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Quantum annealing and quantum approximate optimization algorithms hold a great potential to speed-up optimization problems. This could be game-changing for a plethora of applications. Yet, in order to hope to beat classical solvers, quantum circuits must scale up to sizes and performances much beyond current hardware. In that quest, intense experimental effort has been recently devoted to optimizations on 3-regular graphs, which are computationally hard but experimentally relatively amenable. However, even there, the amount and quality of quantum resources required for quantum solvers to outperform classical ones is unclear. Here, we show that quantum annealing for 3-regular graphs can be classically simulated even at scales of 1000 qubits and 5000000 two-qubit gates with all-to-all connectivity. To this end, we develop a graph tensor-network quantum annealer (GTQA) able of high-precision simulations of Trotterized circuits of near-adiabatic evolutions. Based on a recently proposed belief-propagation technique for tensor canonicalization, GTQA is equipped with re-gauging and truncation primitives that keep approximation errors small in spite of the circuits generating significant amounts of entanglement. As a result, even with a maximal bond dimension as low as 4, GTQA produces solutions competitive with those of state-of-the-art classical solvers. For non-degenerate instances, the unique solution can be read out from the final reduced single-qubit states. In contrast, for degenerate problems, such as MaxCut, we introduce an approximate measurement simulation algorithm for graph tensor-network states. On one hand, our findings showcase the potential of GTQA as a powerful quantum-inspired optimizer. On the other hand, they considerably raise the bar required for experimental demonstrations of quantum speed-ups in combinatorial optimizations., Comment: Preliminary version

Recent determinations of the total rate of the 12C+12C nuclear reaction show non-negligible differences with the reference reaction rate commonly used in previous stellar simulations. In addition, the current uncertainties in determining each exit channel constitute one of the main uncertainties in shaping the inner structure of super asymptotic giant branch stars that could have a measurable impact on the properties of pulsating ultra-massive white dwarfs (WDs). We explore how new determinations of the nuclear reaction rate and its branching ratios affect the evolution of WD progenitors. We show that the current uncertainties in the branching ratios constitute the main uncertainty factor in determining the inner composition of ultra-massive WDs and their progenitors. We found that the use of extreme branching ratios leads to differences in the central abundances of 20Ne of at most 17%, which are translated into differences of at most 1.3 and 0.8% in the cooling times and size of the crystallized core. However, the impact on the pulsation properties is small, less than 1 s for the asymptotic period spacing. We found that the carbon burns partially in the interior of ultra-massive WD progenitors within a particular range of masses, leaving a hybrid CONe-core composition in their cores. The evolution of these new kinds of predicted objects differs substantially from the evolution of objects with pure CO cores. Differences in the size of the crystallized core and cooling times of up to 15 and 6%, respectively leading to distinct patterns in the period spacing distribution., Comment: 12 pages, 14 figures. Accepted for publication in ApJ

Using Ostaszewski's $\clubsuit$-principle, we construct a non-metrizable, locally compact, scattered space $L$ in which the operators on the Banach space $C_0(L \times L)$ exhibit a remarkably simple structure. We provide a detailed analysis and, through a series of decomposition steps, offer an explicit characterization of all operators on $C_0(L \times L)$.

