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The photonic spin Hall effect (PSHE) in surface plasmon resonance (SPR) structures has great potential for various polarization-sensitive applications and devices. Here, using optical weak measurement, we observe spin-dependent and spin-independent angular shifts of the reflected beam, enhanced by SPR in a subwavelength nickel grating. An enhanced in-plane photonic spin Hall effect manifested in the angular splitting of circularly polarized photons with opposite helicity signs is demonstrated. We theoretically and experimentally demonstrate that angular in-plane shifts can be changed from spin-independent (Goos-Hanchen shift) to spin-dependent (PSHE) when the incident beam polarization state changes. The SPR-induced depolarization of light and the mixing of polarization states are analyzed. High purity of spin separation and a high degree of circular polarization are achieved with an optimal polarization state (preselection angle) and a resonance angle of incidence. The spineless spatial separation of two orthogonal components of the field with diagonal linear polarizations is demonstrated., Comment: 20 pages, 5 figures

We show a Springer type theorem for the variety of parabolic subgroups of type $1,2,6$ for all groups of type $E_6$. As far as we know this gives the first example for the validity of the Springer theorem for projective homogeneous varieties of type $^2E_6$ different from varieties of Borel subgroups. The proof combines several topics, notably the Rost invariant, a Tits construction, Cartan's symmetric spaces and indirectly the structure of the Chow motives of projective homogeneous varieties of exceptional type., Comment: 8 pages

Transformer-based recommender systems, such as BERT4Rec or SASRec, achieve state-of-the-art results in sequential recommendation. However, it is challenging to use these models in production environments with catalogues of millions of items: scaling Transformers beyond a few thousand items is problematic for several reasons, including high model memory consumption and slow inference. In this respect, RecJPQ is a state-of-the-art method of reducing the models' memory consumption; RecJPQ compresses item catalogues by decomposing item IDs into a small number of shared sub-item IDs. Despite reporting the reduction of memory consumption by a factor of up to 50x, the original RecJPQ paper did not report inference efficiency improvements over the baseline Transformer-based models. Upon analysing RecJPQ's scoring algorithm, we find that its efficiency is limited by its use of score accumulators for each item, which prevents parallelisation. In contrast, LightRec (a non-sequential method that uses a similar idea of sub-ids) reported large inference efficiency improvements using an algorithm we call PQTopK. We show that it is also possible to improve RecJPQ-based models' inference efficiency using the PQTopK algorithm. In particular, we speed up RecJPQ-enhanced SASRec by a factor of 4.5 x compared to the original SASRec's inference method and by a factor of 1.56 x compared to the method implemented in RecJPQ code on a large-scale Gowalla dataset with more than a million items. Further, using simulated data, we show that PQTopK remains efficient with catalogues of up to tens of millions of items, removing one of the last obstacles to using Transformer-based models in production environments with large catalogues., Comment: Accepted by RecSys 2024

We develop a formalism of poly-vector deformations for Type IIB backgrounds with a block diagonal metric and non-vanishing self-dual 5-form RR field strength. Making use of the embedding of the Type IIB theory into the $\mathrm{E}_{6(6)}$ exceptional field theory we derive explicit transformation rules for four-vector deformations. We prove that the algebraic condition following from the Type IIB realization of exceptional Drinfeld algebras is sufficient for the transformation to generate a solution., Comment: 23 pages + Appendix

YbOH molecule is one of the most sensitive systems for the electron electric dipole moment ($e$EDM) searches. Zeeman splittings of the $e$EDM sensitive levels have significant implications to control and suppress important systematic effects due to stray magnetic field in experiments for $e$EDM searches. The electric-field-dependent g factors of the lowest rotational level of the first excited bending vibrational mode of $^{174}$YbOH are calculated. l-doublet levels with small g factors difference are found and main contributions to the difference are determined.

In this work, we introduce Gemma 2, a new addition to the Gemma family of lightweight, state-of-the-art open models, ranging in scale from 2 billion to 27 billion parameters. In this new version, we apply several known technical modifications to the Transformer architecture, such as interleaving local-global attentions (Beltagy et al., 2020a) and group-query attention (Ainslie et al., 2023). We also train the 2B and 9B models with knowledge distillation (Hinton et al., 2015) instead of next token prediction. The resulting models deliver the best performance for their size, and even offer competitive alternatives to models that are 2-3 times bigger. We release all our models to the community.

