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West central Georgia has become a burgeoning center for advanced manufacturing and logistics. With facilities for global brands across automotive, agriculture, tech, and biotech industries, the region (which includes Carroll, Coweta, Douglas, Haralson, Heard, Meriwether, and Troup counties) has experienced a 100+ percent surge in job demand for manufacturing engineers, machine operators, and material assembly shift technicians alone. This case study explores a cross-sector response to upskilling and reskilling talent in the region through West Georgia Technical College's establishment of a Regional Workforce Training Center, which has fostered impactful employer partnerships to drive skill acquisition for entry-level talent and incumbent workforces, enhance workforce diversity, and meet the evolving needs of both businesses and the community at large.

Inclusive electron scattering cross sections off a hydrogen target at a beam energy of 10.6 GeV have been measured with data collected from the CLAS12 spectrometer at Jefferson Laboratory. These first absolute cross sections from CLAS12 cover a wide kinematic area in invariant mass W of the final state hadrons from the pion threshold up to 2.5 GeV for each bin in virtual photon four-momentum transfer squared $Q^2$ from 2.55 to 10.4~GeV$^2$ owing to the large scattering angle acceptance of the CLAS12 detector. Comparison of the cross sections with the resonant contributions computed from the CLAS results on the nucleon resonance electroexcitation amplitudes has demonstrated a promising opportunity to extend the information on their $Q^2$ evolution up to 10 GeV$^2$. Together these results from CLAS and CLAS12 offer good prospects for probing the nucleon parton distributions at large fractional parton momenta $x$ for $W$ < 2.5 GeV, while covering the range of distances where the transition from the strongly coupled to the perturbative regimes is expected.

We report the presence of frustrated bond order in the form of short-range charge correlations in the triangular lattice antiferromagnetic compounds $Ln$Cd$_3$P$_3$ ($Ln$ = La, Ce, Pr, and Nd). These compounds feature two-dimensional planes of trigonal-planar CdP$_3$ units that separate tetrahedral CdP$_4$ layers; collectively, these sandwich edge-sharing triangular lattice planes of $Ln$P$_6$ octahedra. Diffuse X-ray scattering data reveal an underlying bond instability within the unique CdP$_3$ units that breaks rotational symmetry along one Cd$-$P bond direction, with long-range ordering being frustrated via emergent kagome-ice bond correlations. Our results establish $Ln$Cd$_3$P$_3$ as a rare class of materials where frustrated magnetism across a tunable rare-earth triangular network is embedded within a dopable semiconductor with a frustrated bond order instability., Comment: 11 pages, 5 figures

Chromium is a common transition-metal impurity that is easily incorporated during crystal growth. It is perhaps best known for giving rise to the 694.3 nm (1.786 eV) emission in Cr-doped Al$_2$O$_3$, exploited in ruby lasers. Chromium has also been found in monoclinic gallium oxide, a wide-bandgap semiconductor being pursued for power electronics. In this work, we thoroughly characterize the behavior of Cr in Ga$_2$O$_3$ through theoretical and experimental techniques. $\beta$-Ga$_2$O$_3$ samples are grown with the floating zone method and show evidence of a sharp photoluminescence signal, reminiscent of ruby. We calculate the energetics of formation of Cr from first principles, demonstrating that Cr preferentially incorporates as a neutral impurity on the octahedral site. Cr possesses a quartet ground-state spin and has an internal transition with a zero-phonon line near 1.8 eV. By comparing the calculated and experimentally measured luminescence lineshape function, we elucidate the role of coupling to phonons and uncover features beyond the Franck-Condon approximation. The combination of strong emission with a small Huang-Rhys factor of 0.05 and a technologically relevant host material render Cr in Ga$_2$O$_3$ attractive as a quantum defect.

We study the potential of symbolic regression (SR) to derive compact and precise analytic expressions that can improve the accuracy and simplicity of phenomenological analyses at the Large Hadron Collider (LHC). As a benchmark, we apply SR to equation recovery in quantum electrodynamics (QED), where established analytical results from quantum field theory provide a reliable framework for evaluation. This benchmark serves to validate the performance and reliability of SR before extending its application to structure functions in the Drell-Yan process mediated by virtual photons, which lack analytic representations from first principles. By combining the simplicity of analytic expressions with the predictive power of machine learning techniques, SR offers a useful tool for facilitating phenomenological analyses in high energy physics., Comment: 7 pages, 7 figures, 3 tables. Accepted for the Machine Learning and the Physical Sciences Workshop NeurIPS 2024

