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In this paper, we study the analytic classification of a class of nilpotent singularities of holomorphic foliations in $(\mathbb{C}^2,0)$, those exhibiting a Poincar\'e-Dulac type singularity in their reduction process. This analytic classification is based in the holonomy of a certain component of the exceptional divisor. Finally, as a consequence, we show that these singularities exhibit a formal analytic rigidity., Comment: 15 pages

The recent discoveries of Neptune-sized ultra-short period planets (USPs) challenge existing planet formation theories. It is unclear whether these residents of the Hot Neptune Desert have similar origins to smaller, rocky USPs, or if this discrete population is evidence of a different formation pathway altogether. We report the discovery of TOI-3261b, an ultra-hot Neptune with an orbital period $P$ = 0.88 days. The host star is a $V = 13.2$ magnitude, slightly super-solar metallicity ([Fe/H] $\simeq$ 0.15), inactive K1.5 main sequence star at $d = 300$ pc. Using data from the Transiting Exoplanet Survey Satellite and the Las Cumbres Observatory Global Telescope, we find that TOI-3261b has a radius of $3.82_{-0.35}^{+0.42}$ $R_{\oplus}$. Moreover, radial velocities from ESPRESSO and HARPS reveal a mass of $30.3_{-2.4}^{+2.2}$ $M_{\oplus}$, more than twice the median mass of Neptune-sized planets on longer orbits. We investigate multiple mechanisms of mass loss that can reproduce the current-day properties of TOI-3261b, simulating the evolution of the planet via tidal stripping and photoevaporation. Thermal evolution models suggest that TOI-3261b should retain an envelope potentially enriched with volatiles constituting $\sim$5% of its total mass. This is the second highest envelope mass fraction among ultra-hot Neptunes discovered to date, making TOI-3261b an ideal candidate for atmospheric follow-up observations., Comment: 20 pages, 11 figures, accepted to AJ

We report the discovery of two transiting planets detected by the Transiting Exoplanet Survey Satellite (TESS), TOI-2374 b and TOI-3071 b, orbiting a K5V and an F8V star, respectively, with periods of 4.31 and 1.27 days, respectively. We confirm and characterize these two planets with a variety of ground-based and follow-up observations, including photometry, precise radial velocity monitoring and high-resolution imaging. The planetary and orbital parameters were derived from a joint analysis of the radial velocities and photometric data. We found that the two planets have masses of $(57 \pm 4)$ $M_\oplus$ or $(0.18 \pm 0.01)$ $M_J$, and $(68 \pm 4)$ $M_\oplus$ or $(0.21 \pm 0.01)$ $M_J$, respectively, and they have radii of $(6.8 \pm 0.3)$ $R_\oplus$ or $(0.61 \pm 0.03)$ $R_J$ and $(7.2 \pm 0.5)$ $R_\oplus$ or $(0.64 \pm 0.05)$ $R_J$, respectively. These parameters correspond to sub-Saturns within the Neptunian desert, both planets being hot and highly irradiated, with $T_{\rm eq} \approx 745$ $K$ and $T_{\rm eq} \approx 1812$ $K$, respectively, assuming a Bond albedo of 0.5. TOI-3071 b has the hottest equilibrium temperature of all known planets with masses between $10$ and $300$ $M_\oplus$ and radii less than $1.5$ $R_J$. By applying gas giant evolution models we found that both planets, especially TOI-3071 b, are very metal-rich. This challenges standard formation models which generally predict lower heavy-element masses for planets with similar characteristics. We studied the evolution of the planets' atmospheres under photoevaporation and concluded that both are stable against evaporation due to their large masses and likely high metallicities in their gaseous envelopes., Comment: 24 pages, 22 figures, 10 tables, accepted for publication in MNRAS

We present a detailed study of the Bardeen-Cooper-Schrieffer (BCS) gap equation ``replicae'' or excited vacuum states, orthogonal to the ground-state one, in the chiral-quark sector of the Hamiltonian Coulomb-gauge model of chromodynamics. Analyzing the number of negative eigenmodes of the energy density's Hessian we believe that we have identified all of the (negative energy-density) vacua of this nonlinear system, namely the ground BCS state and two (or one) replicae for slightly massive (or massless) quarks, given the interaction strength typical of the strong interactions. The meson spectrum over each of the replicae looks similar, so the differences are not significant enough given model uncertainties, but matrix elements are more sensitive and allow to distinguish them. We propose to look for such excited vacua in lattice gauge theory by trying to identify excitations with scalar quantum numbers which have energies proportional to the lattice volume (unlike conventional mesons for which the mass stabilizes to a constant upon taking the infinite volume limit)., Comment: 10 pages, 26 plots