Context. S26 is an extragalactic microquasar with the most powerful jets ever discovered. They have a kinetic luminosity of $L_{\rm j}\sim5\times 10^{40}\,{\rm erg\,s^{-1}}$. This implies that the accretion power to the black hole should be super-Eddington, of the order of $L_{\rm acc}\sim L_{\rm j}$. However, the observed X-ray flux of this system indicates an apparent very sub-Eddington accretion luminosity of $L_{\rm X}\approx 10^{37}\,{\rm erg\,s^{-1}}$. Aims. We aim to characterize the nature of S26, explain the system emission, and study the feasibility of super-Eddington microquasars as potential PeVatron sources. Methods. We first analyze X-ray observations of S26 obtained with XMM-Newton and model the super-Eddington disk and its wind. We then develop a jet model and study the particle acceleration and radiative processes that occur in shocks generated near the base of the jet and in its terminal region. Results. We find that the discrepancy between the jet and the apparent disk luminosities in S26 is caused by the complete absorption of the disk radiation by the wind ejected from the super-Eddington disk. The nonthermal X-rays are produced near the base of the jet, and the thermal X-rays are emitted in the terminal regions. The radio emission observed with the Australia Telescope Compact Array can be explained as synchrotron radiation produced at the reverse shock in the lobes. We also find that S26 can accelerate protons to PeV energies in both the inner jet and the lobes. The ultra-high energy protons accelerated in the lobes are injected into the ISM with a total power of $\sim 10^{36}\,{\rm erg\,s^{-1}}$. Conclusions. We conclude that S26 is a super-Eddington microquasar with a dense disk-driven wind that obscures the X-ray emission from the inner disk, and that the supercritical nature of the system allows the acceleration of cosmic rays to PeV energies., Comment: 14 pages, accepted for publication in A&A

Supermassive black holes (SMBHs) at the centers of active galaxies are fed by accretion disks that radiate from the infrared or optical to the X-ray bands. Several types of objects can orbit SMBHs, including massive stars, neutron stars, clouds from the broad- and narrow-line regions, and X-ray binaries. Isolated black holes with a stellar origin (BHs of $\sim10\,M_{\odot}$) should also be present in large numbers within the central parsec of the galaxies. These BHs are expected to form a cluster around the SMBH as a result of the enhanced star formation rate in the inner galactic region and the BH migration caused by gravitational dynamical friction. However, except for occasional microlensing effects on background stars or gravitational waves from binary BH mergers, the presence of a BH population is hard to verify. In this paper, we explore the possibility of detecting electromagnetic signatures of a central cluster of BHs when the accretion rate onto the central SMBH is greater than the Eddington rate. In these supercritical systems, the accretion disk launches powerful winds that interact with the objects orbiting the SMBH. Isolated BHs can capture matter from this dense wind, leading to the formation of small accretion disks around them. If jets are produced in these "single" microquasars, they could be sites of particle acceleration to relativistic energies. These particles in turn are expected to cool by various radiative processes. Therefore, the wind of the SMBH might illuminate the BHs through the production of both thermal and nonthermal radiation. We conclude that, under these circumstances, a cluster of isolated BHs could be detected at X-rays (with Chandra and XMM-Newton) and radio wavelengths (e.g., with the Very Large Array and the Square Kilometer Array) in the center of nearby super-Eddington galaxies., Comment: 11 pages, accepted for publication in A&A

A central challenge in the field of stellar astrophysics lies in accurately determining the mass of isolated stars. However, for pulsating white dwarf (WD) stars, the task becomes more tractable due to the availability of multiple approaches such as spectroscopy, asteroseismology, astrometry, and photometry. The objective of this work is to compare the asteroseismological and spectroscopic mass values of WDs in detail and, in turn, to compare them with the masses derived using astrometric parallaxes/distances and photometry. Our analysis encompasses a selection of pulsating WDs with different surface chemical abundances that define the main classes of variable WDs. We calculated their spectroscopic masses, compiled seismological masses, and determined astrometric masses. We also derived photometric masses, when possible. Subsequently, we compared all the sets of stellar masses obtained through these different methods. To ensure consistency and robustness in our comparisons, we used identical WD models and evolutionary tracks across all four methods. The analysis suggests a general consensus among the these methods regarding the masses of pulsating WD with H-rich atmospheres, known as DAV or ZZ Ceti stars, especially for objects with masses below approximately $0.75 M_{\sun}$, although notable disparities emerge for certain massive stars. For pulsating WD stars with He-rich atmospheres, called DBV or V777 Her stars, we find that astrometric masses generally exceed seismological, spectroscopic, and photometric masses. Finally, while there is agreement among the sets of stellar masses for pulsating WDs with C-, O-, and He-rich atmospheres (designated as GW Vir stars), outliers exist where mass determinations by various methods show significant discrepancies., Comment: 24 pages, 25 figures, 8 tables. To be published in Astronomy and Astrophysics