It has been recognized that the impulsive noise (IN) generated by power devices poses significant challenges to wireless receivers in practice. In this paper, we assess the achievable information rate (AIR) and the performance of practical turbo receiver designs for a well-established Markov-Middleton IN model. We utilize a commonly used commercial transmission setup consisting of a convolutional encoder, bit-level interleaver, and a differential binary phase-shift keying (DBPSK) symbol mapper. Firstly, we conduct a comprehensive assessment of the AIRs of the underlying channel model using DBPSK transmitted symbols across various channel conditions. Additionally, we introduce two robust turbo-like receiver designs. The first design features a separate IN detector and a turbo-demapper-decoder. The second design employs a joint approach, where the extrinsic information of both the detector and demapper is simultaneously updated, forming a turbo-detector-demapper-decoder structure. We show that the joint design consistently outperforms the separate design across all channel conditions, particularly in low AIR situations. However, the maximum performance gain for the channel conditions considered in this paper is merely 0.2 dB, and the joint system incurs significantly greater computational complexity, especially for a high number of turbo iterations. The performance of the two proposed turbo receiver designs is demonstrated to be close to the estimated AIR, with a performance gap dependent on the channel parameters., Comment: 12 pages, 13 figures

Blind estimation of intersymbol interference channels based on the Baum-Welch (BW) algorithm, a specific implementation of the expectation-maximization (EM) algorithm for training hidden Markov models, is robust and does not require labeled data. However, it is known for its extensive computation cost, slow convergence, and frequently converges to a local maximum. In this paper, we modified the trellis structure of the BW algorithm by associating the channel parameters with two consecutive states. This modification enables us to reduce the number of required states by half while maintaining the same performance. Moreover, to improve the convergence rate and the estimation performance, we construct a joint turbo-BW-equalization system by exploiting the extrinsic information produced by the turbo decoder to refine the BW-based estimator at each EM iteration. Our experiments demonstrate that the joint system achieves convergence in 10 EM iterations, which is 8 iterations less than a separate system design for a signal-to-noise ratio (SNR) of 4dB. Additionally, the joint system provides improved estimation accuracy with a mean square error (MSE) of $10^{-4}$ for an SNR of 6dB. We also identify scenarios where a joint design is not preferable, especially when the channel is noisy (e.g., SNR=2dB) and the decoder cannot provide reliable extrinsic information for a BW-based estimator., Comment: Accepted paper for 14th International ITG Conference on Systems, Communications and Coding (SCC)

We present BimArt, a novel generative approach for synthesizing 3D bimanual hand interactions with articulated objects. Unlike prior works, we do not rely on a reference grasp, a coarse hand trajectory, or separate modes for grasping and articulating. To achieve this, we first generate distance-based contact maps conditioned on the object trajectory with an articulation-aware feature representation, revealing rich bimanual patterns for manipulation. The learned contact prior is then used to guide our hand motion generator, producing diverse and realistic bimanual motions for object movement and articulation. Our work offers key insights into feature representation and contact prior for articulated objects, demonstrating their effectiveness in taming the complex, high-dimensional space of bimanual hand-object interactions. Through comprehensive quantitative experiments, we demonstrate a clear step towards simplified and high-quality hand-object animations that excel over the state-of-the-art in motion quality and diversity.

Generalized Parton Distributions (GPDs) are multidimensonal structure functions that encode the information about the internal structure of hadrons. Using privileged channels such as Deeply Virtual Compton Scattering (DVCS) or Timelike Compton Scattering (TCS), it is possible to make direct measurements at points where the momentum fraction of the parton equals the respective scaling variable. Double Deeply Virtual Compton Scattering (DDVCS) is a not yet measured and promising channel for GPD studies as it allows to perform more general measurements at independent momentum fraction and scaling variable values. GPDs are extracted from Compton Form Factors which arise naturally in experimental observables from different combinations of beam and target configurations. In the context of the Continuous Electron Beam Accelerator Facility (CEBAF) and the Electron Ion Collider (EIC), we report the results of an exhaustive study of the DDVCS observables from polarized electron and positron beams directed to a polarized proton target. The study focuses on the sensitivity of the observables to the parton helicity conserving proton GPDs, particularly the consequences for GPDs measurements via DDVCS at CEBAF and EIC based on the VGG and GK19 model predictions., Comment: 5 pages, 3 figures, conference proceedings for the 31st International Workshop on Deep Inelastic Scattering (DIS2024)

We prove an equidistribution result about Hecke orbits on the Picard group of Shimura curves coming from definite quaternion algebras over function fields. In particular, we show the equidistribution of Hecke orbits of supersingular Drinfeld modules of rank 2. Our approach is via the automorphic method, using bounds for coefficients of cuspidal automorphic forms of Drinfeld type as the main tool.

