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Vision-and-Language Navigation in Continuous Environments (VLN-CE) is one of the most intuitive yet challenging embodied AI tasks. Agents are tasked to navigate towards a target goal by executing a set of low-level actions, following a series of natural language instructions. All VLN-CE methods in the literature assume that language instructions are exact. However, in practice, instructions given by humans can contain errors when describing a spatial environment due to inaccurate memory or confusion. Current VLN-CE benchmarks do not address this scenario, making the state-of-the-art methods in VLN-CE fragile in the presence of erroneous instructions from human users. For the first time, we propose a novel benchmark dataset that introduces various types of instruction errors considering potential human causes. This benchmark provides valuable insight into the robustness of VLN systems in continuous environments. We observe a noticeable performance drop (up to -25%) in Success Rate when evaluating the state-of-the-art VLN-CE methods on our benchmark. Moreover, we formally define the task of Instruction Error Detection and Localization, and establish an evaluation protocol on top of our benchmark dataset. We also propose an effective method, based on a cross-modal transformer architecture, that achieves the best performance in error detection and localization, compared to baselines. Surprisingly, our proposed method has revealed errors in the validation set of the two commonly used datasets for VLN-CE, i.e., R2R-CE and RxR-CE, demonstrating the utility of our technique in other tasks. Code and dataset will be made available upon acceptance at https://intelligolabs.github.io/R2RIE-CE, Comment: 3 figures, 8 pages

The detection of blue-shifted absorption lines likely associated with ionized Iron K-shell transitions in the X-ray spectra of many Active Galactic Nuclei (AGN) suggests the presence of a highly ionized gas outflowing with mildly relativistic velocities (0.03c-0.6c), named Ultra-Fast Outflow (UFO). Within the SUBWAYS project we characterized these winds starting from a sample of 22 radio-quiet quasars at 0.1 < z < 0.4, and compared the results with similar studies in the literature on samples of 42 local radio-quiet Seyfert galaxies and 14 high redshift radio-quiet quasars. The scope of our work is a statistical study of UFO parameters and incidence, considering key physical properties of the sources, e.g. supermassive black hole (SMBH) mass, bolometric luminosity, accretion rates and Spectral Energy Distribution, with the aim of gaining new insights into the UFO launching mechanisms. We find indications that highly luminous AGN with steeper X-ray/UV ratio, are more likely to host UFO. The presence of UFO is not significantly related to any other AGN property in our sample. These findings suggest that the UFO phenomenon may be transient. Focusing on AGN with UFO, other important results are: (1) faster UFO have larger ionization parameters and column densities; (2) X-ray radiation plays a more crucial role in driving highly ionized winds compared to UV; (3) the correlation between outflow velocity and luminosity is significantly flatter than what expected for radiatively driven winds; (4) more massive BH experience higher wind mass-losses, suppressing accretion of matter onto the BH; (5) the UFO launching radius is positively correlated with the Eddington ratio. Furthermore, our analysis suggest the involvement of multiple launching mechanisms, including radiation pressure and magneto-hydrodynamic processes, rather than pointing to a single, universally applicable mechanism., Comment: 52 pages, 154 figures and 7 tables. Accepted in Astronomy & Astrophysics, in press

We present the results of the charge ratio ($R$) and polarization ($P^{\mu}_{0}$) measurements using the decay electron events collected from 2008 September to 2022 June by the Super-Kamiokande detector. Because of its underground location and long operation, we performed high precision measurements by accumulating cosmic-ray muons. We measured the muon charge ratio to be $R=1.32 \pm 0.02$ $(\mathrm{stat.}{+}\mathrm{syst.})$ at $E_{\mu}\cos \theta_{\mathrm{Zenith}}=0.7^{+0.3}_{-0.2}$ $\mathrm{TeV}$, where $E_{\mu}$ is the muon energy and $\theta_{\mathrm{Zenith}}$ is the zenith angle of incoming cosmic-ray muons. This result is consistent with the Honda flux model while this suggests a tension with the $\pi K$ model of $1.9\sigma$. We also measured the muon polarization at the production location to be $P^{\mu}_{0}=0.52 \pm 0.02$ $(\mathrm{stat.}{+}\mathrm{syst.})$ at the muon momentum of $0.9^{+0.6}_{-0.1}$ $\mathrm{TeV}/c$ at the surface of the mountain; this also suggests a tension with the Honda flux model of $1.5\sigma$. This is the most precise measurement ever to experimentally determine the cosmic-ray muon polarization near $1~\mathrm{TeV}/c$. These measurement results are useful to improve the atmospheric neutrino simulations., Comment: 29 pages, 45 figures

We present two alternative methods for optimizing minimum energy conical intersection (MECI) molecular geometries without knowledge of the derivative coupling (DC). These methods are based on the utilization of Lagrange multipliers: i) one method uses an approximate calculation of the DC, while the other ii) do not require the DC. Both methods use the fact that information of the DC is contained in the Hessian of the squared energy difference. Tests done on a set of small molecular systems, in comparison with other methods, show the ability of the proposed methods to optimize MECIs. Finally, we apply the methods to the furimamide molecule, to optimize and characterize its S$_1$ /S$_2$ MECI, and to optimizing the S$_0$ /S$_1$ MECI of the silver trimer.