In this paper, we study in detail various solutions, especially kink ones, in different nonlocal scalar field theories, whose kinetic term is described by an arbitrary non-polynomial analytic function of the d'Alembertian operator, and the potential is chosen either to be quadratic or to allow for the kink-like solution. Using the perturbative method, we find corrections of first and second orders in the nonlocality parameter around local solutions for several form factors and generate analytic expressions for the energy density up to the first order in this parameter. Additionally, we also address an inverse problem, that is, we reconstruct the potential corresponding to the given solution obtaining restrictions for the form factor., Comment: 22 pages, minor corrections, references added

We study random permutations arising from reduced pipe dreams. Our main model is motivated by Grothendieck polynomials with parameter $\beta=1$ arising in K-theory of the flag variety. The probability weight of a permutation is proportional to the principal specialization (setting all variables to 1) of the corresponding Grothendieck polynomial. By mapping this random permutation to a version of TASEP (Totally Asymmetric Simple Exclusion Process), we describe the limiting permuton and fluctuations around it as the order $n$ of the permutation grows to infinity. The fluctuations are of order $n^{\frac13}$ and have the Tracy-Widom GUE distribution, which places this algebraic (K-theoretic) model into the Kardar-Parisi-Zhang universality class. We also investigate non-reduced pipe dreams and make progress on a recent open problem on the asymptotic number of inversions of the resulting permutation. Inspired by Stanley's question for the maximal value of principal specializations of Schubert polynomials, we resolve the analogous question for $\beta=1$ Grothendieck polynomials, and provide bounds for general $\beta$., Comment: 46 pages; 16 figures; 2 tables. Including C code for generating random permutations and a CSV list of optimal layered permutations for beta=1 Grothendieck polynomials as ancillary files (see the right panel or the full source code)

To leverage the angular resolution of interferometry at high contrast, one must employ specialized beam-combiners called interferometric nullers. Nullers discard part of the astrophysical information to optimize the recording of light present in the dark fringe of the central source. Asgard/NOTT will deploy a beam-combination scheme offering good instrumental noise rejection when phased appropriately, but for which information is degenerate on the outputs, prompting a dedicated tuning strategy using the science detector. The dispersive effect of water vapor can be corrected with prisms forming a variable thickness of glass. But observations in the L band suffer from an additional and important chromatic effect due to longitudinal atmospheric dispersion coming from a resonance of CO2 at 4.3 micron. To compensate for this effect efficiently, a novel type of compensation device will be deployed leveraging a gas cell of variable length at ambient pressure. After reviewing the impact of water vapor and CO2, we present the design of this atmospheric dispersion compensation device and describe a strategy to maintain this tuning on-sky., Comment: 7 pages, 5 figures, Proc of SPIE Astronomical Telescopes + Instrumentation 2024 Yokohama, Japan, Optical and Infrared Interferometry and Imaging VI

Heavy meson decays with missing energy in the final state offer interesting avenues to search for light invisible new physics such as dark matter (DM). In this context, we show that such new physics (NP) interactions also affect lifetime difference in neutral meson-antimeson mixing. We consider general dimension-six effective quark interactions involving a pair of DM particles and calculate their contributions to lifetime difference in beauty and charm meson systems. We use the latest data on mixing observables to constrain the relevant effective operators. We find that lifetime differences provide novel and complementary flavor constraints compared to those obtained from heavy meson decays., Comment: 19 pages, 5 captioned figures, 1 table; v2: added Bs -> invisible constraint, matches published version