Barred galaxies exhibit boxy/peanut or X-shapes (BP/X) protruding from their disks in edge-on views. Two types of BP/X morphologies exist depending on whether the X-wings meet at the center (CX) or are off-centered (OX). Orbital studies indicate that various orbital types can generate X-shaped structures. Here, we provide a classification approach that identifies the specific orbit families responsible for generating OX and CX-shaped structures. Applying this approach to three different N-body bar models, we show that both OX and CX structures are associated with the x1 orbit family, but OX-supporting orbits possess higher angular momentum (closer to x1 orbits) than orbits in CX structures. Consequently, as the bar slows down the contribution of higher angular momentum OX-supporting orbits decreases and that of lower angular momentum orbits increases resulting in an evolution of the morphology from OX to CX. If the bar does not slow down, the shape of the BP/X structure and the fractions of OX/CX supporting orbits remain substantially unchanged. Bars that do not undergo buckling but that do slow down initially show the OX structure and are dominated by high angular momentum orbits, transitioning to a CX morphology. Bars that buckle exhibit a combination of both OX and CX supporting orbits immediately after the buckling, but become more CX dominated as their pattern speed decreases. This study demonstrates that the evolution of BP/X morphology and orbit populations strongly depends on the evolution of the bar angular momentum., Comment: 16 pages, 12 figures, Accepted for publication in ApJ

The controlled assembly of twisted 2D structures requires precise determination of the crystal orientation of their component layers. In the established procedure, the second-harmonic generation (SHG) intensity of a noncentrosymmetric layer is recorded while rotating the polarization of both the incident laser field and detected SHG, which can be time-consuming and tedious. Here, we demonstrate that the crystal orientation of transition metal dichalcogenides and hexagonal boron nitride can be directly determined by recording SHG images generated by tightly focused laser beams in Fourier space. Using an azimuthally polarized laser beam, the SHG image distinctly reflects the hexagonal structure of the crystal lattice, revealing its orientation quickly and accurately. This technique could significantly impact the field of twistronics, which studies the effects of the relative angle between the layers of a stacked 2D structure, as well as advances the nanofabrication of 2D materials., Comment: 22 (35) pages, 6 (12) figures (including Supplementary Information)

A model for the current-voltage characteristic of the junction between an Ion-Sensitive-Membrane and an electrolyte solution is derived and compared with numerical simulations of the Poisson-Nernst-Planck model for ion transport. The expression resembles that of a semiconductor pn junction with a non-ideality factor of 2. The non-ideality correlated to the voltage drop in the electrolyte induced by the re-arrangement of the counter-ions., Comment: 12 pages, 4 figures, 1 table

Document summarization is a task to shorten texts into concise and informative summaries. This paper introduces a novel dataset designed for summarizing multiple scientific articles into a section of a survey. Our contributions are: (1) SurveySum, a new dataset addressing the gap in domain-specific summarization tools; (2) two specific pipelines to summarize scientific articles into a section of a survey; and (3) the evaluation of these pipelines using multiple metrics to compare their performance. Our results highlight the importance of high-quality retrieval stages and the impact of different configurations on the quality of generated summaries., Comment: 15 pages, 6 figures, 1 table. Submitted to BRACIS 2024