CeRh$_6$Ge$_4$ is unusual in that its ferromagnetic transition can be suppressed continuously to zero temperature, i.e., to a ferromagnetic quantum-critical point (QCP), through the application of modest hydrostatic pressure. This discovery has raised the possibility that the ferromagnetic QCP may be of the Kondo-breakdown type characterized by a jump in Fermi volume, to which thermopower S measurements should be sensitive. Though $S/T$ changes both sign and magnitude around the critical pressure P$_{c}\approx{}0.8$ GPa, these changes are not abrupt but extend over a pressure interval from within the ferromagnetic state up to P$_c$. Together with temperature and pressure variations in electrical resistivity and previously reported heat capacity, thermopower results point to the near coincidence of two sequential effects near P$_c$, delocalization of 4f degrees-of-freedom through orbital-selective hybridization followed by quantum criticality of itinerant ferromagnetism., Comment: 6 pages, 3 figures

The first loading of gadolinium (Gd) into Super-Kamiokande in 2020 was successful, and the neutron capture efficiency on Gd reached 50\%. To further increase the Gd neutron capture efficiency to 75\%, 26.1 tons of $\rm Gd_2(\rm SO_4)_3\cdot \rm 8H_2O$ was additionally loaded into Super-Kamiokande (SK) from May 31 to July 4, 2022. As the amount of loaded $\rm Gd_2(\rm SO_4)_3\cdot \rm 8H_2O$ was doubled compared to the first loading, the capacity of the powder dissolving system was doubled. We also developed new batches of gadolinium sulfate with even further reduced radioactive impurities. In addition, a more efficient screening method was devised and implemented to evaluate these new batches of $\rm Gd_2(\rm SO_4)_3\cdot \rm 8H_2O$. Following the second loading, the Gd concentration in SK was measured to be $333.5\pm2.5$ ppm via an Atomic Absorption Spectrometer (AAS). From the mean neutron capture time constant of neutrons from an Am/Be calibration source, the Gd concentration was independently measured to be 332.7 $\pm$ 6.8(sys.) $\pm$ 1.1(stat.) ppm, consistent with the AAS result. Furthermore, during the loading the Gd concentration was monitored continually using the capture time constant of each spallation neutron produced by cosmic-ray muons,and the final neutron capture efficiency was shown to become 1.5 times higher than that of the first loaded phase, as expected., Comment: 34 pages, 13 figures, submitted to Nuclear Inst. and Methods in Physics Research, A

Among multi-messenger observations of the next galactic core-collapse supernova, Super-Kamiokande (SK) plays a critical role in detecting the emitted supernova neutrinos, determining the direction to the supernova (SN), and notifying the astronomical community of these observations in advance of the optical signal. On 2022, SK has increased the gadolinium dissolved in its water target (SK-Gd) and has achieved a Gd concentration of 0.033%, resulting in enhanced neutron detection capability, which in turn enables more accurate determination of the supernova direction. Accordingly, SK-Gd's real-time supernova monitoring system (Abe te al. 2016b) has been upgraded. SK_SN Notice, a warning system that works together with this monitoring system, was released on December 13, 2021, and is available through GCN Notices (Barthelmy et al. 2000). When the monitoring system detects an SN-like burst of events, SK_SN Notice will automatically distribute an alarm with the reconstructed direction to the supernova candidate within a few minutes. In this paper, we present a systematic study of SK-Gd's response to a simulated galactic SN. Assuming a supernova situated at 10 kpc, neutrino fluxes from six supernova models are used to characterize SK-Gd's pointing accuracy using the same tools as the online monitoring system. The pointing accuracy is found to vary from 3-7$^\circ$ depending on the models. However, if the supernova is closer than 10 kpc, SK_SN Notice can issue an alarm with three-degree accuracy, which will benefit follow-up observations by optical telescopes with large fields of view., Comment: 38 pages, 29 figures, 6 tables

We report on multi-resonance chirped distributed Bragg reflector (DBR) microcavities. These systems are employed to investigate the light-mater interaction with both intra- and inter-layer excitons of transition metal dichalcogenide (TMDC) bilayer heterostructures. The chirped DBRs consisting of SiO2 and Si3N4 layers with gradually changing thickness exhibit a broad stopband with a width exceeding 600 nm. Importantly, and in contrast to conventional single-resonance microcavities, our structures provide multiple resonances across a broad spectral range, which can be matched to spectrally distinct resonances of the embedded TMDC heterostructures. We study cavity-coupled emission of both intra- and inter-layer excitons from an integrated WSe2/MoSe2 heterostructure in a chirped microcavity system. We observe an enhanced interlayer exciton emission with a Purcell factor of 6.67 +- 1.02 at 4 K. Additionally, we take advantage of cavity-enhanced emission of the interlayer exciton to investigate its temperature-dependent luminescence lifetime, which yields a value of 60 ps at room temperature. Our approach provides an intriguing platform for future studies of energetically distant and confined excitons in different semiconducting materials, which paves the way for various applications such as microlasers and single-photon sources by enabling precise control and manipulation of excitonic interactions utilizing multimode resonance light-matter interaction.

The Wide-field Spectroscopic Telescope (WST) is proposed as a new facility dedicated to the efficient delivery of spectroscopic surveys. This white paper summarises the initial concept as well as the corresponding science cases. WST will feature simultaneous operation of a large field-of-view (3 sq. degree), a high multiplex (20,000) multi-object spectrograph (MOS) and a giant 3x3 sq. arcmin integral field spectrograph (IFS). In scientific capability these requirements place WST far ahead of existing and planned facilities. Given the current investment in deep imaging surveys and noting the diagnostic power of spectroscopy, WST will fill a crucial gap in astronomical capability and work synergistically with future ground and space-based facilities. This white paper shows that WST can address outstanding scientific questions in the areas of cosmology; galaxy assembly, evolution, and enrichment, including our own Milky Way; origin of stars and planets; time domain and multi-messenger astrophysics. WST's uniquely rich dataset will deliver unforeseen discoveries in many of these areas. The WST Science Team (already including more than 500 scientists worldwide) is open to the all astronomical community. To register in the WST Science Team please visit https://www.wstelescope.com/for-scientists/participate, Comment: 194 pages, 66 figures. Comments are welcome (wstelescope@gmail.com)

We prove that any sequence of vanishing viscosity Leray-Hopf solutions to the periodic two-dimensional incompressible Navier-Stokes equations does not display anomalous dissipation if the initial vorticity is a measure with positive singular part. A key step in the proof is the use of the Delort-Majda concentration-compactness argument to exclude formation of atoms in the vorticity measure, which in particular implies that the limiting velocity is an admissible weak solution to Euler. This is the first result proving absence of dissipation in a class of solutions in which the velocity fails to be strongly compact in $L^2$, putting two-dimensional turbulence in sharp contrast with respect to that in three dimensions. Moreover, our proof reveals that the amount of energy dissipation can be bounded by the vorticity measure of a disk of size $\sqrt \nu$, matching the two-dimensional Kolmogorov dissipative length scale which is expected to be sharp., Comment: Extended version