Precise millisecond pulsar (MSP) positions determined with very long baseline interferometry (VLBI) hold the key to building the connection between the kinematic and dynamic reference frames respectively used by VLBI and pulsar timing. The frame connection would provide an important pathway to examining the planetary ephemerides used in pulsar timing, and potentially enhancing the sensitivities of pulsar timing arrays used to detect stochastic gravitational-wave background at nano-Hz regime. We aim at significantly improving the VLBI-based MSP position from its current $\gtrsim1\,$mas precision level by reducing the two dominant components in the positional uncertainty -- the propagation-related uncertainty and the uncertainty resulting from the frequency-dependent core shifts of the reference sources. We introduce a new differential astrometry strategy of using multiple calibrators observed at several widely separated frequencies, which we call PINPT (Phase-screen Interpolation plus frequeNcy-dePendent core shifT correction; read as "pinpoint") for brevity. The strategy allows determination of the core-shift and mitigates the impact of residual delay in the atmosphere. We implemented the strategy on PSR J2222-0137, an MSP well constrained astrometrically with VLBI and pulsar timing. Using the PINPT strategy, we determined core shifts for 4 AGNs around PSR J2222-0137, and derived a VLBI-based pulsar position with uncertainty of 0.17 mas and 0.32 mas in right ascension and declination, respectively, approaching the uncertainty level of the best-determined timing-based MSP positions. The realization of the PINPT strategy promises a factor-of-5 positional precision enhancement (over conventional VLBI astrometry) for all kinds of compact radio sources observed at $\lesssim2$ GHz, including most fast radio bursts., Comment: 14 pages, 3 figures, 8 tables, accepted for publication in A&A

In a recent publication by Li $\textit{et al.}$, two phases of beryllene - $\alpha$ and $\beta$ - were predicted to be single-gap superconductors with critical temperatures of 9.9 K and 12.6 K respectively. Moreover, the $\alpha$-beryllene was shown to host type-I Dirac fermions with the existence of nontrivial edge states. We observe significantly weaker superconducting properties of both beryllene configurations. We argue that the superconducting gap evolution with temperature, as shown in Figure 5 (b and d) of Li $\textit{et al.}$, exhibits clearly unphysical trends with increasing temperature, leading to significantly overestimated values of the critical temperature and erroneous conclusions concerning the two-gap superconducting nature of $\beta$-beryllene. On a positive note, we report the value of the gap in the Dirac cone of the topological states of interest that exceeds the temperature range of superconductivity in $\alpha$-beryllene, supporting the coexistence of topological features and superconductivity in this material., Comment: Comment on https://doi.org/10.1016/j.mtphys.2023.101257

We conduct a reverberation mapping (RM) campaign to spectroscopically monitor a sample of selected bright active galactic nuclei with large anticipated broad-line region (BLR) sizes adequate for spectroastrometric observations by the GRAVITY instrument on the Very Large Telescope Interferometer. We report the first results for five objects, IC 4329A, Mrk 335, Mrk 509, Mrk 1239, and PDS 456, among which Mrk 1239 and PDS 456 are for the first time spectroscopically monitored. We obtain multi-year monitoring data and perform multi-component spectral decomposition to extract the broad H$\beta$ profiles. We detect significant time lags between the H$\beta$ and continuum variations, generally obeying the previously established BLR size-luminosity relation. Velocity-resolved H$\beta$ time lags illustrate diverse, possibly evolving BLR kinematics. We further measure the H$\beta$ line widths from mean and rms spectra and the resulting virial products show good consistency among different seasons. Adopting a unity virial factor and the full width at half maximum of the broad H$\beta$ line from the mean spectrum as the measure of velocity, the obtained black hole mass averaged over seasons is $\log M_\bullet/M_\odot=8.02_{-0.14}^{+0.09}$, $6.92_{-0.12}^{+0.12}$, $8.01_{-0.25}^{+0.16}$, $7.44_{-0.14}^{+0.13}$, and $8.59_{-0.11}^{+0.07}$ for the five objects, respectively. The black hole mass estimations using other line width measures are also reported (up to the virial factors). For objects with previous RM campaigns, our mass estimates are in agreement with earlier results. In a companion paper, we will employ BLR dynamical modeling to directly infer the black hole mass and thereby determine the virial factors., Comment: 32 pages, 6 tables, 20 figures. To appear in ApJ