We study classes of constant-depth circuits with gates that compute restricted polynomial threshold functions, recently introduced by [Kum23] as a family that strictly generalizes $\mathsf{AC}^0$. Denoting these circuit families $\mathsf{bPTFC}^0[k]$ for $\textit{bounded polynomial threshold circuits}$ parameterized by an integer-valued degree-bound $k$, we prove three hardness results separating these classes from constant-depth quantum circuits ($\mathsf{QNC}^0$). $\hspace{2em}$ - We prove that the parity halving problem [WKS+19], which $\mathsf{QNC}^0$ over qubits can solve with certainty, remains average-case hard for polynomial size $\mathsf{bPTFC}^0[k]$ circuits for all $k=\mathcal{O}(n^{1/(5d)})$. $\hspace{2em}$ - We construct a new family of relation problems based on computing $\mathsf{mod}\ p$ for each prime $p>2$, and prove a separation of $\mathsf{QNC}^0$ circuits over higher dimensional quantum systems (`qupits') against $\mathsf{bPTFC}^0[k]$ circuits for the same degree-bound parameter as above. $\hspace{2em}$ - We prove that both foregoing results are noise-robust under the local stochastic noise model, by introducing fault-tolerant implementations of non-Clifford $\mathsf{QNC}^0/|\overline{T^{1/p}}>$ circuits, that use logical magic states as advice. $\mathsf{bPTFC}^0[k]$ circuits can compute certain classes of Polynomial Threshold Functions (PTFs), which in turn serve as a natural model for neural networks and exhibit enhanced expressivity and computational capabilities. Furthermore, for large enough values of $k$, $\mathsf{bPTFC}^0[k]$ contains $\mathsf{TC}^0$ as a subclass. The main challenges we overcome include establishing classical average-case lower bounds, designing non-local games with quantum-classical gaps in winning probabilities and developing noise-resilient non-Clifford quantum circuits necessary to extend beyond qubits to higher dimensions.

Objective: Inclusion of individualised electrical conductivities of head tissues is crucial for the accuracy of electrical source imaging techniques based on electro/magnetoencephalography and the efficacy of transcranial electrical stimulation. Parametric electrical impedance tomography (pEIT) is a method to cheaply and non-invasively estimate them using electrode arrays on the scalp to apply currents and measure the resulting potential distribution. Conductivities are then estimated by iteratively fitting a forward model to the measurements, incurring a prohibitive computational cost that is generally lowered at the expense of accuracy. Reducing the computational cost associated with the forward solutions would improve the accessibility of this method and unlock new capabilities. Approach: We introduce reduced order modelling (ROM) to massively speed up the calculations of these solutions for arbitrary conductivity values. Main results: We demonstrate this new ROM-pEIT framework using a realistic head model with six tissue compartments, with minimal errors in both the approximated numerical solutions and conductivity estimations. We show that the computational complexity required to reach a multi-parameter estimation with a negligible relative error is reduced by more than an order of magnitude when using this framework. Furthermore, we illustrate the benefits of this new framework in a number of practical cases, including its application to real pEIT data from three subjects. Significance: Results suggest that this framework can transform the use of pEIT for seeking personalised head conductivities, making it a valuable tool for researchers and clinicians.

To enhance the field of continuous motor health monitoring, we present FAN-COIL-I, an extensive vibration sensor dataset derived from a Fan Coil motor. This dataset is uniquely positioned to facilitate the detection and prediction of motor health issues, enabling a more efficient maintenance scheduling process that can potentially obviate the need for regular checks. Unlike existing datasets, often created under controlled conditions or through simulations, FAN-COIL-I is compiled from real-world operational data, providing an invaluable resource for authentic motor diagnosis and predictive maintenance research. Gathered using a high-resolution 32KHz sampling rate, the dataset encompasses comprehensive vibration readings from both the forward and rear sides of the Fan Coil motor over a continuous two-week period, offering a rare glimpse into the dynamic operational patterns of these systems in a corporate setting. FAN-COIL-I stands out not only for its real-world applicability but also for its potential to serve as a reliable benchmark for researchers and practitioners seeking to validate their models against genuine engine conditions.

Although protons are baryons with an overall vanishing lepton number, they possess a non-trivial leptonic content arising from quantum fluctuations which can be described by lepton parton distribution functions (PDFs) of the proton. These PDFs have been recently computed and can be used to define lepton-induced processes at high-energy colliders. In this article, we propose a novel way to test the computation of lepton PDFs of the proton by analyzing both non-resonant di-lepton and resonant Z gauge boson production processes induced by leptons within the proton at proton-electron colliders like HERA and EIC. Despite the fact that lepton PDFs of the proton are known to be small, this work demonstrates that both processes imply a measurable yield of events at HERA and EIC, which could be used to test these PDFs., Comment: 9 pages, 5 figures, 1 table

