quantization of unimodular gravity with extra Weyl symmetry by using Becchi-Rouet-Stora-Tyutin (BRST) techniques. Here, two gauge symmetries are to be gauge-fixed: transverse diffeomorphisms and Weyl transformations. We perform the gauge-fixing of the transverse diffeomorphism invariance by using BRST transformations that involve antisymmetric ghost fields. We show that these BRST transformations are compatible with the BRST transformations needed to gauge-fix the Weyl symmetry, so that they can be combined in a set of transformations generated by a single BRST operator. Newton's law of gravitation is derived within the BRST formalism we put forward as well as the Slavnov-Taylor equation., Comment: 24 pages, 1 table, 1 figure

Microscopes are essential for biomechanics and hydrodynamical investigation of small aquatic organisms. We report a DIY microscope (GLUBscope) that enables the visualization of organisms from two orthogonal imaging planes (top and side views). Compared to conventional imaging systems, this approach provides a comprehensive visualization strategy of organisms, which could have complex shapes and morphologies. The microscope was constructed by combining custom 3D-printed parts and off-the-shelf components. The system is designed for modularity and reconfigurability. Open-source design files and build instructions are provided in this report. Additionally, proof of use experiments, particularly with Hydra and other organisms that combine the GLUBscope with an analysis pipeline, were demonstrated. Beyond the applications demonstrated, the system can be used or modified for various imaging applications.

The rapidly evolving communication landscape, with the advent of 6G technology, brings new challenges to the design and operation of wireless networks. One of the key concerns is the energy efficiency of the Radio Access Network (RAN), as the exponential growth in wireless traffic demands increasingly higher energy consumption. In this paper, we assess the potential of integrating a High Altitude Platform Station (HAPS) to improve the energy efficiency of a RAN, and quantify the potential energy conservation through meticulously designed simulations. We propose a quantitative framework based on real traffic patterns to estimate the energy consumption of the HAPS integrated RAN and compare it with the conventional terrestrial RAN. Our simulation results elucidate that HAPS can significantly reduce energy consumption by up to almost 30\% by exploiting the unique advantages of HAPS, such as its self-sustainability, high altitude, and wide coverage. We further analyze the impact of different system parameters on performance, and provide insights for the design and optimization of future 6G networks. Our work sheds light on the potential of HAPS integrated RAN to mitigate the energy challenges in the 6G era, and contributes to the sustainable development of wireless communications.

The Aharonov-Bohm effect is a genuine quantum effect typically characterized by a measurable phase shift in the wave function for a charged particle that encircles an electromagnetic field located in a region inaccessible to the mentioned particle. However, this definition is not possible in the majority of the phase space descriptions since they are based on quasiprobability distributions. In this work, we characterize for the first time the Aharonov-Bohm effect within two different formalisms of quantum mechanics. One of them is the phase-space formalism relying on the canonical commutation relations and Weyl transform. In this framework, the aim is to obtain a consistent description of the quantum system by means of the quasiprobability Wigner function. The other one is the Segal-Bargmann formalism, which we mathematically describe and connect with quantum mechanics by means of the commutation relations of the creation and annihilation operators. After an introduction of both formalisms, we study the Aharonov-Bohm effect within them for two specific cases: One determined by a non-zero electric potential, and another determined by a non-zero magnetic vector potential. Subsequently, we obtain a more general description of the Aharonov-Bohm effect that encompasses the two previous cases and that we prove to be equivalent to the well-known description of this effect in the usual quantum mechanics formalism in configuration space. Finally, we delve into the Aharonov-Bohm effect, employing a density operator to depict states with positional and momentum uncertainty, showcasing its manifestation through distinctive interference patterns in the temporal evolution of Wigner functions under an electric potential, and emphasizing the intrinsically quantum nature of this phenomenon.

