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The steepest-entropy-ascent quantum thermodynamics (SEAQT) framework is employed to describe the adsorption process of arsenic (V) onto graphene oxide both in and out of equilibrium. The steepest-entropy-ascent principle is used to derive a non-equilibrium equation of motion applicable to a system composed of five species: water, arsenic, two functional groups of graphene oxide, and hydrogen ions. The equation of motion is solved using the system's energy eigenstructure. This eigenstructure is constructed with the Replica-Exchange Wang-Landau algorithm and used to train an artificial neural network that predicts the energy eigenstructure for dilute arsenic concentrations in the range of groundwater contamination. For a specified initial pH and specified initial concentrations of Ar and graphene oxide, the framework predicts arsenic adsorption capacity and the stable equilibrium arsenic concentration. Equilibrium results match well with equilibrium experimental data, demonstrating the efficacy of this framework for describing the adsorption process. Finally, the model is used to predict non-equilibrium adsorption behavior and the influence of solution pH upon arsenic removal efficiency., Comment: 17 pages, 13 figures

This work outlines the foundations for being able to do a first-principle study of the adsorption process using the steepest-entropy-ascent quantum thermodynamic (SEAQT) framework, a framework able to predict the unique non-equilibrium path taken by a system from some initial state to stable equilibrium. To account for the process of multi-component adsorption, the SEAQT framework incorporates the particle number operator for each absorbed species directly into its equation of motion. The theoretical models developed are validated via some initial comparisons with experimental data found in the literature, demonstrating good agreement. The findings reveal that this framework can be an effective tool for describing the adsorption process out of equilibrium. It is able to do so without $a \; priori$ knowledge of the specific adsorption mechanism(s) involved. It also aligns well with the anticipated predictions of equilibrium models. In addition, within this framework, all intensive thermodynamic properties are characterized by out-of-equilibrium fluctuations, highlighting the significance of non-equilibrium thermodynamics in predicting measurable physical quantities., Comment: 13 pages, 3 figures

We present indirect constraints on the absolute escape fraction of ionizing photons ($f_{\rm esc}^{\rm LyC}$) of the system GN 42912 which comprises two luminous galaxies ($M_{\rm UV}$ magnitudes of -20.89 and -20.37) at $z\sim7.5$, GN 42912-NE and GN 42912-SW, to determine their contribution to the ionizing photon budget of the Epoch of Reionization (EoR). The high-resolution James Webb Space Telescope NIRSpec and NIRCam observations reveal the two galaxies are separated by only ~0.1$"$ (0.5 kpc) on the sky and have a 358 km s$^{-1}$ velocity separation. GN 42912-NE and GN 42912-SW are relatively massive for this redshift (log($M_\ast/M_\odot$) $\sim$ 8.4 and 8.9, respectively), with gas-phase metallicities of 18 per cent and 23 per cent solar, O$_{32}$ ratios of 5.3 and $>5.8$, and $\beta$ slopes of $-1.92$ and $-1.51$, respectively. We use the Mg II$\lambda\lambda$2796,2803 doublet to constrain $f_{\rm esc}^{\rm LyC}$. Mg II has an ionization potential close to that of neutral hydrogen and, in the optically thin regime, can be used as an indirect tracer of the LyC leakage. We establish realistic conservative upper limits on $f_{\rm esc}^{\rm LyC}$ of 8.5 per cent for GN 42912-NE and 14 per cent for GN 42912-SW. These estimates align with $f_{\rm esc}^{\rm LyC}$ trends observed with $\beta$, O$_{32}$, and the H$\beta$ equivalent width at $z<4$. The small inferred ionized region sizes ($<0.3$ pMpc) around both galaxies indicate they have not ionized a significant fraction of the surrounding neutral gas. While these $z>7$ $f_{\rm esc}^{\rm LyC}$ constraints do not decisively determine a specific reionization model, they support a minor contribution from these two relatively luminous galaxies to the EoR., Comment: 18 pages, submitted to MNRAS