Recent observations have found a large number of supermassive black holes already in place in the first few hundred million years after Big Bang. The channels of formation and growth of these early, massive black holes are not clear, with scenarios ranging from heavy seeds to light seeds experiencing bursts of high accretion rate. Here we present the detection, from the JADES survey, of broad Halpha emission in a galaxy at z=6.68, which traces a black hole with mass of ~ 4 * 10^8 Msun and accreting at a rate of only 0.02 times the Eddington limit. The host galaxy has low star formation rate (~ 1 Msun/yr, a factor of 3 below the star forming main sequence). The black hole to stellar mass ratio is ~ 0.4, i.e. about 1,000 times above the local relation, while the system is closer to the local relations in terms of dynamical mass and velocity dispersion of the host galaxy. This object is most likely the tip of the iceberg of a much larger population of dormant black holes around the epoch of reionisation. Its properties are consistent with scenarios in which short bursts of super-Eddington accretion have resulted in black hole overgrowth and massive gas expulsion from the accretion disk; in between bursts, black holes spend most of their life in a dormant state., Comment: 38 pages, 18 figures. Submitted

The recently proposed non-additive stochastic model (NSM) offers a coherent physical interpretation for diffusive phenomena in glass-forming systems. This model presents non-exponential relationships between viscosity, activation energy, and temperature, characterizing the non-Arrhenius behavior observed in supercooled liquids. In this work, we fit the NSM viscosity equation to experimental temperature-dependent viscosity data corresponding to twenty-five glass-forming liquids and compare the fit parameters with those obtained using the Vogel-Fulcher-Tammann (VFT), Avramov-Milchev (AM), and Mauro-Yue-Ellison-Gupta-Allan (MYEGA) models. The results demonstrate that the NSM provides an effective fitting equation for modeling viscosity experimental data in comparison with other established models (VFT, AM and MYEGA), characterizing the activation energy in fragile liquids, presenting a reliable indicator of the degree of fragility of the glass-forming liquids.

This work investigates observational properties, namely the shadow and photon ring structure, of emission profiles originated near compact objects. In particular, we consider a distorted and deformed compact object characterized by quadrupoles and surrounded by an optically thin and geometrically thin accretion disk with different emission profiles modeled by the Johnson's Standard-Unbound (SU) distribution in the reference frame of the emitter. Under these assumptions, we produce the observed intensity profiles and shadow images for a face-on observer. Our results indicate that, due to the fact that modifications of the quadrupole parameters affect the radius of the innermost stable circular orbit (ISCO) and the photon sphere (PS), the observed shadow images and their properties are significantly influenced by the quadrupole parameters and emission profiles. Furthermore, we analyze the impact of the presence of a dark matter halo in the observational imprints considered and verify that both the increase in the matter contained in the halo or decrease in the length-scale of the halo lead to an increase in the size of the observed shadow. Our results indicate potential degeneracies between the observational features of distorded and deformed compact objects with those of spherically symmetric blackholes, which could be assessed by a comparison with the current and future generation of optical experiments in gravitational physics.

We used the Imaging X-ray Polarimetry Explorer (IXPE) satellite to measure, for the first time, the 2-8 keV polarization of NGC 1068. We pointed IXPE for a net exposure time of 1.15 Ms on the target, in addition to two ~ 10 ks each Chandra snapshots in order to account for the potential impact of several ultraluminous X-ray source (ULXs) within IXPE's field-of-view. We measured a 2 - 8 keV polarization degree of 12.4% +/- 3.6% and an electric vector polarization angle of 101{\deg} +/- 8{\deg} at 68% confidence level. If we exclude the spectral region containing the bright Fe K lines and other soft X-ray lines where depolarization occurs, the polarization fraction rises up to 21.3% +/- 6.7% in the 3.5 - 6.0 keV band, with a similar polarization angle. The observed polarization angle is found to be perpendicular to the parsec scale radio jet. Using a combined Chandra and IXPE analysis plus multi-wavelength constraints, we estimated that the circumnuclear "torus" may sustain a half-opening angle of 50{\deg} - 55{\deg} (from the vertical axis of the system). Thanks to IXPE, we have measured the X-ray polarization of NGC 1068 and found comparable results, both in terms of polarization angle orientation with respect to the radio-jet and torus half-opening angle, to the X-ray polarimetric measurement achieved for the other archetypal Compton-thick AGN : the Circinus galaxy. Probing the geometric arrangement of parsec-scale matter in extragalactic object is now feasible thanks to X-ray polarimetry., Comment: 9 pages, 5 figures, 2 tables, submited to A&A

Mukai proved that the moduli space of simple sheaves on a smooth projective K3 surface is symplectic, and in \cite{FM2} we gave two constructions allowing one to construct new locally closed Lagrangian/isotropic subspaces of the moduli from old ones. In this paper, we extend both Mukai's result and our construction to reduced projective K3 surfaces; for the former we need to restrict our attention to perfect sheaves. There are two key points where we cannot get a straightforward generalization. In each, we need to prove that a certain differential form on the moduli space of simple, perfect sheaves vanishes, and we introduce a smoothability condition to complete the proof., Comment: Comments and remarks are welcome

Let $\mathbb{D}$ denote the unit disc in $\mathbb{C}$. We define the generalized Ces\`aro operator as follows $$ C_{\omega}(f)(z)=\int_0^1 f(tz)\left(\frac{1}{z}\int_0^z B^{\omega}_t(u)\,du\right)\,\omega(t)dt,$$ where $\{B^{\omega}_\zeta\}_{\zeta\in\mathbb{D}}$ are the reproducing kernels of the Bergman space $A^2_\omega$ induced by a radial weight $\omega$ in the unit disc $\mathbb{D}$. We study the action of the operator $C_{\omega}$ on weighted Hardy spaces of analytic functions $\mathcal{H}_{\gamma}$, $\gamma >0$ and on general weighted Bergman spaces $A^2_{\mu}$.