We formulate a new class of modified gravity models, that is, generalized four-dimensional Chern-Pontryagin models, whose action is characterized by an arbitrary function of the Ricci scalar $R$ and the Chern-Pontryagin topological term ${}^*RR$, i.e., $f(R, {}^*RR)$. Within this framework, we derive the gravitational field equations and solve them for a particular model, $f(R, {}^*RR)=R+\beta ({}^*RR)^2$, considering two ansatzes: the slowly rotating metric and first-order perturbations of G\"{o}del-type metrics. For the former, we find a first-order correction to the frame-dragging effect boosted by the parameter $L$, which characterizes the departures from general relativity results. For the latter, G\"{o}del-type metrics hold unperturbed. We conclude this paper by displaying that generalized four-dimensional Chern-Pontryagin models admit a scalar-tensor representation, whose explicit form presents two scalar fields: $\Phi$, a dynamical degree of freedom, while the second, $\vartheta$, a non-dynamical degree of freedom. In particular, the scalar field $\vartheta$ emerges coupled with the Chern-Pontryagin topological term ${}^*RR$, i.e., $\vartheta {}^*RR$, which is nothing more than Chern-Simons term., Comment: 23 pages, version accepted to EPJ C

The Spin Physics Detector collaboration proposes to install a universal detector in the second interaction point of the NICA collider under construction (JINR, Dubna) to study the spin structure of the proton and deuteron and other spin-related phenomena using a unique possibility to operate with polarized proton and deuteron beams at a collision energy up to 27 GeV and a luminosity up to $10^{32}$ cm$^{-2}$ s$^{-1}$. As the main goal, the experiment aims to provide access to the gluon TMD PDFs in the proton and deuteron, as well as the gluon transversity distribution and tensor PDFs in the deuteron, via the measurement of specific single and double spin asymmetries using different complementary probes such as charmonia, open charm, and prompt photon production processes. Other polarized and unpolarized physics is possible, especially at the first stage of NICA operation with reduced luminosity and collision energy of the proton and ion beams. This document is dedicated exclusively to technical issues of the SPD setup construction.

In this paper, we study the one-loop effective potential of a derivative four-fermion model. As a result, an exact bumblebee-like potential is radiatively generated. Afterwards, we generalize our study for a finite temperature case and explicitly demonstrate the possibility of phase transitions allowing for the restoration of the Lorentz symmetry. We also investigate the low-energy effective action, from which we obtain the usual kinetic term and the corresponding bumblebee potential., Comment: 14 pages, version accepted to EPJ C

In this study, we investigate the signatures of a non-commutative black hole solution. Initially, we calculate the thermodynamic properties of the system, including entropy, heat capacity, and Hawking radiation. For the latter quantity, we employ two distinct methods: surface gravity and the topological approach. Additionally, we examine the emission rate and remnant mass within this context. Remarkably, the lifetime of the black hole, after reaching its final state due to the evaporation process, is expressed analytically up to a grey-body factor. We estimate the lifetime for specific initial and final mass configurations. Also, we analyze the tensorial quasinormal modes using the 6th-order WKB method. Finally, we study the deflection angle, i.e., gravitational lensing, in both the weak and strong deflection limits., Comment: 27 pages, 13 figures and 4 tables

We present a baseline science operations plan for the Black Hole Explorer (BHEX), a space mission concept aiming to confirm the existence of the predicted sharp ``photon ring" resulting from strongly lensed photon trajectories around black holes, as predicted by general relativity, and to measure its size and shape to determine the black hole's spin. BHEX will co-observe with a ground-based very long baseline interferometric (VLBI) array at high-frequency radio wavelengths, providing unprecedented high resolution with the extension to space that will enable photon ring detection and studies of active galactic nuclei. Science operations require a simultaneous coordination between BHEX and a ground array of large and small radio apertures to provide opportunities for surveys and imaging of radio sources, while coordination with a growing network of optical downlink terminals provides the data rates necessary to build sensitivity on long baselines to space. Here we outline the concept of operations for the hybrid observatory, the available observing modes, the observation planning process, and data delivery to achieve the mission goals and meet mission requirements., Comment: 12 pages, 10 figures, submitted to SPIE Astronomical Telescopes + Instrumentation (AS24)

Fine-tuning large language models on small, high-quality datasets can enhance their performance on specific downstream tasks. Recent research shows that fine-tuning on benign, instruction-following data can inadvertently undo the safety alignment process and increase a model's propensity to comply with harmful queries. Although critical, understanding and mitigating safety risks in well-defined tasks remains distinct from the instruction-following context due to structural differences in the data. Our work addresses the gap in our understanding of these risks across diverse types of data in closed models - where providers control how user data is utilized in the fine-tuning process. We demonstrate how malicious actors can subtly manipulate the structure of almost any task-specific dataset to foster significantly more dangerous model behaviors, while maintaining an appearance of innocuity and reasonable downstream task performance. To address this issue, we propose a novel mitigation strategy that mixes in safety data which mimics the task format and prompting style of the user data, showing this is more effective than existing baselines at re-establishing safety alignment while maintaining similar task performance.