One of the fundamental questions of cosmology is the origin and mechanism(s) responsible for the reionization of the Universe beyond $z\sim6$. To address this question, many studies over the past decade have focused on local ($z\sim0.3$) galaxies which leak ionizing radiation (Lyman continuum or LyC). However, line-of-sight effects and data quality have prohibited deeper insight into the nature of LyC escape. To circumvent these limitations, we analyze stacks of a consolidated sample of {\it HST}/COS observations of the LyC in 89 galaxies at $z\sim0.3$. From fitting of the continuum, we obtain information about the underlying stellar populations and neutral ISM geometry. We find that most LyC non-detections are not leaking appreciable LyC ($f_{esc}^{\rm LyC}<1$\%) but also that exceptional cases point to spatial variations in the LyC escape fraction $f_{esc}^{\rm LyC}$. Stellar populations younger than 3 Myr lead to an increase in ionizing feedback, which in turn increases the isotropy of LyC escape. Moreover, mechanical feedback from supernovae in 8-10 Myr stellar populations is important for anisotropic gas distributions needed for LyC escape. While mechanical feedback is necessary for any LyC escape, high $f_{esc}^{\rm LyC}$ ($>5$\%) also requires a confluence of young stars and ionizing feedback. A two-stage burst of star formation could facilitate this optimal LyC escape scenario., Comment: Submitted to AAS publications, 42 pages, 25 figures

Feedback is widely recognized as an essential condition for Lyman continuum (LyC) escape in star-forming galaxies. However, the mechanisms by which galactic outflows clear neutral gas and dust remain unclear. In this paper, we model the Mg II 2796\r{A}, 2804\r{A} absorption + emission lines in 29 galaxies taken from the Low-z LyC Survey (LzLCS) to investigate the impact of (radiation + mechanical) feedback on LyC escape. Using constraints on Mg$^+$ and photoionization models, we map the outflows' neutral hydrogen content and predict $f_{esc}^{LyC}$ with a multiphase wind model. We measure mass, momentum, and energy loading factors for the neutral winds, which carry up to 10% of the momentum and 1% of the energy in SFR-based deposition rates. We use SED template fitting to determine the relative ages of stellar populations, allowing us to identify radiation feedback dominant systems. We then examine feedback related properties (stellar age, loading factors, etc.) under conditions that optimize feedback efficiency, specifically high star formation rate surface density and compact UV half-light radii. Our findings indicate that the strongest leakers are radiation feedback dominant, lack Mg II outflows, but have extended broad components in higher ionization lines like [O III] 5007\r{A}, as observed by Amor\'in et al. (2024). In contrast, galaxies experiencing supernovae feedback typically exhibit weaker $f_{esc}^{LyC}$ and show evidence of outflows in both Mg II and higher ionization lines. We attribute these findings to rapid or "catastrophic" cooling in the radiation-dominant systems, which, given the low metallicities in our sample, are likely experiencing delayed supernovae., Comment: 34 pages, 16 figures, 7 tables

In \cite{Ha86} Harer explicitly constructed a spine for the decorated Teichm\"uller space of orientable surfaces with at least one puncture and negative Euler characteristic. In this paper we point out some instances where his computation of the dimension of this spine is off by $1$ and give the correct dimension., Comment: 10 pages, 4 figures

In this paper we consider a competitive weakly coupled elliptic system in which each species is attracted to a small region and repelled from its complement. In this setting, we establish the existence of infinitely many solutions and of a nonnegative least energy solution. We show that, as the regions of attraction shrink, least energy solutions of the system concentrate. We study this behavior and characterize their limit profile. In particular, we show that if each component of a least energy solution is attracted to a different region, then the components decouple in the limit, whereas if all the components are attracted to the same region, they remain coupled., Comment: Revised version. The assumption N\geq 3 is added in all the results

Transportation missions in aerospace are limited to the capability of each aerospace robot and the properties of the target transported object, such as mass, inertia, and grasping locations. We present a novel decentralized adaptive controller design for multiple robots that can be implemented in different kinds of aerospace robots. Our controller adapts to unknown objects in different gravity environments. We validate our method in an aerial scenario using multiple fully actuated hexarotors with grasping capabilities, and a space scenario using a group of space tugs. In both scenarios, the robots transport a payload cooperatively through desired three-dimensional trajectories. We show that our method can adapt to unexpected changes that include the loss of robots during the transportation mission., Comment: This paper has been accepted by DARS2024 Conference. The permission for the preprint version on Arxiv has been approved through the DARS2024 Committee and Springer Press