One of the leading mechanisms invoked to explain the existence of the radius valley is atmospheric mass loss driven by X-ray and extreme-ultraviolet irradiation, with this process stripping the primordial envelopes of young, small planets to produce the observed bimodal distribution. We present an investigation into the TOI-431 and $\nu^2$ Lupi planetary systems, both of which host planets either side of the radius valley, to determine if their architectures are consistent with evolution by the XUV mechanism. With $\textit{XMM-Newton}$, we measure the current X-ray flux of each star, and see evidence for a stellar flare in the TOI-431 observations. We then simulate the evolution of all of the transiting planets across the two systems in response to the high-energy irradiation over their lifetimes. We use the measured X-ray fluxes as an anchor point for the XUV time evolution in our simulations, and employ several different models of estimating mass loss rates. While the simulations for TOI-431b encountered a problem with the initial calculated radii, we estimate a likely short ($\sim$ Myr) timespan for primordial envelope removal using reasonable assumptions for the initial planet. $\nu^2$ Lupi b is likely harder to strip, but is achieved in a moderate fraction of our simulations. None of our simulations stripped any of the lower density planets of their envelope, in line with prediction. We conclude that both systems are consistent with expectations for generation of the radius valley through XUV photoevaporation., Comment: 14 pages, 12 figures, 5 tables; accepted for publication in MNRAS

The paper introduces Hands-Free VR, a voice-based natural-language interface for VR. The user gives a command using their voice, the speech audio data is converted to text using a speech-to-text deep learning model that is fine-tuned for robustness to word phonetic similarity and to spoken English accents, and the text is mapped to an executable VR command using a large language model that is robust to natural language diversity. Hands-Free VR was evaluated in a controlled within-subjects study (N = 22) that asked participants to find specific objects and to place them in various configurations. In the control condition participants used a conventional VR user interface to grab, carry, and position the objects using the handheld controllers. In the experimental condition participants used Hands-Free VR. The results confirm that: (1) Hands-Free VR is robust to spoken English accents, as for 20 of our participants English was not their first language, and to word phonetic similarity, correctly transcribing the voice command 96.71% of the time; (2) Hands-Free VR is robust to natural language diversity, correctly mapping the transcribed command to an executable command in 97.83% of the time; (3) Hands-Free VR had a significant efficiency advantage over the conventional VR interface in terms of task completion time, total viewpoint translation, total view direction rotation, and total left and right hand translations; (4) Hands-Free VR received high user preference ratings in terms of ease of use, intuitiveness, ergonomics, reliability, and desirability.

The Neptunian desert is a region in period-radius parameter space with very few Neptune-sized planets at short orbital periods. Amongst these, LTT 9779 b is the only known Neptune with a period shorter than one day to retain a significant H-He atmosphere. If the Neptune desert is the result of X-ray/EUV-driven photoevaporation, it is surprising that the atmosphere of LTT 9779 b survived the intense bombardment of high energy photons from its young host star. However, the star has low measured rotational broadening, which points to the possibility of an anomalously slow spin period and hence a faint X-ray emission history that may have failed to evaporate the planet's atmosphere. We observed LTT 9779 with XMM-Newton and measured an upper limit for its X-ray luminosity that is a factor of fifteen lower than expected for its age. We also simulated the evaporation past of LTT 9779 b and found that the survival of its atmosphere to the present day is consistent with an unusually faint XUV irradiation history that matches both the X-ray and rotation velocity measurements. We conclude that the anomalously low X-ray irradiation of the one Neptune seen to survive in Neptunian desert supports the interpretation of the desert as primarily a result of photoevaporation., Comment: 8 pages, 4 figures. Accepted to MNRAS

To date, thousands of planets have been discovered, but there are regions of the orbital parameter space that are still bare. An example is the short period and intermediate mass/radius space known as the Neptunian desert, where planets should be easy to find but discoveries remain few. This suggests unusual formation and evolution processes are responsible for the planets residing here. We present the discovery of TOI-332 b, a planet with an ultra-short period of $0.78$ d that sits firmly within the desert. It orbits a K0 dwarf with an effective temperature of $5251 \pm 71$ K. TOI-332 b has a radius of $3.20^{+0.16}_{-0.12}$ R$_{\oplus}$, smaller than that of Neptune, but an unusually large mass of $57.2 \pm 1.6$ M$_{\oplus}$. It has one of the highest densities of any Neptune-sized planet discovered thus far at $9.6^{+1.1}_{-1.3}$ gcm$^{-3}$. A 4-layer internal structure model indicates it likely has a negligible hydrogen-helium envelope, something only found for a small handful of planets this massive, and so TOI-332 b presents an interesting challenge to planetary formation theories. We find that photoevaporation cannot account for the mass loss required to strip this planet of the Jupiter-like envelope it would have been expected to accrete. We need to look towards other scenarios, such as high-eccentricity migration, giant impacts, or gap opening in the protoplanetary disc, to try and explain this unusual discovery., Comment: 20 pages, 14 figures, 6 tables, accepted for publication in MNRAS