We report correlations in underground seismic measurements with horizontal separations of several hundreds of meters to a few kilometers in the frequency range 0.01Hz to 40Hz. These seismic correlations could threaten science goals of planned interferometric gravitational-wave detectors such as the Einstein Telescope as well as atom interferometers such as MIGA and ELGAR. We use seismic measurements from four different sites, i.e. the former Homestake mine (USA) as well as two candidate sites for the Einstein Telescope, Sos Enattos (IT) and Euregio Maas-Rhein (NL-BE-DE) and the site housing the MIGA detector, LSBB (FR). At all sites, we observe significant coherence for at least 50% of the time in the majority of the frequency region of interest. Based on the observed correlations in the seismic fields, we predict levels of correlated Newtonian noise from body waves. We project the effect of correlated Newtonian noise from body waves on the capabilities of the triangular design of the Einstein Telescope's to observe an isotropic gravitational-wave background (GWB) and find that, even in case of the most quiet site, its sensitivity will be affected up to $\sim$20Hz. The resolvable amplitude of a GWB signal with a negatively sloped power-law behaviour would be reduced by several orders of magnitude. However, the resolvability of a power-law signal with a slope of e.g. $\alpha=0$ ($\alpha=2/3$) would be more moderately affected by a factor $\sim$ 6-9 ($\sim$3-4) in case of a low noise environment. Furthermore, we bolster confidence in our results by showing that transient noise features have a limited impact on the presented results.

In this paper, we consider the best multivalued polynomial approximation operator for functions in an Orlicz Space $L^{\varphi}(\Omega)$. We obtain its characterization involving $\psi^-$ and $\psi^+$, which are the left and right derivatives functions of $\varphi$. And then, we extend the operator to $L^{\psi^+}(\Omega)$. We also get pointwise convergence of this extension, where the Calder\'on-Zygmund class $t_m^p (x)$ adapted to $L^{\psi^+}(\Omega)$ plays an important role.

This work reports experimental evidence of random magnetic behavior observed in modified barium hexagonal ferrites. We observe a significant transition in the magnetic properties of this system when divalent cations (Ni2+, Cu2+, Mn2+) are incorporated into the structure and give rise to a magnetic nanocomposite. Such introduction randomly occurs throughout each sample and creates conditions for such materials to behave as random anisotropy magnets. We verify the occurrence of such behavior in our samples by fitting the magnetization in approaching saturation to the corresponding theoretical model. We therefore analyze the microwave absorption capacities of random anisotropy magnets in the GHz range and predict large and broad absorption signals under certain conditions. The findings presented here postulate, for the first time, ceramic materials as promising random anisotropy magnets and underline their potential as microwave absorbers, in good agreement with recent theoretical models.

We introduce and study a general notion of spatial localization on spacelike smooth Cauchy surfaces of quantum systems in Minkowski spacetime. The notion is constructed in terms of a coherent family of normalized POVMs, one for each said Cauchy surface. We prove that a family of POVMs of this type automatically satisfies a causality condition which generalizes Castrigiano's one and implies it when restricting to flat spacelike Cauchy surfaces. As a consequence no conflict with Hegerfeldt's theorem arises. We furthermore prove that such families of POVMs do exist for massive Klein-Gordon particles, since some of them are extensions of already known spatial localization observables. These are constructed out of positive definite kernels or are defined in terms of the stress-energy tensor operator. Some further features of these structures are investigated, in particular, the relation with the triple of Newton-Wigner selfadjoint operators and a modified form of Heisenberg inequality in the rest $3$-spaces of Minkowski reference frames, Comment: Final version, 59 Pages, no figures, further references and comments added, several typos corrected, accepted for publication in Lett. Math. Phys

Black holes in General Relativity are described by space-time metrics that are simpler in comparison to non-vacuum compact objects. However, given the universality of the gravitational pull, it is expected that dark matter accumulates around astrophysical black holes, which can have an impact in the overall gravitational field, especially at galactic centers, and induce non-negligible effects in their observational imprints. In this work we study the optical appearance of a spherically symmetric black hole both when orbited by isotropically emitting light sources and when surrounded by a (geometrically and optically thin) accretion disk, while immersed in a dark matter halo. The black hole geometry plus the dark matter halo come as a solution of Einstein's field equations coupled to an anisotropic fluid whose density component follows a Hermquist-type distribution. Even in situations in which the geodesic description differs profoundly from the isolated black hole case, we find minor modifications to the primary and secondary tracks of the isotropic orbiting sources, and to the width, location, and relative luminosity of the corresponding photon rings as compared to the Schwarzschild black hole at equal black hole mass and emission models. This fact troubles distinguishing between both geometries using present observations of very-long baseline interferometry., Comment: 21 pages, 17 figures

Policy Brief on "Regional and Global Collaborations in Astronomy", distilled from the corresponding panel that was part of the discussions during S20 Policy Webinar on Astroinformatics for Sustainable Development held on 6-7 July 2023. Astronomy brings together advanced scientific research, state-of-the-art technology, and educational initiatives, all while captivating and stimulating people of all ages. By doing so, it possesses the potential to serve as a powerful catalyst for sustainable global development and the resolution of global societal issues. It attracts a diverse range of scientists and experts from various fields, fostering collaboration and innovation. By leveraging their resources, influence, and diplomatic initiatives, S20 academies can foster an enabling environment for international collaborations in astronomy, facilitate knowledge exchange, and drive scientific advancements that benefit humanity. This policy brief explores the opportunities and challenges presented by regional and global collaborations in astronomy. The policy webinar took place during the G20 presidency in India (2023). A summary based on the seven panels can be found here: arxiv:2401.04623., Comment: 6 pages. The panel videos including keynotes and the white papers are available on the S20 site at: https://s20india.org/science-policy-webinar-astroinformatics-for-sustainable-development/

Control of topological edge modes is desirable for encoding quantum information resiliently against external noise. Their implementation on quantum hardware, however, remains a long-standing problem due to current limitations of circuit depth and noise, which grows with the number of time steps. By utilizing recently developed constant-depth quantum circuits in which the circuit depth is independent of time, we demonstrate successful long-time dynamics simulation of bulk and surface modes in topological insulators on noisy intermediate-scale quantum (NISQ) processors, which exhibits robust signatures of localized topological modes. We further identify a class of one-dimensional topological Hamiltonians that can be readily simulated with NISQ hardware. Our results provide a pathway towards stable long-time implementation of topological quantum spin systems on present day quantum processors.