We study the existence and concentration of positive and nodal solutions to a Schr\"odinger equation in the presence of a shrinking self-focusing core of arbitrary shape. Via a suitable rescaling, the concentration gives rise to a limiting profile that solves a nonautonomous elliptic semilinear equation with a sharp sign change in the nonlinearity. We characterize the (radial or foliated Schwarz) symmetries and the (polynomial) decay of the least-energy positive and nodal limiting profiles., Comment: Revised version

The spin-exotic hybrid meson $\pi_{1}(1600)$ is predicted to have a large decay rate to the $\omega\pi\pi$ final state. Using 76.6~pb$^{-1}$ of data collected with the GlueX detector, we measure the cross sections for the reactions $\gamma p \to \omega \pi^+ \pi^- p$, $\gamma p \to \omega \pi^0 \pi^0 p$, and $\gamma p\to\omega\pi^-\pi^0\Delta^{++}$ in the range $E_\gamma =$ 8-10 GeV. Using isospin conservation, we set the first upper limits on the photoproduction cross sections of the $\pi^{0}_{1}(1600)$ and $\pi^{-}_{1}(1600)$. We combine these limits with lattice calculations of decay widths and find that photoproduction of $\eta'\pi$ is the most sensitive two-body system to search for the $\pi_1(1600)$., Comment: 6 pages, 3 figures plus supplemental materials

We measure the spin-density matrix elements (SDMEs) of the $\Delta^{++}(1232)$ in the photoproduction reaction $\gamma p \to \pi^-\Delta^{++}(1232)$ with the GlueX experiment in Hall D at Jefferson Lab. The measurement uses a linearly--polarized photon beam with energies from $8.2$ to $8.8$~GeV and the statistical precision of the SDMEs exceeds the previous measurement by three orders of magnitude for the momentum transfer squared region below $1.4$ GeV$^2$. The data are sensitive to the previously undetermined relative sign between couplings in existing Regge-exchange models. Linear combinations of the extracted SDMEs allow for a decomposition into natural and unnatural--exchange amplitudes. We find that the unnatural exchange plays an important role in the low momentum transfer region.

JWST is uncovering the properties of ever increasing numbers of galaxies at z>6, during the epoch of reionization. Connecting these observed populations to the process of reionization requires understanding how efficiently they produce Lyman continuum (LyC) photons and what fraction (fesc) of these photons escape into the intergalactic medium. By applying the Cox proportional hazards model, a survival analysis technique, to the Low-redshift Lyman Continuum Survey (LzLCS), we develop new, empirical, multivariate predictions for fesc. The models developed from the LzLCS reproduce the observed fesc for z~3 samples, which suggests that LyC emitters may share similar properties at low and high redshift. Our best-performing models for the z~3 galaxies include information about dust attenuation, ionization, and/or morphology. We then apply these models to z$\gtrsim$6 galaxies. For large photometric samples, we find a median predicted fesc=0.047-0.14. For smaller spectroscopic samples, which may include stronger emission line galaxies, we find that $\geq$33% of the galaxies have fesc >0.2, and we identify several candidate extreme leakers with fesc $\geq$0.5. The current samples show no strong trend between predicted fesc and UV magnitude, but limited spectroscopic information makes this result uncertain. Multivariate predictions can give significantly different results from single variable predictions, and the predicted fesc for high-redshift galaxies can differ significantly depending on whether star formation rate surface density or radius is used as a measure of galaxy morphology. We provide all parameters necessary to predict fesc for additional samples of high-redshift galaxies using these models., Comment: Accepted for publication in ApJ. 33 pages, 9 figures, 10 tables, plus appendix