The celebrated canonical Ramsey theorem of Erd\H{o}s and Rado implies that for $2\leq k\in \mathbb{N}$, any colouring of the edges of $K_n$ with $n$ sufficiently large gives a copy of $C_{2k}$ which has one of three canonical colour patterns: monochromatic, rainbow or lexicographic. In this paper we show that if $p=\omega(n^{-1+1/(2k-1)}\log n)$, then ${\mathbf{G}}(n,p)$ will asymptotically almost surely also have the property that any colouring of its edges induces canonical copies of $C_{2k}$. This determines the threshold for the canonical Ramsey property with respect to even cycles, up to a $\log$ factor., Comment: 24 pages + 4 pages of appendix, 1 figure

The kagome motif is a versatile platform for condensed matter physics, hosting rich interactions between magnetic, electronic, and structural degrees of freedom. In recent years, the discovery of a charge density wave (CDW) in the AV$_3$Sb$_5$ superconductors and structurally-derived bond density waves in FeGe and ScV$_6$Sn$_6$ have stoked the search for new kagome platforms broadly exhibiting density wave (DW) transitions. In this work, we evaluate the known AM$_6$X$_6$ chemistries and construct a stability diagram that summarizes the structural relationships between the $\approx$125 member family. Subsequently we introduce our discovery of the broader LnNb$_6$Sn$_6$ (Ln:Ce-Nd,Sm,Gd-Tm,Lu,Y) family of kagome metals and an analogous DW transition in LuNb$_6$Sn$_6$. Our X-ray scattering measurements clearly indicate a (1/3, 1/3, 1/3) ordering wave vector ($\sqrt{3}\times\sqrt{3}\times3$ superlattice) and diffuse scattering on half-integer $L$-planes. Our analysis of the structural data supports the ``rattling mode'' DW model proposed for ScV$_6$Sn$_6$ and paints a detailed picture of the steric interactions between the rare-earth filler element and the host Nb-Sn kagome scaffolding. We also provide a broad survey of the magnetic properties within the HfFe$_6$Ge$_6$-type LnNb$_6$Sn$_6$ members, revealing a number of complex antiferromagnetic and metamagnetic transitions throughout the family. This work integrates our new LnNb$_6$Sn$_6$ series of compounds into the broader AM$_6$X$_6$ family, providing new material platforms and forging a new route forward at the frontier of kagome metal research.

Myosin motors are fundamental biological actuators, powering diverse mechanical tasks in eukaryotic cells via ATP hydrolysis. Recent work revealed that myosin's velocity-dependent detachment rate can bridge actomyosin dynamics to macroscale Hill muscle predictions. However, the influence of this microscale unbinding, which we characterize by a dimensionless parameter $\alpha$, on macroscale energetic flows-such as power consumption, output and efficiency-remains elusive. Here we develop an analytical model of myosin dynamics that relates unbinding rates $\alpha$ to energetics. Our model agrees with published in-vivo muscle data and, furthermore, uncovers a performance-efficiency tradeoff governed by $\alpha$. To experimentally validate the tradeoff, we build HillBot, a robophysical model of Hill's muscle that mimics nonlinearity. Through HillBot, we decouple $\alpha$'s concurrent effect on performance and efficiency, demonstrating that nonlinearity drives efficiency. We compile 136 published measurements of $\alpha$ in muscle and myoblasts to reveal a distribution centered at $\alpha^* = 3.85 \pm 2.32$. Synthesizing data from our model and HillBot, we quantitatively show that $\alpha^*$ corresponds to a class of generalist actuators that are both relatively powerful and efficient, suggesting that the performance-efficiency tradeoff underpins the prevalence of $\alpha^*$ in nature. We leverage these insights and propose a nonlinear variable-impedance protocol to shift along a performance-efficiency axis in robotic applications., Comment: 23 pages, 6 figures. PDF of supplemental information available in zip download