This paper explores the renormalization of scale-free quadratic gravity coupled to the bumblebee field and its potential for dynamically breaking Lorentz symmetry. We conduct one-loop renormalization of the model and calculate the associated renormalization group functions. Furthermore, we compute the one-loop effective potential for the bumblebee field, demonstrating that it acquires a non-trivial vacuum expectation value (VEV) through radiative corrections -- a phenomenon known as the Coleman-Weinberg mechanism. This spontaneous breaking of scale invariance, driven by the non-zero VEV of the bumblebee field, leads to Lorentz symmetry violation. As a result, the non-minimal coupling between the bumblebee and gravitational fields induces a spontaneous generation of an Einstein-Hilbert term via radiative corrections, suggesting a possible link between the Planck scale and Lorentz violation phenomena., Comment: 21 pages, references added, version accepted to PRD

Using partial knowledge of a quantum state to control multiqubit entanglement is a largely unexplored paradigm in the emerging field of quantum interactive dynamics with the potential to address outstanding challenges in quantum state preparation and compression, quantum control, and quantum complexity. We present a deep reinforcement learning (RL) approach to constructing short disentangling circuits for arbitrary 4-, 5-, and 6-qubit states using an actor-critic algorithm. With access to only two-qubit reduced density matrices, our agent decides which pairs of qubits to apply two-qubit gates on; requiring only local information makes it directly applicable on modern NISQ devices. Utilizing a permutation-equivariant transformer architecture, the agent can autonomously identify qubit permutations within the state, and adjusts the disentangling protocol accordingly. Once trained, it provides circuits from different initial states without further optimization. We demonstrate the agent's ability to identify and exploit the entanglement structure of multiqubit states. For 4-, 5-, and 6-qubit Haar-random states, the agent learns to construct disentangling circuits that exhibit strong correlations both between consecutive gates and among the qubits involved. Through extensive benchmarking, we show the efficacy of the RL approach to find disentangling protocols with minimal gate resources. We explore the resilience of our trained agents to noise, highlighting their potential for real-world quantum computing applications. Analyzing optimal disentangling protocols, we report a general circuit to prepare an arbitrary 4-qubit state using at most 5 two-qubit (10 CNOT) gates., Comment: The source code as well as a demo in the form of an interactive Jupyter notebook are available on Github: https://github.com/mgbukov/RL_disentangle

For decades, the terahertz (THz) frequency band had been primarily explored in the context of radar, imaging, and spectroscopy, where multi-gigahertz (GHz) and even THz-wide channels and the properties of terahertz photons offered attractive target accuracy, resolution, and classification capabilities. Meanwhile, the exploitation of the terahertz band for wireless communication had originally been limited due to several reasons, including (i) no immediate need for such high data rates available via terahertz bands and (ii) challenges in designing sufficiently high power terahertz systems at reasonable cost and efficiency, leading to what was often referred to as "the terahertz gap". This roadmap paper first reviews the evolution of the hardware design approaches for terahertz systems, including electronic, photonic, and plasmonic approaches, and the understanding of the terahertz channel itself, in diverse scenarios, ranging from common indoors and outdoors scenarios to intra-body and outer-space environments. The article then summarizes the lessons learned during this multi-decade process and the cutting-edge state-of-the-art findings, including novel methods to quantify power efficiency, which will become more important in making design choices. Finally, the manuscript presents the authors' perspective and insights on how the evolution of terahertz systems design will continue toward enabling efficient terahertz communications and sensing solutions as an integral part of next-generation wireless systems., Comment: 31 pages. Accepted to the Proceedings of the IEEE, 2024. \c{opyright}2024 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material, creating new works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