To understand how galaxies reionized the universe, we must determine how the escape fraction of Lyman Continuum (LyC) photons (fesc) depends on galaxy properties. Using the z~0.3 Low-redshift Lyman Continuum Survey (LzLCS), we develop and analyze new multivariate predictors of fesc. These predictions use the Cox proportional hazards model, a survival analysis technique that incorporates both detections and upper limits. Our best model predicts the LzLCS fesc detections with a root-mean-square (RMS) scatter of 0.31 dex, better than single-variable correlations. According to ranking techniques, the most important predictors of fesc are the equivalent width (EW) of Lyman-series absorption lines and the UV dust attenuation, which track line-of-sight absorption due to HI and dust. The HI absorption EW is uniquely crucial for predicting fesc for the strongest LyC emitters, which show properties similar to weaker LyC emitters and whose high fesc may therefore result from favorable orientation. In the absence of HI information, star formation rate surface density ($\Sigma_{\rm SFR}$) and [O III]/[O II] ratio are the most predictive variables and highlight the connection between feedback and fesc. We generate a model suitable for z>6, which uses only the UV slope, $\Sigma_{\rm SFR}$, and [O III]/[O II]. We find that $\Sigma_{\rm SFR}$ is more important in predicting fesc at higher stellar masses, whereas [O III]/[O II] plays a greater role at lower masses. We also analyze predictions for other parameters, such as the ionizing-to-non ionizing flux ratio and Ly=alpha escape fraction. These multivariate models represent a promising tool for predicting fesc at high redshift., Comment: Accepted for publication in ApJ. 34 pages + appendix, 12 figures

This work presents an analysis of the evolution of perturbed Bell diagonal states using the equation of motion of steepest-entropy-ascent quantum thermodynamics (SEAQT), the Lindblad equation, and various measures of loss of entanglement. First, a brief derivation is presented showing that Bell diagonal states are stationary states that are not stable equilibrium states relative to the SEAQT equation of motion, highlighting the need for the development of perturbation methods to study the evolutions of nearby states. This contrasts with the Lindblad equation of motion for which only some of the Bell diagonal states are stationary. Next, two perturbation methods are presented. The first is a weighted-average method for perturbing bi-partite system states and the second is a general bi-partite method based on a set of unitary operations that are constrained to hold the system energy and system entropy constant. Sets of density operators are randomly generated with each method and the resulting time-varying characteristics of the system's entanglement are analyzed using the SEAQT and Lindblad frameworks. The findings reveal that the evolutions associated with the constrained perturbations accurately predict the loss of non-locality and align well with the measured concurrence. In addition, using the SEAQT framework, the deep connection between the thermodynamic states of the state evolution of the system and the loss of non-locality is quantitatively demonstrated., Comment: 15 Pages, 14 Figures

We establish the existence of a solution to a nonlinear competitive Schr\"odinger system whose scalar potential tends to a positive constant at infinity with an appropriate rate. This solution has the property that all components are invariant under the action of a group of linear isometries and each component is obtained from the previous one by composing it with some fixed linear isometry. We call it a pinwheel solution. We describe the asymptotic behavior of the least energy pinwheel solutions when the competing parameter tends to zero and to minus infinity. In the latter case the components are segregated and give rise to an optimal pinwheel partition for the Schr\"odinger equation, that is, a partition formed by invariant sets that are mutually isometric through a fixed isometry., Comment: 24 pages

We provide an explicit computation of the cohomology groups (with untwisted coefficients) of semidirect products of the form $\mathbb{Z}^n\rtimes \mathbb{Z}/m$ with $m$ free of squares, by means of formulas that only depend on $n$, $m$ and the action of $\mathbb{Z}/m$ on $\mathbb{Z}^n$. We want to highlight the fact that we are not impossing any conditions on the $\mathbb{Z}/m$-action on $\mathbb{Z}^n$, and as far as we know our formulas are the first in the literature in this generality. This generalizes previous computations of L\"uck-Davis and Adem-Ge-Pan-Petrosyan. In order to show that our formulas are usable, we develop a concrete example of the form $\mathbb{Z}^5\rtimes \mathbb{Z}/6$ where its cohomology groups are described in full detail.