Super Jupiters are giant planets with several Jupiter masses. It remains an open question whether these planets originate with such high masses or grow through collisions. Previous work demonstrates that warm super Jupiters tend to have more eccentric orbits compared to regular-mass warm Jupiters. This correlation between mass and eccentricity may indicate that planet-planet interactions significantly influence the warm giant planet demographics. Here we conducted a detailed characterization of a warm super Jupiter, TOI-2145b. This analysis utilized previous observations from TESS and Keck/HIRES, enhanced by new Rossiter-McLaughlin effect data from the NEID spectrometer on the 3.5 m WIYN Telescope. TOI-2145b is a $5.68^{+0.37}_{-0.34} M_{\rm Jup}$ planet on a moderate eccentricity ($e = 0.214^{+0.014}_{-0.014}$), 10.26-day orbit, orbiting an evolved A-star. We constrain the projected stellar obliquity to be $\lambda = 6.8^{+2.9}_{-3.8}$$^\circ$ from two NEID observations. Our $N$-body simulations suggest that the formation of super Jupiter TOI-2145b could involve either of two scenarios: a high initial mass or growth via collisions. On a population level, however, the collision scenario can better describe the mass-eccentricity distribution of observed warm Jupiters., Comment: 13 pages, 5 figures, 1 table, AJ accepted

In this article, we characterize both Lusin's theorem and the existence of Borel representatives via the regularity properties of the measure in general topological measure spaces. As a corollary, we prove that Borel regularity of the measure is both a necessary and sufficient condition for these results to hold true in metric measure spaces.

The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the detected partitioning. In this paper, we provide theoretical results that permits us to build 2D empirical wavelet filters based on an arbitrary partitioning of the frequency domain. We also propose an algorithm to detect such partitioning from an image spectrum by combining a scale-space representation to estimate the position of dominant harmonic modes and a watershed transform to find the boundaries of the different supports making the expected partition. This whole process allows us to define the empirical watershed wavelet transform. We illustrate the effectiveness and the advantages of such adaptive transform, first visually on toy images, and next on both unsupervised texture segmentation and image deconvolution applications.

This paper analyzes the design and competitiveness of four neural network (NN) architectures recently proposed as decoders for forward error correction (FEC) codes. We first consider the so-called single-label neural network (SLNN) and the multi-label neural network (MLNN) decoders which have been reported to achieve near maximum likelihood (ML) performance. Here, we show analytically that SLNN and MLNN decoders can always achieve ML performance, regardless of the code dimensions -- although at the cost of computational complexity -- and no training is in fact required. We then turn our attention to two transformer-based decoders: the error correction code transformer (ECCT) and the cross-attention message passing transformer (CrossMPT). We compare their performance against traditional decoders, and show that ordered statistics decoding outperforms these transformer-based decoders. The results in this paper cast serious doubts on the application of NN-based FEC decoders in the short and medium block length regime., Comment: 6 pages, 4 figures, submitted for possible presentation in a conference (v2: Pre-FEC BER curves are corrected)

Attention mechanisms have revolutionized several domains of artificial intelligence, such as natural language processing and computer vision, by enabling models to selectively focus on relevant parts of the input data. While recent work has characterized the optimization dynamics of gradient descent (GD) in attention-based models and the structural properties of its preferred solutions, less is known about more general optimization algorithms such as mirror descent (MD). In this paper, we investigate the convergence properties and implicit biases of a family of MD algorithms tailored for softmax attention mechanisms, with the potential function chosen as the $p$-th power of the $\ell_p$-norm. Specifically, we show that these algorithms converge in direction to a generalized hard-margin SVM with an $\ell_p$-norm objective when applied to a classification problem using a softmax attention model. Notably, our theoretical results reveal that the convergence rate is comparable to that of traditional GD in simpler models, despite the highly nonlinear and nonconvex nature of the present problem. Additionally, we delve into the joint optimization dynamics of the key-query matrix and the decoder, establishing conditions under which this complex joint optimization converges to their respective hard-margin SVM solutions. Lastly, our numerical experiments on real data demonstrate that MD algorithms improve generalization over standard GD and excel in optimal token selection.

Gaia astrometry of nearby stars is precise enough to detect the tiny displacements induced by substellar companions, but radial velocity data are needed for definitive confirmation. Here we present radial velocity follow-up observations of 28 M and K stars with candidate astrometric substellar companions, which led to the confirmation of two systems, Gaia-4b and Gaia-5b, and the refutation of 21 systems as stellar binaries. Gaia-4b is a massive planet ($M = 11.8 \pm 0.7 \:\mathrm{M_J}$) in a $P = 571.3 \pm 1.4\:\mathrm{day}$ orbit with a projected semi-major axis $a_0=0.312 \pm 0.040\:\mathrm{mas}$ orbiting a $0.644 \pm 0.02 \:\mathrm{M_\odot}$ star. Gaia-5b is a brown dwarf ($M = 20.9 \pm 0.5\:\mathrm{M_J}$) in a $P = 358.58 \pm 0.19\:\mathrm{days}$ eccentric $e=0.6412 \pm 0.0027$ orbit with a projected angular semi-major axis of $a_0 = 0.947 \pm 0.038\:\mathrm{mas}$ around a $0.34 \pm 0.03 \mathrm{M_\odot}$ star. Gaia-4b is one of the first exoplanets discovered via the astrometric technique, and is one of the most massive planets known to orbit a low-mass star., Comment: Submitted to AAS journals. 26 pages, 12 figures, 4 tables