We report the results of a statistical study of cyclical period changes in cataclysmic variables (CVs). Assuming the third-body hypothesis as the cause of period changes, we estimate the third-body mass, $m_3$, and its separation from the binary, $a_3$, for 21 CVs showing cyclical period changes from well-sampled observed-minus-calculated diagrams covering more than a decade of observations. The inferred $a_3$ values are independent of the binary orbital period, $P_\mathrm{orb}$, whereas the $m_3$ values increase with $P_\mathrm{orb}$ by an order of magnitude from the shortest period (oldest) to the longest period (youngest) systems, implying significant mass loss from the third body with time. A model for the time evolution of the triple system is not able to simultaneously explain the observed behavior of the $m_3(P_\mathrm{orb})$ and $a_3(P_\mathrm{orb})$ distributions because the combined mass loss from the binary and the third body demands an increase in orbital separation by factors $\sim 140$ as the binary evolves toward shorter $P_\mathrm{orb}$'s, in clear disagreement with the observed distribution. We conclude that the third-body hypothesis is statistically inconsistent and cannot be used to explain cyclical period changes observed in CVs. On the other hand, the diagram of the amplitude of the period change versus the CV donor-star mass is consistent both with the alternative hypothesis that the observed cyclical period changes are a consequence of magnetic activity in the solar-type donor star, and with the standard evolutionary scenario for CVs., Comment: 12 pages, 2 figures, prepared with AASLatex; to appear in The Astrophysical Journal

In recent years, deep learning techniques have been used to develop sign language recognition systems, potentially serving as a communication tool for millions of hearing-impaired individuals worldwide. However, there are inherent challenges in creating such systems. Firstly, it is important to consider as many linguistic parameters as possible in gesture execution to avoid ambiguity between words. Moreover, to facilitate the real-world adoption of the created solution, it is essential to ensure that the chosen technology is realistic, avoiding expensive, intrusive, or low-mobility sensors, as well as very complex deep learning architectures that impose high computational requirements. Based on this, our work aims to propose an efficient sign language recognition system that utilizes low-cost sensors and techniques. To this end, an object detection model was trained specifically for detecting the interpreter's face and hands, ensuring focus on the most relevant regions of the image and generating inputs with higher semantic value for the classifier. Additionally, we introduced a novel approach to obtain features representing hand location and movement by leveraging spatial information derived from centroid positions of bounding boxes, thereby enhancing sign discrimination. The results demonstrate the efficiency of our handcrafted features, increasing accuracy by 7.96% on the AUTSL dataset, while adding fewer than 700 thousand parameters and incurring less than 10 milliseconds of additional inference time. These findings highlight the potential of our technique to strike a favorable balance between computational cost and accuracy, making it a promising approach for practical sign language recognition applications., Comment: 28 pages, 12 figures, submitted to Image and Vision Computing Journal

In this work, we study the existence and multiplicity of solutions for the following problem \begin{equation}\label{probaa1} \left\{ \begin{aligned} -(\Delta)_{p}^{s} u + V(x)|u|^{p-2}u &= \lambda f(u),&x\in\Omega; u&=0,&x\in \R^{N}\backslash\Omega, \end{aligned} \right. \end{equation} where $\Omega\subset\R^{N}$ is an open bounded set with Lipschitz boundary $\partial\Omega$, $N\geqslant 2,$ $V\in L^{\infty}(\R^{N})$, and $(-\Delta)_p^s$ denotes the fractional $p$-Laplacian with $s\in(0,1), 10$, and $f:\R\rightarrow\R$ is a continuous function. We extend the results of Lopera {\it et al.} in \cite{Lopera1} by proving the existence of a second weak solution for problem (\ref{probaa1}). We apply a variant of the mountain-pass theorem due to Hofer \cite{Hofer2} and infinite-dimensional Morse theory to obtain the existence of at least two solutions.