Here we present high spectral resolution $\textit{JWST}$ NIRSpec observations of GN42437, a low-mass (log(M$_\ast/M_\odot)=7.9$), compact ($r_e < 500$pc), extreme starburst galaxy at $z=5.59$ with 13 emission line detections. GN42437 has a low-metallicity (5-10% Z$_\odot$) and its rest-frame H$\alpha$ equivalent width suggests nearly all of the observed stellar mass formed within the last 3 Myr. GN42437 has an extraordinary 7$\sigma$ significant [Ne V] 3427 $\mathring{\rm A}$ detection. The [Ne V] line has a rest-frame equivalent width of $11\pm2\mathring{\rm A}$, [Ne V]/H$\alpha =0.04\pm0.007$, [Ne V]/[Ne III] 3870$\mathring{\rm A} = 0.26\pm0.04$, and [Ne V]/He II 4687 $\mathring{\rm A} = 1.2\pm0.5$. Ionization from massive stars, shocks, or high-mass X-ray binaries cannot simultaneously produce these [Ne V] and low-ionization line ratios. Reproducing the complete nebular structure requires both massive stars and accretion onto a black hole. We do not detect broad lines nor do the traditional diagnostics indicate that GN42437 has an accreting black hole. Thus, the very-high-ionization emission lines powerfully diagnose faint narrow-line black holes at high-redshift. We approximate the black hole mass in a variety of ways as log(M$_{\rm BH}/M_\odot) \sim 5-7$. This black hole mass is consistent with local relations between the black hole mass and the observed velocity dispersion, but significantly more massive than the stellar mass would predict. Very-high-ionization emission lines may reveal samples to probe the formation and growth of the first black holes in the universe., Comment: 18 pages, submitted to MNRAS. Comments encouraged

We study the optimal boundary regularity of solutions to Dirichlet problems involving the logarithmic Laplacian. Our proofs are based on the construction of suitable barriers via the Kelvin transform and direct computations. As applications of our results, we show a Hopf-type Lemma for nonnegative weak solutions and the uniqueness of solutions to some nonlinear problems., Comment: Revised version, 30 pages

The geometry of the neutral gas in and around galaxies is a key regulator of the escape of ionizing photons. We present the first statistical study aiming at linking the neutral and ionized gas distributions to the Lyman continuum (LyC) escape fraction (fesc(LyC)) in a sample of 22 confirmed LyC leakers and non-leakers at z~0.35 using the Keck Cosmic Web Imager (Keck/KCWI) and the Low Resolution Spectrograph 2 (HET/LRS2). Our integral field unit data enable the detection of neutral and low-ionization gas, as traced by Mg II, and ionized gas, as traced by [O II], extending beyond the stellar continuum for 7 and 10 objects, respectively. All but one object with extended Mg II emission also shows extended [O II] emission; in this case, Mg II emission is always more extended than [O II] by a factor 1.3 on average. Most of the galaxies with extended emission are non or weak LyC leakers (fesc(LyC) < 5%), but we find a large diversity of neutral gas configurations around these weakly LyC-emitting galaxies. Conversely, the strongest leakers (fesc(LyC) > 10%) appear uniformly compact in both Mg II and [O II] with exponential scale lengths <1 kpc. We also find a trend between fesc(LyC) and the spatial offsets of the nebular gas and the stellar continuum emission. Moreover, we find significant anti-correlations between the spatial extent of the neutral gas and the [O III]/[O II] ratio, and H$\beta$ equivalent width, as well as positive correlations with metallicity and UV size, suggesting that galaxies with more compact neutral gas sizes are more highly ionized. The observations suggest that strong LyC emitters do not have extended neutral gas halos and ionizing photons may be emitted in many directions. Combined with high ionization diagnostics, we propose the Mg II, and potentially [O II], spatial compactness are indirect indicators of LyC emitting galaxies at high-redshift., Comment: 31 pages, 24 figures, 4 tables, submitted to A&A

The fusion of non-Abelian anyons or topological defects is a fundamental operation in measurement-only topological quantum computation. In topological superconductors, this operation amounts to a determination of the shared fermion parity of Majorana zero modes. As a step towards this, we implement a single-shot interferometric measurement of fermion parity in indium arsenide-aluminum heterostructures with a gate-defined nanowire. The interferometer is formed by tunnel-coupling the proximitized nanowire to quantum dots. The nanowire causes a state-dependent shift of these quantum dots' quantum capacitance of up to 1 fF. Our quantum capacitance measurements show flux h/2e-periodic bimodality with a signal-to-noise ratio of 1 in 3.7 $\mu$s at optimal flux values. From the time traces of the quantum capacitance measurements, we extract a dwell time in the two associated states that is longer than 1 ms at in-plane magnetic fields of approximately 2 T. These results are consistent with a measurement of the fermion parity encoded in a pair of Majorana zero modes that are separated by approximately 3 $\mu$m and subjected to a low rate of poisoning by non-equilibrium quasiparticles. The large capacitance shift and long poisoning time enable a parity measurement error probability of 1%., Comment: Added data on a second measurement of device A and a measurement of device B, expanded discussion of a trivial scenario. Refs added, author list updated