In this paper we introduce a reconciliation protocol with a two-step error correction scheme using a short blocklength low rate code and a long blocklength high rate code. We show that by using this two-step decoding method it is possible to achieve secret key rates beyond the Devetak-Winter bound. We simulate the protocol using short blocklength low-density parity check code, and show that we can obtain reconciliation efficiencies up to 1.5. Using these high reconciliation efficiencies, it is possible double the achievable distances of CV-QKD systems., Comment: Pre-print

The spin structure functions of the proton and the deuteron were measured during the EG4 experiment at Jefferson Lab in 2006. Data were collected for longitudinally polarized electron scattering off longitudinally polarized NH$_3$ and ND$_3$ targets, for $Q^2$ values as small as 0.012 and 0.02 GeV$^2$, respectively, using the CEBAF Large Acceptance Spectrometer (CLAS). This is the archival paper of the EG4 experiment that summaries the previously reported results of the polarized structure functions $g_1$, $A_1F_1$, and their moments $\overline \Gamma_1$, $\overline \gamma_0$, and $\overline I_{TT}$, for both the proton and the deuteron. In addition, we report on new results on the neutron $g_1$ extracted by combining proton and deuteron data and correcting for Fermi smearing, and on the neutron moments $\overline \Gamma_1$, $\overline \gamma_0$, and $\overline I_{TT}$ formed directly from those of the proton and the deuteron. Our data are in good agreement with the Gerasimov-Drell-Hearn sum rule for the proton, deuteron, and neutron. Furthermore, the isovector combination was formed for $g_1$ and the Bjorken integral $\overline \Gamma_1^{p-n}$, and compared to available theoretical predictions. All of our results provide for the first time extensive tests of spin observable predictions from chiral effective field theory ($\chi$EFT) in a $Q^2$ range commensurate with the pion mass. They motivate further improvement in $\chi$EFT calculations from other approaches such as the lattice gauge method., Comment: 33 pages. 26 figures. Data table provided as supplementary material (30 pages latex and csv tables)

This article deals with dihedral group actions on compact Riemann surfaces and the interplay between different geometric data associated to them. First, a bijective correspondence between geometric signatures and analytic representations is obtained. Second, a refinement of a result of Bujalance, Cirre, Gamboa and Gromadzki about signature realization is provided. Finally, we apply our results to isogeny decompositions of Jacobians by Prym varieties and by elliptic curves, extending results of Carocca, Recillas and Rodr\'iguez. In particular, we give a complete classification of Jacobians with dihedral action whose group algebra decomposition induces a decomposition into factors of the same dimension., Comment: 32 pages

Recent observations on the large-scale structure of the universe indicate that the cosmological constant cannot be the definitive answer to the nature of dark energy. Therefore, it is a good time to propose alternatives to understand the late-accelerated expansion of the universe. In this work we study the possibility that the acceleration of space-time is due to the topology of the universe. We assume that the topology of the universe is a principal fiber bundle whose base space is our 4-dimensional spacetime and the fiber is an $N$-dimensional Lie group that evolves with time. For the base space we consider a homogeneous and isotropic spacetime, we find that the base space is currently accelerating for $1 < N$ compact semi-simple Lie groups whose scale-factors are equal and for $1 < N$ non-Abelian Lie groups whose scale-factors are different and as long as its structure constants satisfy some conditions. However when we study the evolution of the density parameters these differ from the evolution within the $\Lambda$CDM model, this led us to think in the possibility of use a different group as fiber in order to obtain the right evolution of the density parameters. We conclude that it is possible that the accelerated expansion of the universe is due to consider a different topology of the universe as a principal fiber bundle., Comment: 16 pages, 5 figures

Bell's states are among the most useful in quantum computing. These state are an orthonormal base of entagled states with two qubits. We propose alternative bases of entangled states. Some of these states depend on a continuous parameter. We present the quantum circuit and code of these alternative bases. In addition, we study quantum teleportation with these entangled states and present their quantum circuits and codes associated., Comment: 39 pages, 15 figures, minor corrections. Comments welcome