We show that optimal control of the electron dynamics is able to prepare molecular ground states, within chemical accuracy, with evolution times approaching the bounds imposed by quantum mechanics. We propose a specific parameterization of the molecular evolution only in terms of interaction already present in the molecular Hamiltonian. Thus, the proposed method solely utilizes quantum simulation routines, retaining their favourable scalings. Due to the intimate relationships between variational quantum algorithms and optimal control we compare, when possible, our results with state-of-the-art methods in literature. We found that the number of parameters needed to reach chemical accuracy and algorithmic scaling are in line with compact adaptive strategies to build variational ansatze. The algorithm, which is also suitable for quantum simulators, is implemented emulating a digital quantum processor (up to 16 qubits) and tested on different molecules and geometries spanning different degrees of electron correlation.

We explore the effect of a finite two-body energy in the discrete scale symmetry regime of two heavy bosonic impurities immersed in a light bosonic system. By means of the Born-Oppenheimer approximation in non-integer dimensions $(D)$, we discuss the effective potential of the heavy-particles Schrodinger equation. We study how including the two-body energy in the effective potential changes the light-particles wave function and the ratio between successive Efimov states. We present the limit cycles associated with correlation between the energy of successive levels for the three and four-body systems. Our study is exemplified by considering a system composed of $N$-bosons, namely two Rubidium atoms interacting with $N-2$ Lithium ones ($^7$Li$_{N-2}-^{87}$Rb$_2$), which represent compounds of current experimental interest.

We deal with Perazzo hypersurfaces $X=V(f)$ in $\PP^{n+2}$ defined by a homogeneous polynomial $f(x_0,x_1,\dots,x_n,u,v)=p_0(u,v)x_0+p_1(u,v)x_1+\cdots +p_n(u,v)x_n+g(u,v)$, where $p_0,p_1,\dots ,p_n$ are algebraically dependent but linearly independent forms of degree $d-1$ in $K[u,v]$ and $g$ is a form in $K[u,v]$ of degree $d$. Perazzo hypersurfaces have vanishing hessian and, hence, the associated graded artinian Gorenstein algebra $A_f$ fails the strong Lefschetz property. In this paper, we first determine the maximum and minimum Hilbert function of $A_f$, we prove that the Hilbert function of $A_f$ is always unimodal and we determine when $A_f$ satisfies the weak Lefschetz property. We illustrate our results with many examples and we show that our results do not generalize to Perazzo hypersurfaces $X=V(f)$ in $\PP^{n+3}$ defined by a homogeneous polynomial $f(x_0,x_1,\dots,x_{n},u,v,w)=p_0(u,v,w)x_0+p_1(u,v,w)x_1+\cdots +p_{n}(u,v,w)x_{n}+g(u,v,w)$, where $p_0,p_1,\dots ,p_{n}$ are algebraically dependent but linearly independent forms of degree $d-1$ in $K[u,v,w]$ and $g$ is a form in $K[u,v,w]$ of degree $d$., Comment: To be published in Journal of Algebra

In this paper we formally define the hierarchical clustering network problem (HCNP) as the problem to find a good hierarchical partition of a network. This new problem focuses on the dynamic process of the clustering rather than on the final picture of the clustering process. To address it, we introduce a new ierarchical clustering algorithm in networks, based on a new shortest path betweenness measure. To calculate it, the communication between each pair of nodes is weighed by he importance of the nodes that establish this communication. The weights or importance associated to each pair of nodes are calculated as the Shapley value of a game, named as the linear modularity game. This new measure, (the node-game shortest path betweenness measure), is used to obtain a hierarchical partition of the network by eliminating the link with the highest value. To evaluate the performance of our algorithm, we introduce several criteria that allow us to compare different dendrograms of a network from two point of view: modularity and homogeneity. Finally, we propose a faster algorithm based on a simplification of the node-game shortest path betweenness measure, whose order is quadratic on sparse networks. This fast version is competitive from a computational point of view with other hierarchical fast algorithms, and, in general, it provides better results., Comment: 29 pages

High-quality Extragalactic Legacy-field Monitoring (HELM) is a long-term observing program that photometrically monitors several well-studied extragalactic legacy fields with the Dark Energy Camera (DECam) imager on the CTIO 4m Blanco telescope. Since Feb 2019, HELM has been monitoring regions within COSMOS, XMM-LSS, CDF-S, S-CVZ, ELAIS-S1, and SDSS Stripe 82 with few-day cadences in the $(u)gri(z)$ bands, over a collective sky area of $\sim 38$ deg${\rm ^2}$. The main science goal of HELM is to provide high-quality optical light curves for a large sample of active galactic nuclei (AGNs), and to build decades-long time baselines when combining past and future optical light curves in these legacy fields. These optical images and light curves will facilitate the measurements of AGN reverberation mapping lags, as well as studies of AGN variability and its dependences on accretion properties. In addition, the time-resolved and coadded DECam photometry will enable a broad range of science applications from galaxy evolution to time-domain science. We describe the design and implementation of the program and present the first data release that includes source catalogs and the first $\sim 3.5$ years of light curves during 2019A--2022A., Comment: 11 pages, 8 figures, 4 tables, submitted to ApJS. Median source catalogs and light curves of individual objects are publicly available at https://ariel.astro.illinois.edu/helm/