We report observational evidence of highly turbulent ionized gas kinematics in a sample of 20 Lyman continuum (LyC) emitters (LCEs) at low redshift ($z\sim 0.3$). Detailed Gaussian modeling of optical emission line profiles in high-dispersion spectra consistently shows that both bright recombination and collisionally excited lines can be fitted as one or two narrow components with intrinsic velocity dispersion of $\sigma$ $\sim$ 40-100 km s$^{-1}$, in addition to a broader component with $\sigma \sim$ 100-300 km s$^{-1}$, which contributes up to $\sim$40% of the total flux and is preferentially blueshifted from the systemic velocity. We interpret the narrow emission as highly ionized gas close to the young massive star clusters and the broader emission as a signpost of unresolved ionized outflows, resulting from massive stars and supernova feedback. We find a significant correlation between the width of the broad emission and the LyC escape fraction, with strong LCEs exhibiting more complex and broader line profiles than galaxies with weaker or undetected LyC emission. We provide new observational evidence supporting predictions from models and simulations; our findings suggest that gas turbulence and outflows resulting from strong radiative and mechanical feedback play a key role in clearing channels through which LyC photons escape from galaxies. We propose that the detection of blueshifted broad emission in the nebular lines of compact extreme emission-line galaxies can provide a new indirect diagnostic of Lyman photon escape, which could be useful to identify potential LyC leakers in the epoch of reionization with the JWST., Comment: 11 Pages, 7 Figures. A&A in Press

We establish the validity of a strong unique continuation property for weakly coupled elliptic systems, including competitive ones. Our proof exploits the system structure and uses Carleman estimates. We apply this result to obtain some nonexistence results for critical systems.

The objective of the Cyclotron Radiation Emission Spectroscopy (CRES) technology is to build precise particle energy spectra. This is achieved by identifying the start frequencies of charged particle trajectories which, when exposed to an external magnetic field, leave semi-linear profiles (called tracks) in the time-frequency plane. Due to the need for excellent instrumental energy resolution in application, highly efficient and accurate track reconstruction methods are desired. Deep learning convolutional neural networks (CNNs) - particularly suited to deal with information-sparse data and which offer precise foreground localization - may be utilized to extract track properties from measured CRES signals (called events) with relative computational ease. In this work, we develop a novel machine learning based model which operates a CNN and a support vector machine in tandem to perform this reconstruction. A primary application of our method is shown on simulated CRES signals which mimic those of the Project 8 experiment - a novel effort to extract the unknown absolute neutrino mass value from a precise measurement of tritium $\beta^-$-decay energy spectrum. When compared to a point-clustering based technique used as a baseline, we show a relative gain of 24.1% in event reconstruction efficiency and comparable performance in accuracy of track parameter reconstruction., Comment: submitted to Machine Learning: Science and Technology

Consider the following Lane-Emden system with Dirichlet boundary conditions: \[ -\Delta U = |V|^{\beta-1}V,\ -\Delta V = |U|^{\alpha-1}U \text{ in }\Omega,\qquad U=V= 0 \text{ on }\partial \Omega, \] in a bounded domain $\Omega$, for $(\alpha,\beta)$ subcritical. We study the asymptotic behavior of least-energy solutions when $\beta\to \infty$, for any fixed $\alpha$ which, in the case $N\geq 3$, is smaller than $2/(N-2)$. We show that these solutions converge to least-energy solutions of a semilinear equation involving the 1-bilaplacian operator, establishing a new relationship between these objects. As a corollary, we deduce the asymptotic behavior of solutions to $p$-bilaplacian Lane-Emden equations as the power in the nonlinearity goes to infinity. For the proof, we rely on the reduction by inversion method and on tools from nonsmooth analysis, considering an auxiliary nonlinear eigenvalue problem. We characterize its value in terms of the Green function, and prove a Faber-Krahn type result. In the case of a ball, we can characterize explicitly the eigenvalue, as well as the limit profile of least-energy solutions to the system as $\beta\to\infty$., Comment: 28 pages, 2 figures