We study transits of several ``hot Jupiter'' systems - including WASP-12 b, WASP-43 b, WASP-103 b, HAT-P-23 b, KELT-16 b, WD 1856+534 b, and WTS-2 b - with the goal of detecting tidal orbital decay and extending the baselines of transit times. We find no evidence of orbital decay in any of the observed systems except for that of the extensively studied WASP-12 b. Although the orbit of WASP-12 b is unequivocally decaying, we find no evidence for acceleration of said orbital decay, with measured $\ddot{P} = (-7 \pm 8) \times 10^{-14} \rm ~s^{-1}$, against the expected acceleration decay of $\ddot{P} \approx -10^{-23} \rm ~s^{-1}$. In the case of WD 1856+534 b, there is a tentative detection of orbital growth with $\dot{P} = (5.0 \pm 1.5) \times 10^{-10}$. While statistically significant, we err on the side of caution and wait for longer follow-up observations to consider the measured $\dot{P}$ real. For most systems, we provide a 95\%-confidence lower limit on the tidal quality factor, $Q_\star'$. The possibility of detecting orbital decay in hot Jupiters via long-term radial velocity (RV) measurements is also explored. We find that $\sim 1 \rm ~m~s^{-1}$ precision in RVs will be required to detect orbital decay of WASP-12 b with only 3 yr of observations. Currently available RV measurements and precision are unable to detect orbital decay in any of the systems studied here., Comment: 14 pages, 11 figures; Accepted in MNRAS on 2024 August 30. Received 2024 August 29; in original form 2024 February 13

A code is locally recoverable when each symbol in one of its code words can be reconstructed as a function of $r$ other symbols. We use bundles of projective spaces over a line to construct locally recoverable codes with availability; that is, evaluation codes where each code word symbol can be reconstructed from several disjoint sets of other symbols. The simplest case, where the code's underlying variety is a plane, exhibits noteworthy properties: When $r = 1$, $2$, $3$, they are optimal; when $r \geq 4$, they are optimal with probability approaching $1$ as the alphabet size grows. Additionally, their information rate is close to the theoretical limit. In higher dimensions, our codes form a family of asymptotically good codes., Comment: 25 pages, 3 figures

We present the discovery of a low-density planet orbiting the high-metallicity early M-dwarf TOI-5688 A b. This planet was characterized as part of the search for transiting giant planets ($R \gtrsim8$ M${}_\oplus$) through the Searching for GEMS (Giant Exoplanets around M-dwarf Stars) survey. The planet was discovered with the Transiting Exoplanet Survey Satellite (TESS), and characterized with ground-based transits from Red Buttes Observatory (RBO), the Table Mountain Observatory of Pomona College, and radial velocity (RV) measurements with the Habitable-Zone Planet Finder (HPF) on the 10 m Hobby Eberly Telescope (HET) and NEID on the WIYN 3.5 m telescope. From the joint fit of transit and RV data, we measure a planetary mass and radius of $124\pm24$ M$_\oplus$ ($0.39\pm0.07$ M${}_J$) and $10.4\pm0.7$ R$_\oplus$ ($0.92\pm0.06$ R${}_J$) respectively. The spectroscopic and photometric analysis of the host star TOI-5688 A shows that it is a metal-rich ([Fe/H] $ = 0.47\pm0.16$ dex) M2V star, favoring the core-accretion formation pathway as the likely formation scenario for this planet. Additionally, Gaia astrometry suggests the presence of a wide-separation binary companion, TOI-5688 B, which has a projected separation of $\sim5"$ (1110 AU) and is an M4V, making TOI-5688 A b part of the growing number of GEMS in wide-separation binary systems., Comment: 20 pages, 7 figures, Accepted in AJ

Continuous-variable quantum key distribution (CV-QKD) has been proposed as a method for securely exchanging keys to protect against the security concerns caused by potential advancements in quantum computing. In addition to optical fibre transmission, the free-space optical (FSO) channel is an interesting channel for CV-QKD, as it is possible to share keys over this channel wirelessly. The instability of the FSO channel caused by turbulence-induced fading, however, can cause a degradation in the system's performance. One of the most important aspects of CV-QKD is the reconciliation step, which significantly impacts the performance of the CV-QKD system. Hence, rate-adaptive reconciliation is necessary for CV-QKD over FSO to combat the fluctuations in the channel and improve secret key rates (SKRs). Therefore, in this paper, we simulate the impact of discrete modulation on the reconciliation efficiency and consider the use of $d$-dimensional reconciliation with $d > 8$ to mitigate this impact, improving reconciliation efficiencies by up to 3.4%. We validate our results by experimentally demonstrating CV-QKD over a turbulent FSO link and demonstrate SKR gains by up to 165%. Furthermore, we optimise the reconciliation efficiency for FSO links, achieving additional SKR gains of up to 7.6%., Comment: Pre-print JLT