In this manuscript we study the Wehrl entropy of entangled oscillators. This semiclassical entropy associated with the phase-space description of quantum mechanics can be used for formulating uncertainty relations and for a quantification of entanglement. We focus on a system of two coupled oscillators described within its Segal-Bargmann space. This Hilbert space of holomorphic functions integrable with respect to a given Gaussian-like measure is particularly convenient to deal with harmonic oscillators. Indeed, the Stone-von Neumann theorem allows us to work in this space in a full correspondence with the ladder operators formalism. In addition, the Husimi pseudoprobability distribution is directly computed within the Segal-Bargmann formalism. Once we obtain the Husimi function, we analyze the Wehrl entropy and mutual information., Comment: 20 pages, 3 figures

Federated Learning (FL) is a machine learning technique that addresses the privacy challenges in terms of access rights of local datasets by enabling the training of a model across nodes holding their data samples locally. To achieve decentralized federated learning, blockchain-based FL was proposed as a distributed FL architecture. In decentralized FL, the chief is eliminated from the learning process as workers collaborate between each other to train the global model. Decentralized FL applications need to account for the additional delay incurred by blockchain-based FL deployments. Particularly in this setting, to detect targeted/untargeted poisoning attacks, we investigate the end-to-end learning completion latency of a realistic decentralized FL process protected against poisoning attacks. We propose a technique which consists in decoupling the monitoring phase from the detection phase in defenses against poisoning attacks in a decentralized federated learning deployment that aim at monitoring the behavior of the workers. We demonstrate that our proposed blockchain-based monitoring improved network scalability, robustness and time efficiency. The parallelization of operations results in minimized latency over the end-to-end communication, computation, and consensus delays incurred during the FL and blockchain operations.

We consider real hypersurfaces $M$ in complex projective space equipped with both the Levi-Civita and generalized Tanaka-Webster connections. For any nonnull constant $k$ and any symmetric tensor field of type (1,1) $L$ on $M$ we can define two tensor fields of type (1,2) on $M$, $L_F^{(k)}$ and $L_T^{(k)}$, related to both connections. We study the behaviour of the structure operator $\phi$ with respect to such tensor fields in the particular case of $L=A$, the shape operator of $M$, and obtain some new characterizations of ruled real hypersurfaces in complex projective space.

In this work, we introduce a Variational Multi-Scale (VMS) method for the numerical approximation of parabolic problems, where sub-grid scales are approximated from the eigenpairs of associated elliptic operator. The abstract method is particularized to the one-dimensional advection-diffusion equations, for which the sub-grid components are exactly calculated in terms of a spectral expansion when the advection velocity is approximated by piecewise constant velocities on the grid elements. We prove error estimates that in particular imply that when Lagrange finite element discretisations in space are used, the spectral VMS method coincides with the exact solution of the implicit Euler semi-discretisation of the advection-diffusion problem at the Lagrange interpolation nodes. We also build a feasible method to solve the evolutive advection-diffusion problems by means of an offline/online strategy with reduced computational complexity. We perform some numerical tests in good agreement with the theoretical expectations, that show an improved accuracy with respect to several stabilised methods.

The almost contact metric structure that we have on a real hypersurface $M$ in the complex quadric $Q^{m}=SO_{m+2}/SO_mSO_2$ allows us to define, for any nonnull real number $k$, the $k$-th generalized Tanaka-Webster connection on $M$, $\hat{\nabla}^{(k)}$. Associated to this connection we have Cho and torsion operators, $F_X^{(k)}$ and $T_X^{(k)}$, respectively, for any vector field $X$ tangent to $M$. From them and for any symmetric operator $B$ on $M$ we can consider two tensor fields of type (1,2) on $M$ that we will denote by $B_F^{(k)}$ and $B_T^{(k)}$, respectively. We will classify real hypersurfaces $M$ in $Q^m$ for which any of those tensors identically vanishes, in the particular case of $B$ being the structure Lie operator $L_{\xi}$ on $M$., Comment: 9 pages

Let $M$ be a real hypersurface in complex projective space. The almost contact metric structure on $M$ allows us to consider, for any nonnull real number $k$, the corresponding $k$-th generalized Tanaka-Webster connection on $M$ and, associated to it, a differential operator of first order of Lie type. Considering such a differential operator and Lie derivative we define, from the structure Jacobi operator $R_{\xi}$ on $M$ a tensor field of type (1,2), $R_{{\xi}_T}^{(k)}$. We obtain some classifications of real hypersurfaces for which $R_{{\xi}_T}^{(k)}$ is either symmetric or skew symmetric.