We present the discovery of an exoplanet transiting TOI-908 (TIC-350153977) using data from TESS sectors 1, 12, 13, 27, 28 and 39. TOI-908 is a T = 10.7 mag G-dwarf ($T_{eff}$ = 5626 $\pm$ 61 K) solar-like star with a mass of 0.950 $\pm$ 0.010 $M_{\odot}$ and a radius of 1.028 $\pm$ 0.030 $R_{\odot}$. The planet, TOI-908 b, is a 3.18 $\pm$ 0.16 $R_{\oplus}$ planet in a 3.18 day orbit. Radial velocity measurements from HARPS reveal TOI-908 b has a mass of approximately 16.1 $\pm$ 4.1 $M_{\oplus}$ , resulting in a bulk planetary density of 2.7+0.2-0.4 g cm-3. TOI-908 b lies in a sparsely-populated region of parameter space known as the Neptune desert. The planet likely began its life as a sub-Saturn planet before it experienced significant photoevaporation due to X-rays and extreme ultraviolet radiation from its host star, and is likely to continue evaporating, losing a significant fraction of its residual envelope mass., Comment: 17 pages, 17 figures

This paper is a contribution to the study of foliations on $\mathbb{CP}^2$ with a unique singularity. We provide an explicit example in degree 7 of such a foliation, in the non dicritical case, having a divergent separatrix, and subsequently, we study different families of such foliations in low degree., Comment: 22 pages

We present the discovery and confirmation of a transiting hot, bloated Super-Neptune using photometry from TESS and LCOGT and radial velocity measurements from HARPS. The host star TOI-2498 is a V = 11.2, G-type (T$_{eff}$ = 5905 $\pm$ 12K) solar-like star with a mass of 1.12 $\pm$ 0.02 M$_{\odot}$ and a radius of 1.26 $\pm$ 0.04 R$_{\odot}$. The planet, TOI-2498 b, orbits the star with a period of 3.7 days, has a radius of 6.1 $\pm$ 0.3 R$_{\oplus}$, and a mass of 35 $\pm$ 4 M$_{\oplus}$. This results in a density of 0.86 $\pm$ 0.25 g cm$^{-3}$. TOI-2498 b resides on the edge of the Neptune desert; a region of mass-period parameter space in which there appears to be a dearth of planets. Therefore TOI-2498 b is an interesting case to study to further understand the origins and boundaries of the Neptune desert. Through modelling the evaporation history, we determine that over its $\sim$3.6 Gyr lifespan, TOI-2498 b has likely reduced from a Saturn sized planet to its current radius through photoevaporation. Moreover, TOI-2498 b is a potential candidate for future atmospheric studies searching for species like water or sodium in the optical using high-resolution, and for carbon based molecules in the infra-red using JWST., Comment: 13 pages, 11 figures, accepted for publication in MNRAS

We model the evaporation histories of the three planets around K2-136, a K-dwarf in the Hyades open cluster with an age of 700 Myr. The star hosts three transiting planets, with radii of 1.0, 3.0 and 1.5 Earth radii, where the middle planet lies above the radius-period valley and the inner and outer planets are below. We use an XMM-Newton observation to measure the XUV radiation environment of the planets, finding that the X-ray activity of K2-136 is lower than predicted by models but typical of similar Hyades members. We estimate the internal structure of each planet, and model their evaporation histories using a range of structure and atmospheric escape formulations. While the precise X-ray irradiation history of the system may be uncertain, we exploit the fact that the three planets must have shared the same history. We find that the Earth-sized K2-136b is most likely rocky, with any primordial gaseous envelope being lost within a few Myr. The sub-Neptune, K2-136c, has an envelope contributing 1-1.7% of its mass that is stable against evaporation thanks to the high mass of its rocky core, whilst the super-Earth, K2-136d, must have a mass at the upper end of the allowed range in order to retain any of its envelope. Our results are consistent with all three planets beginning as sub-Neptunes that have since been sculpted by atmospheric evaporation to their current states, stripping the envelope from planet b and removing most from planet d whilst preserving planet c above the radius-period valley., Comment: Accepted for publication on MNRAS