The gravitationally lensed quasar J014516.6-094517 at z=2.719 has been observed with the ESPRESSO instrument at the ESO VLT to obtain high-fidelity spectra of the two images A and B with a resolving power R=70000. At the redshifts under investigation (2.1 < z < 2.7), the Lyman forests along the two sightlines are separated by sub-kiloparsec physical distances and exhibit a strong correlation. We find that the two forests are indistinguishable at the present level of signal-to-noise ratio and do not show any global velocity shift, with the cross-correlation peaking at $\Delta v = 12 \pm 48$ m/s. The distribution of the difference in velocity of individual Lyman-$\alpha$ features is compatible with a null average and a mean absolute deviation of 930 m/s. Significant differences in NHI column density are not detected, putting a limit to the RMS fluctuation in the baryon density on $\leq 1$ proper kpc scales of $\Delta \rho / \rho < 3$%. On the other hand, metal lines show significant differences both in velocity structure and in column density. A toy model shows that the difference in velocity of the metal features between the two sightlines is compatible with the the motions of the baryonic component associated to dark matter halos of typical mass $M\simeq 2\times 10^{10} M_\odot$, also compatible with the observed incidence of the metal systems. The present observations confirm the feasibility of the Sandage test of the cosmic redshift drift with high-fidelity spectroscopy of the Lyman forest of distant, bright quasars, but also provide an element of caution about the intrinsic noise associated to the usage of metal features for the same purpose., Comment: 17 pages, 10 figures, 5 tables, accepted for publication in MNRAS

In this paper we define a new auction, called the Draw auction. It is based on the implementation of a draw when a minimum price of sale is not reached. We find that a Bayesian Nash equilibrium is reached in the Draw auction when each player bids his true personal valuation of the object. Furthermore, we show that the expected profit for the seller in the Draw auction is greater than in second price auctions, with or without minimum price of sale. We make this affirmation for objects whose valuation can be modeled as a bimodal density function in which the first mode is much greater than the second one. Regarding the Myerson auction, we show that the expected profit for the seller in the Draw auction is nearly as good as the expected profit in the optimal auction, with the difference that our method is much more simple to implement than Myerson's one. All these results are shown by computational tests, for whose development we have defined an algorithm to calculate Myerson auction., Comment: 37 pages, 5 figures, 5 tables

In this paper we introduce the concept of multiple bipolar fuzzy measures as a generalization of a bipolar fuzzy measure. We also propose a new definition of a group, which is based on the multidimensional bipolar fuzzy relations of its elements. Taking into account this information, we provide a novel procedure (based on the well-known Louvain algorithm) to deal with community detection problems. This new method considers the multidimensional bipolar information provided by multiple bipolar fuzzy measures, as well as the information provided by a graph. We also give some detailed computational tests, obtained from the application of this algorithm in several benchmark models., Comment: 14 pages

On the basis of network analysis, and within the context of modeling imprecision or vague information with fuzzy sets, we propose an innovative way to analyze, aggregate and apply this uncertain knowledge into community detection of real-life problems. This work is set on the existence of one (or multiple) soft information sources, independent of the network considered, assuming this extra knowledge is modeled by a vector of fuzzy sets (or a family of vectors). This information may represent, for example, how much some people agree with a specific law, or their position against several politicians. We emphasize the importance of being able to manage the vagueness which usually appears in real life because of the common use of linguistic terms. Then, we propose a constructive method to build fuzzy measures from fuzzy sets. These measures are the basis of a new representation model which combines the information of a network with that of fuzzy sets, specifically when it comes to linguistic terms. We propose a specific application of that model in terms of finding communities in a network with additional soft information. To do so, we propose an efficient algorithm and measure its performance by means of a benchmarking process, obtaining high-quality results., Comment: 22 pages

In this paper we address the problem of fuzzy measures index calculation. On the basis of fuzzy sets, Murofushi and Soneda proposed an interaction index to deal with the relations between two individuals. This index was later extended in a common frame-work by Grabisch. Both indices are fundamental in the literature of fuzzy measures. Nevertheless, the corresponding calculation still presents a highly complex problem for which no approximation solution has been proposed yet. Then, using a representation of the Shapley based on orders, here we suggest an alternative calculation of the interaction index, both for the simple case of pairs of individuals, and for the more complex situation in which any set could be considered. This alternative representation facilitates the handling of these indices. Moreover, we draw on this representation to define two polynomial methods based on sampling to estimate the interaction index, as well as a method to approximate the generalized version of it. We provide some computational results to test the goodness of the proposed algorithms., Comment: 17 pages

In this paper, by applying the multiplier method we obtain a complete classification of low-order local conservation laws for a generalized seventh-order KdV equation depending on seven arbitrary nonzero parameters. We apply the Lie method in order to classify all point symmetries admitted by the equation in terms of the arbitrary parameters. We find that there are no special cases of the parameters for which the equation admits extra symmetries, other than those that can be found by inspection (scaling symmetry and space and time translation symmetries). We consider the reduced ordinary differential equations and we determined all integrating factors of the reduced equation from the combined $x$- and $t$- translation symmetries. Finally, we observe that all integrating factors arise by reduction of the low-order multipliers of the generalized seventh-order KdV equation., Comment: 12 pages

In this paper, we address one of the most important topics in the field of Social Networks Analysis: the community detection problem with additional information. That additional information is modeled by a fuzzy measure that represents the risk of polarization. Particularly, we are interested in dealing with the problem of taking into account the polarization of nodes in the community detection problem. Adding this type of information to the community detection problem makes it more realistic, as a community is more likely to be defined if the corresponding elements are willing to maintain a peaceful dialogue. The polarization capacity is modeled by a fuzzy measure based on the JDJpol measure of polarization related to two poles. We also present an efficient algorithm for finding groups whose elements are no polarized. Hereafter, we work in a real case. It is a network obtained from Twitter, concerning the political position against the Spanish government taken by several influential users. We analyze how the partitions obtained change when some additional information related to how polarized that society is, is added to the problem., Comment: 27 pages

In this paper we consider a generalized Kuramoto-Sivashinsky equation. The equivalence group of the class under consideration has been constructed. This group allows us to perform a comprehensive study and a clear and concise formulation of the results. We have constructed the optimal system of subalgebras of the projections of the equivalence algebra on the space formed by the dependent variable and the arbitrary functions. By using this optimal system, all nonequivalent equations admitting an extension by one of the principal Lie algebra of the class under consideration can be determined. Taking into account the additional symmetries obtained we reduce some partial differential equations belonging to the class into ordinary differential equations. We derive some exact solutions of these equations., Comment: 18 pages