The Mapper algorithm is a popular tool for visualization and data exploration in topological data analysis. We investigate an inverse problem for the Mapper algorithm: Given a dataset $X$ and a graph $G$, does there exist a set of Mapper parameters such that the output Mapper graph of $X$ is isomorphic to $G$? We provide constructions that affirmatively answer this question. Our results demonstrate that it is possible to engineer Mapper parameters to generate a desired graph., Comment: 13 pages, 4 figures

Rings are complex structures surrounding giant planets and some minor bodies in the Solar System. While some formation mechanisms could also potentially foster their existence around (regular or irregular) satellites, none of these bodies currently bear these structures. We aim to understand the underlying mechanisms that govern the potential formation, stability, and/or decay of hypothetical circumsatellital rings (CSRs), orbiting the largest moons in the Solar System. This extends to the exploration of short-term morphological features within these rings, providing insights into the ring survival time-scales and the interactions that drive their evolution. To conduct this study, we use numerical N-body simulations under the perturbing influence of the host planet and other moon companions. We found that moons with a lower Roche-to-Hill radius can preserve their rings over extended periods. Moreover, the gravitational environment in which these rings are immersed influences the system's morphological evolution, inducing gaps through the excitation of eccentricity and inclination of constituent particles. Specifically, our results show that Iapetus' and Rhea's rings experience minimal variations in their orbital parameters, enhancing their long-term stability. This agrees with the hypothesis that some of the features of Iapetus and Rhea were produced by ancient ring systems, for example, the huge ridge in Iapetus equator as a result of a decaying ring. From a dynamical perspective, we found that there are no mechanisms that preclude the existence of CSRs and we attribute their current absence to non-gravitational phenomena. Effects such as stellar radiation, magnetic fields, and the influence of magnetospheric plasma can significantly impact the dynamics of constituent particles and trigger their decay, highlighing the importance of future studies on these effects., Comment: Accepted for publication in Astronomy & Astrophysics

We present the design of the mechanical structure of the miniBeBe detector, a subsystem of the Multi-Purpose Detector, soon to enter into operation at the Nuclotron based Ion Collider fAcility of the Joint Institute for Nuclear Research. The miniBeBe detector was designed and is currently being developed by the MexNICA Collaboration to contribute to the level-zero trigger of the Time of Flight. The mechanical structure meets the requirements of minimizing the material budget and be free of ferromagnetic materials, without compromising its robustness. The design also allows easy module replacement for maintenance and overall removal at the end of the first stage of the experiment, without affecting the rest of the subsystems, to leave room for the installation of the Inner Tracking System. In addition, a Finite Element Method analysis of the mechanical components under load was performed. Based on this analysis, it was determined that the design meets the space constraints within the Multi-Purpose Detector, as well as a deformation of less than 1 mm with overall stress of less than 2 MPa, such that no material used in the design is at risk of mechanical failure during operation. A cooling system heat transfer analysis was performed showing that the detector Silicon Photo-Multipliers can be kept within a temperature range of 19$^{\circ}$C to 23$^{\circ}$C, which is adequate for their optimal performance., Comment: 15 pages, 13 figures, 6 tables

Modern artificial intelligence (AI) systems are powered by foundation models. This paper presents a new set of foundation models, called Llama 3. It is a herd of language models that natively support multilinguality, coding, reasoning, and tool usage. Our largest model is a dense Transformer with 405B parameters and a context window of up to 128K tokens. This paper presents an extensive empirical evaluation of Llama 3. We find that Llama 3 delivers comparable quality to leading language models such as GPT-4 on a plethora of tasks. We publicly release Llama 3, including pre-trained and post-trained versions of the 405B parameter language model and our Llama Guard 3 model for input and output safety. The paper also presents the results of experiments in which we integrate image, video, and speech capabilities into Llama 3 via a compositional approach. We observe this approach performs competitively with the state-of-the-art on image, video, and speech recognition tasks. The resulting models are not yet being broadly released as they are still under development.