Supermassive black hole binaries (SMBHBs) present us with exciting opportunities for multi-messenger science. These systems are thought to form naturally in galaxy mergers and therefore have the potential to produce electromagnetic (EM) radiation as well as gravitational waves (GWs) detectable with pulsar timing arrays (PTAs). Once GWs from individually resolved SMBHBs are detected, the identification of the host galaxy will be a major challenge due to the ambiguity in possible EM signatures and the poor localization capability of PTAs. In order to aid EM observations in choosing which sources to follow up, we attempt to quantify the number of plausible hosts in both realistic and idealistic scenarios. We outline a host galaxy identification pipeline that injects a single-source GW signal into a simulated PTA dataset, uses production-level techniques to recover the signal, quantifies the localization region and number of galaxies contained therein, and finally imposes cuts on the galaxies using the binary parameters estimated from the GW search. In an ideal case, we find that the 90% credible areas span 29 deg^2 to 241 deg^2, containing about 14 to 341 galaxies. After cuts, the number of galaxies remaining ranges from 22 at worst to 1 (the true host) at best. In a more realistic case, if the signal is sufficiently localized, the sky areas range from 287 deg^2 to 530 deg^2 and enclose about 285 to 1238 galaxies. After cuts, the number of galaxies is 397 at worst and 27 at best. While the signal-to-noise ratio is the primary determinant of the localization area of a given source, we find that the size of the area is also influenced by the proximity of nearby pulsars on the sky and the chirp mass of the source., Comment: Published in ApJ

Observations of the rotational spectrum of lead monofluoride, PbF, have been extended up to transitions in the \textit{v} = 7 level for $^{208}$PbF in the lowest $X_1\,^2\Pi_{1/2}$ state of the radical and \textit{v} = 5 for the $^{207}$Pb and $^{206}$Pb isotopologues. The data also include a few measurements for $^{204}$PbF in \textit{v} = 0. These new measurements have been combined with existing near-IR measurements of the $X_2 - X_1$ fine-structure transition and a simultaneous multi-isotope fit of the data to an effective isotope-independent ro-vibronic Hamiltonian has been carried out. The resulting parameters fully characterize the vibrational, rotational and hyperfine structure of the combined $X_1 \, / \, X_2$ state of the radical. A pair of opposite parity levels with total angular momentum quantum number, $F=1/2$, in the lowest rotational level, $J=1/2$ of \PbF \,are close in energy and their spacing decreases with vibrational excitation. The experimental results show the spacing decreases to less than 20 MHz at $v=7$ and 8. The experimental work is complemented by new \textit{ab initio} calculations which support the results and allow predictions outside the experimental data range. The calculated radiative lifetimes of the relevant vibrationally excited states are of the order of 50 ms. This work was motivated by interest in using \PbF\, as a vehicle for future probes of the standard model of physics such as placing limits on the electron's electric dipole moment (\eEDM), molecular charge-parity non-conservation and Born-Oppenheimer breakdown effects for example., Comment: 36 pages, 4 figures, 5 page Appendix. Accepted by Phys FRev A, 2024-09-04

Zero-shot and in-context learning enable solving tasks without model fine-tuning, making them essential for developing generative model solutions. Therefore, it is crucial to understand whether a pretrained model can be prompted to approximate any function, i.e., whether it is a universal in-context approximator. While it was recently shown that transformer models do possess this property, these results rely on their attention mechanism. Hence, these findings do not apply to fully recurrent architectures like RNNs, LSTMs, and the increasingly popular SSMs. We demonstrate that RNNs, LSTMs, GRUs, Linear RNNs, and linear gated architectures such as Mamba and Hawk/Griffin can also serve as universal in-context approximators. To streamline our argument, we introduce a programming language called LSRL that compiles to these fully recurrent architectures. LSRL may be of independent interest for further studies of fully recurrent models, such as constructing interpretability benchmarks. We also study the role of multiplicative gating and observe that architectures incorporating such gating (e.g., LSTMs, GRUs, Hawk/Griffin) can implement certain operations more stably, making them more viable candidates for practical in-context universal approximation., Comment: Published at NeurIPS 2024, Code at https://github.com/AleksandarPetrov/LSRL