In a Lie group equipped with a left-invariant metric, we study the minimizing properties of geodesics through the presence of conjugate points. We give criteria for the existence of conjugate points along steady and nonsteady geodesics, using different strategies in each case. We consider both general Lie groups and quadratic Lie groups, where the metric in the Lie algebra $g(u,v)=\langle u,\Lambda v\rangle$ is defined from a bi-invariant bilinear form and a symmetric positive definite operator $\Lambda$. By way of illustration, we apply our criteria to $SO(n)$ equipped with a generalized version of the rigid body metric, and to Lie groups arising from Cheeger's deformation technique, which include Zeitlin's $SU(3)$ model of hydrodynamics on the $2$-sphere. Along the way we obtain formulas for the Ricci curvatures in these examples, showing that conjugate points occur even in the presence of some negative curvature., Comment: 38 pages

Technological advances facilitate the ability to acquire multimodal data, posing a challenge for recognition systems while also providing an opportunity to use the heterogeneous nature of the information to increase the generalization capability of models. An often overlooked issue is the cost of the labeling process, which is typically high due to the need for a significant investment in time and money associated with human experts. Existing semi-supervised learning methods often focus on operating in the feature space created by the fusion of available modalities, neglecting the potential for cross-utilizing complementary information available in each modality. To address this problem, we propose Cross-Modality Clustering-based Self-Labeling (CMCSL). Based on a small set of pre-labeled data, CMCSL groups instances belonging to each modality in the deep feature space and then propagates known labels within the resulting clusters. Next, information about the instances' class membership in each modality is exchanged based on the Euclidean distance to ensure more accurate labeling. Experimental evaluation conducted on 20 datasets derived from the MM-IMDb dataset indicates that cross-propagation of labels between modalities -- especially when the number of pre-labeled instances is small -- can allow for more reliable labeling and thus increase the classification performance in each modality., Comment: 10 pages, 5 figures, 9 tables

Since the introduction of the self-attention mechanism and the adoption of the Transformer architecture for Computer Vision tasks, the Vision Transformer-based architectures gained a lot of popularity in the field, being used for tasks such as image classification, object detection and image segmentation. However, efficiently leveraging the attention mechanism in vision transformers for the Monocular 3D Object Detection task remains an open question. In this paper, we present LAM3D, a framework that Leverages self-Attention mechanism for Monocular 3D object Detection. To do so, the proposed method is built upon a Pyramid Vision Transformer v2 (PVTv2) as feature extraction backbone and 2D/3D detection machinery. We evaluate the proposed method on the KITTI 3D Object Detection Benchmark, proving the applicability of the proposed solution in the autonomous driving domain and outperforming reference methods. Moreover, due to the usage of self-attention, LAM3D is able to systematically outperform the equivalent architecture that does not employ self-attention., Comment: 6 pages. Accepted to MMSP 2024

In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are naturally interpreted as spatially homogeneous and isotropic on ``large scales". In order to show the well-posedness and applicability of such a scheme, we specialize in a class of spacetimes filled with the general homogeneous perfect fluid and inhomogeneous viscoelastic matter. We prove the existence, uniqueness, and relative stability of solutions, and an additional inequality for the energy density. As a consequence of our theorems, a new mechanism of energy transfer appears involving the different components of matter. A class of exact solutions is also obtained to exemplify the general results., Comment: 18 pages; 3 figures

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.

The Southern Photometric Local Universe Survey (S-PLUS) is a project to map $\sim9300$ sq deg of the sky using twelve bands (seven narrow and five broadbands). Observations are performed with the T80-South telescope, a robotic telescope located at the Cerro Tololo Observatory in Chile. The survey footprint consists of several large contiguous areas, including fields at high and low galactic latitudes, and towards the Magellanic Clouds. S-PLUS uses fixed exposure times to reach point source depths of about $21$ mag in the $griz$ and $20$ mag in the $u$ and the narrow filters. This paper describes the S-PLUS Data Release 4 (DR4), which includes calibrated images and derived catalogues for over 3000 sq deg, covering the aforementioned area. The catalogues provide multi-band photometry performed with the tools \texttt{DoPHOT} and \texttt{SExtractor} -- point spread function (\PSF) and aperture photometry, respectively. In addition to the characterization, we also present the scientific potential of the data. We use statistical tools to present and compare the photometry obtained through different methods. Overall we find good agreement between the different methods, with a slight systematic offset of 0.05\,mag between our \PSF and aperture photometry. We show that the astrometry accuracy is equivalent to that obtained in previous S-PLUS data releases, even in very crowded fields where photometric extraction is challenging. The depths of main survey (MS) photometry for a minimum signal-to-noise ratio $S/N = 3$ reach from $\sim19.5$ for the bluer bands to $\sim21.5$ mag on the red. The range of magnitudes over which accurate \PSF photometry is obtained is shallower, reaching $\sim19$ to $\sim20.5$ mag depending on the filter. Based on these photometric data, we provide star-galaxy-quasar classification and photometric redshift for millions of objects., Comment: 26 pages, 17 figures, 14 tables, accepted for A&A