Let $u_s$ denote a solution of the fractional Poisson problem $$ (-\Delta)^s u_s = f\quad\text{ in }\Omega,\qquad u_s=0\quad \text{ on }\mathbb{R}^N\setminus \Omega, $$ where $N\geq 2$ and $\Omega\subset \mathbb{R}^N$ is a bounded domain of class $C^2$. We show that the solution mapping $s\mapsto u_s$ is differentiable in $L^\infty(\Omega)$ at $s=1$, namely, at the nonlocal-to-local transition. Moreover, using the logarithmic Laplacian, we characterize the derivative $\partial_s u_s$ as the solution to a boundary value problem. This complements the previously known differentiability results for $s$ in the open interval $(0,1)$. Our proofs are based on an asymptotic analysis to describe the collapse of the nonlocality of the fractional Laplacian as $s$ approaches 1. We also provide a new representation of $\partial_s u_s$ for $s \in (0,1)$ which allows us to refine previously obtained Green function estimates., Comment: 20 pages

We present the numerical analysis of a finite element method (FEM) for one-dimensional Dirichlet problems involving the logarithmic Laplacian (the pseudo-differential operator that appears as a first-order expansion of the fractional Laplacian as the exponent $s\to 0^+$). Our analysis exhibits new phenomena in this setting; in particular, using recently obtained regularity results, we prove rigorous error estimates and provide a logarithmic order of convergence in the energy norm using suitable $\log$-weighted spaces. Numerical evidence suggests that this type of rate cannot be improved. Moreover, we show that the stiffness matrix of logarithmic problems can be obtained as the derivative of the fractional stiffness matrix evaluated at $s=0$. Lastly, we investigate the relationship between the discrete eigenvalue problem and its convergence to the continuous one., Comment: This version revised Sections 3 and 6 and updated references

We apply Wald's formalism to a Lagrangian within generalised Proca gravity that admits a Schwarzschild black hole with a non-trivial vector field. The resulting entropy differs from that of the same black hole in General Relativity by a logarithmic correction modulated by the only independent charge of the vector field. We find conditions on this charge to guarantee that the entropy is a non-decreasing function of the black hole area, as is the case in GR. If this requirement is extended to black hole mergers, we find that for Planck scale black holes, a non-decreasing entropy is possible only if the area of the final black hole is several times larger than the initial total area of the merger. Finally, we discuss some implications of the vector Galileon entropy from the point of view of entropic gravity.

Sources that leak Lyman-continuum (LyC) photons and lead to the reionisation of the universe are intensely studied using multiple observing facilities. Recently, the Low-redshift LyC Survey (LzLCS) has found the first large sample of LyC emitting galaxies at low redshift ($z\sim 0.3$) with the Hubble Space Telescope/Cosmic Origins Spectrograph. The LzLCS sample contains a robust estimate of the LyC escape fraction ($f_\mathrm{esc}^\mathrm{LyC}$) for 66 galaxies spanning a wide range of $f_\mathrm{esc}^\mathrm{LyC}$. Here we, for the first time, aim to study the radio continuum (RC) properties of LzLCS sources and their dependence on $f_\mathrm{esc}^\mathrm{LyC}$. We present Karl G. Jansky Very Large Array RC observations at C (4-8 GHz), S (2-4 GHz) and L (1-2 GHz) bands for a sub-sample of the LzLCS sources. The radio spectral index ($\alpha^{\mathrm{3GHz}}_\mathrm{6GHz}$) spans a wide range from being flat ( $\geq -0.1$) to very steep ($\leq -1.0$). The strongest leakers in our sample show flat $\alpha^{\mathrm{3GHz}}_\mathrm{6GHz}$, weak leakers have $\alpha^{\mathrm{3GHz}}_\mathrm{6GHz}$ close to normal star-forming galaxies, and non-leakers are characterized by steep $\alpha^{\mathrm{3GHz}}_\mathrm{6GHz}$. We argue that a combination of young ages, free-free absorption, and a flat cosmic-ray energy spectrum can altogether lead to a flat $\alpha^{\mathrm{3GHz}}_\mathrm{6GHz}$ for strong leakers. Non-leakers are characterized by steep spectra which can arise due to break/cutoff at high frequencies. Such a cutoff in the spectrum can arise in a single injection model of CRs characteristic of galaxies which have recently stopped star formation. Such a relation between $\alpha^{\mathrm{3GHz}}_\mathrm{6GHz}$ and $f_\mathrm{esc}^\mathrm{LyC}$ hints at the interesting role of supernovae, CRs, and magnetic fields in facilitating the escape ( and/or the lack) of LyC photons. (Abridged), Comment: 20 pages, 17 figures, 4 tables, 8 appendix pages, Astronomy & Astrophysics in press