Quantum photon effects in vacuum provide an interesting setting to test quantum electrodynamics, serving as a source for predictions about physics beyond the Standard Model. In this paper, we investigate these effects by calculating the one-loop Euler-Heisenberg-like effective action within a Lorentz-violating scalar quantum electrodynamics framework. In both CPT-even and CPT-odd scenarios, we obtain the exact result in all orders of the stress tensor $F_{\mu\nu}$ and evaluate explicitly the lower orders of this effective action. We identify the quantum effects coming from Lorentz violation in an explicitly gauge invariant way. Nonlinear Lorentz-violating contributions that may affect photon-photon scattering are explicitly evaluated., Comment: 9 pages

Context: MATISSE, the mid-infrared spectro-imaging instrument of VLTI, was designed to deliver its advertised performance when paired with an external second generation fringe tracker. Science observation started in 2019, demonstrating imaging capabilities and faint science target observations. Now, The GRAVITY fringe tracker stabilizes the MATISSE fringes which allows using all spectroscopic modes and improves sensitivity and data accuracy. Aims: We present how the MATISSE and GRAVITY instruments were adapted to make the GRAVITY fringe tracker work with MATISSE, under the umbrella of the aptly-named GRA4MAT project, led by ESO in collaboration with the two instrument consortia. Methods: We detail the software modifications needed to implement an acquisition and observing sequence specific to GRA4MAT, including simultaneous fringe tracking and chopping and a narrow off-axis capability inspired by the galactic center and exoplanet capability of GRAVITY. We explain the modified data collection and reduction processes. We show how we leveraged the recent fringe tracker upgrade to implement features specific to its use with MATISSE, e.g. fringe jumps mitigation with an improved group delay control and simultaneous fringe tracking and chopping with a new state machine. Results: We successfully demonstrate significant improvements to the MATISSE instrument. Observations can now be performed at higher spectral resolutions of up to $R\sim3300$ and across the full LM bands at once. Long detector integration times, made possible with stabilized fringes, have improved the LM-bands sensitivity by a factor of 10. Low flux biases in coherently-reduced N-band data have been eliminated. The L-band transfer function is now higher and more stable. We finally illustrate the scientific potential of GRA4MAT with a preview of the first exoplanet observation made by MATISSE on $\beta$ Pictoris b., Comment: Revised after language editing

We consider polynomials $Q:=\sum _{j=0}^da_jx^j$, $a_j\in \mathbb{R}^*$, with all roots real. When the {\em sign pattern} $\sigma (Q):=({\rm sgn}(a_d),{\rm sgn}(a_{d-1})$, $\ldots$, ${\rm sgn}(a_0))$ has $\tilde{c}$ sign changes, the polynomial $Q$ has $\tilde{c}$ positive and $d-\tilde{c}$ negative roots. We suppose the moduli of these roots distinct. The {\em order} of these moduli is defined when in their string as points of the positive half-axis one marks the places of the moduli of negative roots. A sign pattern $\sigma^0$ is {\em universal} when for any possible order of the moduli there exists a polynomial $Q$ with $\sigma (Q)=\sigma^0$ and with this order of the moduli of its roots. We show that when the polynomial $P_{m,n}:=(x-1)^m(x+1)^n$ has no vanishing coefficients, the sign pattern $\sigma (P_{m,n})$ is universal. We also study the question when $P_{m,n}$ can have vanishing coefficients.

Federated learning works by aggregating locally computed gradients from multiple clients, thus enabling collaborative training without sharing private client data. However, prior work has shown that the data can actually be recovered by the server using so-called gradient inversion attacks. While these attacks perform well when applied on images, they are limited in the text domain and only permit approximate reconstruction of small batches and short input sequences. In this work, we propose DAGER, the first algorithm to recover whole batches of input text exactly. DAGER leverages the low-rank structure of self-attention layer gradients and the discrete nature of token embeddings to efficiently check if a given token sequence is part of the client data. We use this check to exactly recover full batches in the honest-but-curious setting without any prior on the data for both encoder- and decoder-based architectures using exhaustive heuristic search and a greedy approach, respectively. We provide an efficient GPU implementation of DAGER and show experimentally that it recovers full batches of size up to 128 on large language models (LLMs), beating prior attacks in speed (20x at same batch size), scalability (10x larger batches), and reconstruction quality (ROUGE-1/2 > 0.99).