We provide a complete classification of point symmetries and low-order local conservation laws of the generalized quasilinear KdV equation in terms of the arbitrary function. The corresponding interpretation of symmetry transformation groups are given. In addition, a physical description of the conserved quantities is included. Finally, few travelling wave solutions have been obtained., Comment: 14 pages

In this work we analyze the possibility of sudden cosmological singularities, also known as type-II singularities, in the background of a Friedmann-Lema\^itre-Robertson-Walker (FLRW) geometry in an extension of General Relativity (GR) known as Aether scalar-tensor theories (AeST). Similarly to several scalar-tensor theories, we observe that sudden singularities may occur in certain AeST models at the level of the second-order time derivative of the scale factor. These singularities can either be induced by AeST's scalar field itself in the absence of a fluid matter component, or by a divergence of the pressure component of the fluid. In the latter case, one observes that the second-order time derivative of the scalar field $Q$ is also divergent at the instant the sudden singularity happens. We show that the sudden singularities can be prevented by an appropriate choice of the action, for which a divergence in the scalar field compensates the divergence in the pressure component of the matter fluid, thus preserving the regularity of the scale factor and all its time derivatives. For the models featuring a sudden singularity in the second-order time derivative of the scale factor, an analysis of the cosmographic parameters, namely the Hubble and the deceleration parameters, indicates that cosmological models featuring sudden singularities are allowed by the current cosmological measurements. Furthermore, an analysis of the jerk parameter favours cosmological models that attain a sudden singularity at a faster rate, up to a time of at most $t_s\sim 1.2 t_0$, where $t_0$ is the current age of the universe, and with negative values for the cosmological snap parameter., Comment: 14 pages, 9 figures

Ionic liquids (ILs) are an extremely exciting class of electrolytes for energy storage applications because of their unique combination of properties. Upon dissolving alkali metal salts, such as Li or Na based salts, with the same anion as the IL, an intrinsically asymmetric electrolyte can be created for use in batteries, known as a salt-in-ionic liquid (SiIL). These SiILs have been well studied in the bulk, where negative transference numbers of the alkali metal cation have been observed from the formation of small, negatively charged clusters. The properties of these SiILs at electrified interfaces, however, have received little to no attention. Here, we develop a theory for the electrical double layer (EDL) of SiILs where we consistently account for the thermoreversible association of ions into Cayley tree aggregates. The theory predicts that the IL cations first populate the EDL at negative voltages, as they are not strongly bound to the anions. However at large negative voltages which are strong enough to break the alkali metal cation-anion associations, these IL cations are exchanged for the alkali metal cation because of their higher charge density. At positive voltages, we find that the SiIL actually becomes $\textit{more aggregated while screening the electrode charge}$ from the formation of large, negatively charged aggregates. Therefore, in contrast to conventional intuition of associations in the EDL, SiILs appear to become more associated in certain electric fields. We present these theoretical predictions to be verified by molecular dynamics simulations and experimental measurements.

We investigate the topological superconductor candidate UTe$_2$ using high-resolution valence-band resonant inelastic x-ray scattering at the U $M_{4,5}$-edges. We observe atomic-like low-energy excitations that support the correlated nature of this unconventional superconductor. These excitations originate from the U $5f^2$ configuration, which is unexpected since the short Te2-Te2 distances exclude Te2 being 2-. By utilizing the photoionization cross-section dependence of the photoemission spectra in combination with band structure calculations, we infer that the stabilization of the U $5f^2$ configuration is due to the U $6d$ bonding states in the U-dimers acting as a charge reservoir. Our results emphasize that the description of the physical properties should commence with a $5f^2$ $ansatz$., Comment: 9 pages, 5 figures, article

In this paper, a family of variable-coefficient fifth-order KdV equations has been considered. By using an infinitesimal method based on the determination of the equivalence group, differential invariants and invariant equations are obtained. Invariants provide an alternative way to find equations from the family which may be equivalent to a specific subclass of the same family and the invertible transformation which maps both equivalent equations. Here, differential invariants are applied to obtain exact solutions., Comment: 14 pages

In this work we study a generalized variable-coefficient Gardner equation from the point of view of Lie symmetries in partial differential equations. We find conservation laws by using the multipliers method of Anco and Bluman which does not require the use of a variational principle. We also construct conservation laws using Ibragimov theorem which is based on the concept of adjoint equation for nonlinear differential equations., Comment: 19 pages. arXiv admin note: text overlap with arXiv:2402.02601

Kinematically-persistent planes of satellites (KPPs) are fixed sets of satellites co-orbiting around their host galaxy, whose orbital poles are conserved and clustered across long cosmic time intervals. They play the role of 'skeletons', ensuring the long-term durability of positional planes. We explore the physical processes behind their formation in terms of the dynamics of the local Cosmic Web (CW), characterized via the so-called Lagrangian Volumes (LVs) built up around two zoom-in, cosmological hydro-simulations of MW-mass disk galaxy + satellites systems, where three KPPs have been identified. By analyzing the LVs deformations in terms of the reduced Tensor of Inertia (TOI), we find an outstanding alignment between the LV principal directions and KPP satellites' orbital poles. The most compressive local mass flows (along the $\hat{e}_3$ eigenvector) are strong at early times, feeding the so-called $\hat{e}_3$-structure, while the smallest TOI axis rapidly decreases. The $\hat{e}_3$-structure collapse marks the end of this regime and is the timescale for the establishment of satellite orbital pole clustering when the Universe is $\lesssim$ 4 Gyr old. KPP proto-satellites aligned with $\hat{e}_3$ are those whose orbital poles are either aligned from early times, or have been successfully bent at $\hat{e}_3$-structure collapse. KPP satellites associated to $\hat{e}_1$ tend to have early trajectories already parallel to $\hat{e}_3$. We show that KPPs can arise as a result of the $\Lambda$CDM-predicted large-scale dynamics acting on particular sets of proto-satellites, the same dynamics that shape the local CW environment., Comment: 27 pages, 12 figures, 2 tables. Accepted for publication in The Astrophysical Journal