Given a closed subscheme $Z$ of a polarized abelian variety $(A,\ell)$ we define its vanishing threshold with respect to $\ell$ and relate it to the Seshadri constant of the ideal defining $Z.$ As a particular case, we introduce the notion of jets-separation thresholds, which naturally arise as the vanishing threshold of the $p$-infinitesimal neighborhood of a point. Afterwards, by means of Fourier-Mukai methods we relate the jets-separation thresholds with the surjectivity of certain higher Gauss-Wahl maps. As a consequence we obtain a criterion for the surjectivity of those maps in terms of the Seshadri constant of the polarization $\ell.$, Comment: 22 pages

In this paper we point out the natural relation between $\mathbb Q$-twisted objects of the derived category of abelian varieties, cohomological rank functions, and semihomogeneous vector bundles. We apply this to two basic classes of corresponding objects via the Fourier-Mukai-Poincar\'e transform: positive twists of the ideal sheaf of one point, and evaluation complexes of ample semihomogeneous vector bundles. This leads to $\mathbb Q^{\ge 0}$- graded section modules associated to line bundles on abelian varieties (containing the usual section rings), built by means of semihomogeneous vector bundles. We prove a duality relation between such section modules associated to dual polarizations. Other applications include formulas relating the thresholds of relevant cohomological rank functions appearing in this context. As a consequence we produce non-trivial obstructions to surjectivity of multiplication maps of global sections of certain line bundles., Comment: 19 pages

We show that quantum entanglement states are associated with multilinear polynomials that cannot be factored. By using these multilinear polynomials, we propose a geometric representation for entanglement states. In particular, we show that the Bell's states are associated with non-factorable real multilinear polynomial, which can be represented geometrically by three-dimensional surfaces. Furthermore, in this framework, we show that a quantum circuit can be seen as a geometric transformations of plane geometry. This phenomenon is analogous to gravity, where matter curves space-time. In addition, we show an analogy between quantum teleportation and operations involving multilinear polynomials., Comment: 16 pages, 2 figures. Minor corrections. Comments welcome

The first generation of ELT instruments includes an optical-infrared high-resolution spectrograph, indicated as ELT-HIRES and recently christened ANDES (ArmazoNes high Dispersion Echelle Spectrograph). ANDES consists of three fibre-fed spectrographs ([U]BV, RIZ, YJH) providing a spectral resolution of $\sim$100,000 with a minimum simultaneous wavelength coverage of 0.4-1.8 $\mu$m with the goal of extending it to 0.35-2.4 $\mu$m with the addition of a U arm to the BV spectrograph and a separate K band spectrograph. It operates both in seeing- and diffraction-limited conditions and the fibre feeding allows several, interchangeable observing modes including a single conjugated adaptive optics module and a small diffraction-limited integral field unit in the NIR. Modularity and fibre-feeding allow ANDES to be placed partly on the ELT Nasmyth platform and partly in the Coud\'e room. ANDES has a wide range of groundbreaking science cases spanning nearly all areas of research in astrophysics and even fundamental physics. Among the top science cases, there are the detection of biosignatures from exoplanet atmospheres, finding the fingerprints of the first generation of stars, tests on the stability of Nature's fundamental couplings, and the direct detection of the cosmic acceleration. The ANDES project is carried forward by a large international consortium, composed of 35 Institutes from 13 countries, forming a team of almost 300 scientists and engineers which include the majority of the scientific and technical expertise in the field that can be found in ESO member states., Comment: SPIE astronomical telescope and instrumentation 2024, in press

Here we resolve the real-space nature of the high-temperature, short-range charge correlations in the kagome metal ScV$_6$Sn$_6$. Diffuse scattering appears along a frustrated wave vector $\textbf{q}_H=(\frac{1}{3},\frac{1}{3},\frac{1}{2})$ at temperatures far exceeding the charge order transition $T_{CO}=92~\mathrm{K}$, preempting long-range charge order with wave vectors along $\textbf{q}_{\bar{K}}=(\frac{1}{3},\frac{1}{3},\frac{1}{3})$. Using a combination of real space and reciprocal space analysis, we resolve the nature of the interactions between the primary out-of-plane Sc-Sn chain instability and the secondary strain-mediated distortion of the in-plane V kagome network. A minimal model of the diffuse scattering data reveals a high-temperature, short-ranged "zig-zag" phase of in-plane correlations that maps to a frustrated triangular lattice Ising model with antiferromagnetic interactions and provides a real-space understanding of the origin of frustrated charge order in this material., Comment: 7 pages, 4 figures