This work combines algorithms based on word embeddings, dimensionality reduction, and clustering. The objective is to obtain topics from a set of unclassified texts. The algorithm to obtain the word embeddings is the BERT model, a neural network architecture widely used in NLP tasks. Due to the high dimensionality, a dimensionality reduction technique called UMAP is used. This method manages to reduce the dimensions while preserving part of the local and global information of the original data. K-Means is used as the clustering algorithm to obtain the topics. Then, the topics are evaluated using the TF-IDF statistics, Topic Diversity, and Topic Coherence to get the meaning of the words on the clusters. The results of the process show good values, so the topic modeling of this process is a viable option for classifying or clustering texts without labels.

This work combined different audio features to obtain a more robust fingerprint to be used in a music recommendation process. The combination of these methods resulted in a high-dimensional vector. To reduce the number of values, PCA was applied to the set of resulting fingerprints, selecting the number of principal components that corresponded to an explained variance of $95\%$. Finally, with these PCA-fingerprints, the similarity matrix of each fingerprint with the entire data set was calculated. The process was applied to 200 songs from a personal music library; the songs were tagged with the artists' corresponding genres. The recommendations (fingerprints of songs with the closest similarity) were rated successful if the recommended songs' genre matched the target songs' genre. With this procedure, it was possible to obtain an accuracy of $89\%$ (successful recommendations out of total recommendation requests).

Cyclotron Radiation Emission Spectroscopy (CRES) is a technique for precision measurement of the energies of charged particles, which is being developed by the Project 8 Collaboration to measure the neutrino mass using tritium beta-decay spectroscopy. Project 8 seeks to use the CRES technique to measure the neutrino mass with a sensitivity of 40~meV, requiring a large supply of tritium atoms stored in a multi-cubic meter detector volume. Antenna arrays are one potential technology compatible with an experiment of this scale, but the capability of an antenna-based CRES experiment to measure the neutrino mass depends on the efficiency of the signal detection algorithms. In this paper, we develop efficiency models for three signal detection algorithms and compare them using simulations from a prototype antenna-based CRES experiment as a case-study. The algorithms include a power threshold, a matched filter template bank, and a neural network based machine learning approach, which are analyzed in terms of their average detection efficiency and relative computational cost. It is found that significant improvements in detection efficiency and, therefore, neutrino mass sensitivity are achievable, with only a moderate increase in computation cost, by utilizing either the matched filter or machine learning approach in place of a power threshold, which is the baseline signal detection algorithm used in previous CRES experiments by Project 8.

Recent Reference-Based image super-resolution (RefSR) has improved SOTA deep methods introducing attention mechanisms to enhance low-resolution images by transferring high-resolution textures from a reference high-resolution image. The main idea is to search for matches between patches using LR and Reference image pair in a feature space and merge them using deep architectures. However, existing methods lack the accurate search of textures. They divide images into as many patches as possible, resulting in inefficient memory usage, and cannot manage large images. Herein, we propose a deep search with a more efficient memory usage that reduces significantly the number of image patches and finds the $k$ most relevant texture match for each low-resolution patch over the high-resolution reference patches, resulting in an accurate texture match. We enhance the Super Resolution result adding gradient density information using a simple residual architecture showing competitive metrics results: PSNR and SSMI., Comment: 5 pages, 3 figures, 3 tables