Voltage phase angle measurements are often unavailable from sensors in distribution networks and transmission network boundaries. Therefore, this paper addresses the conditions for estimating sensitivities of voltage magnitudes with respect to complex (active and reactive) electric power injections based on sensor measurements. These sensitivities represent submatrices of the inverse power flow Jacobian. We extend previous results to show that the sensitivities of a bus voltage magnitude with respect to active power injections are unique and different from those with respect to reactive power. The classical Newton-Raphson power flow model is used to derive a novel representation of bus voltage magnitudes as an underdetermined linear operator of the active and reactive power injections; parameterized by the bus power factors. Two conditions that ensure the existence of unique complex power injections given voltage magnitudes are established for this underdetermined linear system, thereby compressing the solution space. The first is a sufficient condition based on the bus power factors. The second is a necessary and sufficient condition based on the system eigenvalues. We use matrix completion theory to develop estimation methods for recovering sensitivity matrices with varying levels of sensor availability. Simulations verify the results and demonstrate engineering use of the proposed methods., Comment: 14 pages, 10 figures. Code corresponding to this work is publicly available at https://github.com/samtalki/PowerSensitivities.jl

We study the X-ray irradiation and likely photoevaporation of the three planets around the star K2-136. These are the Earth-sized K2-136 b, the mini-Neptune K2-136 c, and the super-Earth K2-136 d. XMM-Newton observations of the star indicate an X-ray luminosity of $(1.18\pm0.1)\times10^{28}$ erg s$^{-1}$ in the range 0.15 to 2.4 keV, resulting in an activity of $L_X/L_{\rm bol}=(1.80\pm0.68)\times10^{-5}$. The evaporation past of the planets were modelled using the XUV stellar tracks by Johnstone et al. (2021), the energy limited mass loss formulation (Lecavelier des Etangs et al. 2007, Erkaev et al. 2007), and the thermal evolution formulation by Lopez & Fortney (2014). Our results suggest that planets b and d are most probably purely rocky and have been stripped of their envelopes. On the other hand, planet c likely still has an envelope consisting of 0.8% of the total mass, with its core being relatively large (2.3 $R_{\rm E}$)., Comment: This paper has been submitted as a proceedings article to Astronomische Nachrichten (AN) as part of the XMM-Newton 2021 Science Workshop

Dynamical symmetry breaking can happen through a Higgs mechanism but also spontaneously within a strongly-enough coupled theory. We treat a field-theoretical quark model of QCD based on a linear+Coulomb Cornell potential (to account for the longitudinal interaction), together with a transverse interaction (to account for Coulomb-gauge gluons) in BCS approximation. After extracting the well-known BCS ground state on which abundant hadron phenomenology implementing dynamical chiral symmetry breaking has been built, we find two excited replica vacuumlike states shown in figure 1. At the BCS level they are classically unstable, but second quantization blocks transitions between them in volumes much larger than a hadron size. Mesons built over the replica vacua have relative masses similar to normal mesons on the ordinary vacuum; we find no negative-mass mode, confirming their stability found earlier with a harmonic oscillator potential., Comment: 4 pages, 4 plots, proceedings of EPS-HEP21

The emergence of SARS-CoV-2 variants of concern endangers the long-term control of COVID-19, especially in countries with limited genomic surveillance. In this work, we explored genomic drivers of contagion in Chile. We sequenced 3443 SARS-CoV-2 genomes collected between January and July 2021, where the Gamma (P.1), Lambda (C.37), Alpha (B.1.1.7), B.1.1.348, and B.1.1 lineages were predominant. Using a Bayesian model tailored for limited genomic surveillance, we found that Lambda and Gamma variants' reproduction numbers were about 5% and 16% larger than Alpha's, respectively. We observed an overabundance of mutations in the Spike gene, strongly correlated with the variant's transmissibility. Furthermore, the variants' mutational signatures featured a breakpoint concurrent with the beginning of vaccination (mostly CoronaVac, an inactivated virus vaccine), indicating an additional putative selective pressure. Thus, our work provides a reliable method for quantifying novel variants' transmissibility under subsampling (as newly-reported Delta, B.1.617.2) and highlights the importance of continuous genomic surveillance.

In this paper we show that if an entire function $f(z_1,z_2)$ of two (or more) complex variables verifies $\norm{f(z_1,z_2)}\leq K(\norm{P(z_1,z_2)})$, where $P(z_1,z_2)$ is a polynomial that is not a power in $\CC[[z_1,z_2]]$, and $K$ is any positive-valued real function, then $f(z_1,z_2)$ can be written as a holomorphic function of $P$.

The goal of this article is to establish tauberian theorems for the $k$--summability processes defined by germs of analytic functions in several complex variables. The proofs are based on the tauberian theorems for $k$--summability in one variable and in monomials, and a method of monomialization of germs of analytic functions., Comment: 20 pages