A fifth-order KdV equation with time dependent coefficients and linear damping has been studied. Symmetry groups have several different applications in the context of nonlinear differential equations. For instance, they can be used to determine conservation laws. We obtain the symmetries of the model applying Lie's classical method. The choice of some arbitrary functions of the equation by the equivalence transformation enhances the study of Lie symmetries of the equation. We have determined the subclasses of the equation which are nonlinearly self-adjoint. This allow us to obtain conservation laws by using a theorem proved by Ibragimov which is based on the concept of adjoint equation for nonlinear differential equations., Comment: 13 pages

The present study examines the factor structure of a Portuguese version of the Perceived Vulnerability to Disease Scale (PVD), designed to assess individual differences in chronic concerns about transmission of infectious diseases. Method: Data from a Portuguese convenience sample (n=1203), collected during the first Covid-19 pandemic lockdown. Results: the scale revealed, through an exploratory factor analysis (EFA) and a confirmatory factor analysis (CFA), a slight superiority of a three-factor model over the existing two-factor models of the 15-item original PVD and of the 10-item PVD established with another Portuguese sample (Ferreira et al., 2022). Conclusions: This higher level of differentiation in terms of a perceived resistance to infectious diseases could be explained by the pandemic context which may have differentiated the responses regarding the perception of Resistance. On the other hand, this new factor increases the comprehensive and evaluative dimension and implications of the construct assessed by PVD., Comment: 25 pages, 3 figures, 4 tables

We present photometric and spectroscopic data sets for SN 2020pvb, a Type IIn-P supernova (SN) similar to SNe 1994W, 2005cl, 2009kn and 2011ht, with a precursor outburst detected (PS1 w-band ~ -13.8 mag) around four months before the B-band maximum light. SN 2020pvb presents a relatively bright light curve peaking at M_B = -17.95 +- 0.30 mag and a plateau lasting at least 40 days before it went in solar conjunction. After this, the object is no longer visible at phases > 150 days above -12.5 mag in the B-band, suggesting that the SN 2020pvb ejecta interacts with a dense spatially confined circumstellar envelope. SN 2020pvb shows in its spectra strong Balmer lines and a forest of FeII lines with narrow P Cygni profiles. Using archival images from the Hubble Space Telescope, we constrain the progenitor of SN 2020pvb to have a luminosity of log(L/L_sun) <= 5.4, ruling out any single star progenitor over 50 M_sun. All in all, SN 2020pvb is a Type IIn-P whose progenitor star had an outburst ~ 0.5 yr before the final explosion, the material lost during this outburst is probably playing a role in shaping the physical properties of the supernova., Comment: 14 pages + 10 appendix pages, 12 figures + 2 appendix figures, 8 appendix tables. Accepted for publication in A&A

In this paper we study the generalized variable-coefficient Gardner equations of the form $u_t + A(t)u^n\,u_x+ C(t)\,u^{2n}u_x + B(t)\,u_{xxx} + Q(t)\,u =0$. This class broadens out many other equations previously considered: Johnpillai and Khalique (2010), Molati and Ramollo (2012) and Vaneeva, Kuriksha and Sophocleous (2015). Equivalence group of the class under consideration has been constructed which permit an exhaustive study and a simple and clear formulation of the results. Some conservation laws are derived for the nonlinearly self-adjoint equations, based on differential substitutions, and by using the direct method of the multipliers., Comment: 16 pages

We report on X-ray polarization measurements of the extra-galactic Crab-like PSR B0540-69 and its Pulsar Wind Nebula (PWN) in the Large Magellanic Cloud (LMC), using a ~850 ks Imaging X-ray Polarimetry Explorer (IXPE) exposure. The PWN is unresolved by IXPE. No statistically significant polarization is detected for the image-averaged data, giving a 99% confidence polarization upper limit (MDP99) of 5.3% in 2-8 keV energy range. However, a phase-resolved analysis detects polarization for both the nebula and pulsar in the 4-6 keV energy range. For the PWN defined as the off-pulse phases, the polarization degree (PD) of (24.5 ${\pm}$ 5.3)% and polarization angle (PA) of (78.1 ${\pm}$ 6.2){\deg} is detected at 4.6${\sigma}$ significance level, consistent with the PA observed in the optical band. In a single on-pulse window, a hint of polarization is measured at 3.8${\sigma}$ with polarization degree of (50.0 ${\pm}$ 13.1)% and polarization angle of (6.2 ${\pm}$ 7.4){\deg}. A 'simultaneous' PSR/PWN analysis finds two bins at the edges of the pulse exceeding 3${\sigma}$ PD significance, with PD of (68 ${\pm}$ 20)% and (62 ${\pm}$ 20)%; intervening bins at 2-3${\sigma}$ significance have lower PD, hinting at additional polarization structure., Comment: 10 pages, 7 figures, 4 tables, author's version of the paper accepted for publication in ApJ

This article introduces NB-Whisper, an adaptation of OpenAI's Whisper, specifically fine-tuned for Norwegian language Automatic Speech Recognition (ASR). We highlight its key contributions and summarise the results achieved in converting spoken Norwegian into written forms and translating other languages into Norwegian. We show that we are able to improve the Norwegian Bokm{\aa}l transcription by OpenAI Whisper Large-v3 from a WER of 10.4 to 6.6 on the Fleurs Dataset and from 6.8 to 2.2 on the NST dataset.

Silicon is a material whose technological application is well established, and obtaining this material in nanostructured form increases its possibility of integration in current technology. Silicene is a natural compatibility with current silicon-based electronics industry. Furthermore, doping is a technique that can be often used to adjust the band gap of silicene and at the same time introduce new functions. Here we investigate Several aspects of silicene doping with chromium, such as dopant solubility limits, site preference for adsorption and doping, and formation of magnetic domains. In this work we carried out investigation on diffusion and doping of chromium atoms on silicene. We use density-functional theory to identify the electronic and magnetic properties of tchromium atoms on monolayer and bilayer silicene. We find that magnetization depends on key parameters such as buckling, interlayer distance and adsorption site.