We study liquidity provision in the presence of exogenous competition. We consider a `reference market maker' who monitors her inventory and the aggregated inventory of the competing market makers. We assume that the competing market makers use a `rule of thumb' to determine their posted depths, depending linearly on their inventory. By contrast, the reference market maker optimises over her posted depths, and we assume that her fill probability depends on the difference between her posted depths and the competition's depths in an exponential way. For a linear-quadratic goal functional, we show that this model admits an approximate closed-form solution. We illustrate the features of our model and compare against alternative ways of solving the problem either via an Euler scheme or state-of-the-art reinforcement learning techniques.

This paper provides two characterizations of regularity for near-vector spaces: first, by expressing them as a direct sum of vector spaces over division rings formed by distributive elements; second, by expressing their dimension in term of the dimension of these summands. These results offer new insights into the structure and properties of near-vector spaces.

We study the perfect information Nash equilibrium between a broker and her clients -- an informed trader and an uniformed trader. In our model, the broker trades in the lit exchange where trades have instantaneous and transient price impact with exponential resilience, while both clients trade with the broker. The informed trader and the broker maximise expected wealth subject to inventory penalties, while the uninformed trader is not strategic and sends the broker random buy and sell orders. We characterise the Nash equilibrium of the trading strategies with the solution to a coupled system of forward-backward stochastic differential equations (FBSDEs). We solve this system explicitly and study the effect of information, profitability, and inventory control in the trading strategies of the broker and the informed trader., Comment: 24 pages, 3 figures

This paper develops an adaptive Proximal Alternating Direction Method of Multipliers (P-ADMM) for solving linearly-constrained, weakly convex, composite optimization problems. This method is adaptive to all problem parameters, including smoothness and weak convexity constants. It is assumed that the smooth component of the objective is weakly convex and possibly nonseparable, while the non-smooth component is convex and block-separable. The proposed method is tolerant to the inexact solution of its block proximal subproblem so it does not require that the non-smooth component has easily computable block proximal maps. Each iteration of our adaptive P-ADMM consists of two steps: (1) the sequential solution of each block proximal subproblem, and (2) adaptive tests to decide whether to perform a full Lagrange multiplier and/or penalty parameter update(s). Without any rank assumptions on the constraint matrices, it is shown that the adaptive P-ADMM obtains an approximate first-order stationary point of the constrained problem in a number of iterations that matches the state-of-the-art complexity for the class of P-ADMMs. The two proof-of-concept numerical experiments that conclude the paper suggest our adaptive P-ADMM enjoys significant computational benefits.

Rudin's version of the classical Julia-Wolff-Carath\'eodory theorem is a cornerstone of holomorphic function theory in the unit ball of $\mathbb{C}^d$. In this paper we obtain a complete generalization of Rudin's theorem for a holomorphic map $f\colon D\to D'$ between convex domains of finite type. In particular, given a point $\xi\in \partial D$ with finite dilation we show that the $K$-limit of $f$ at $\xi$ exists and is a point $\eta\in \partial D'$, and we obtain asymptotic estimates for all entries of the Jacobian matrix of the differential $df_z$ in terms of the multitypes at the points $\xi$ and at $\eta$. We introduce a generalization of Bracci-Patrizio-Trapani's pluricomplex Poisson kernel which, together with the dilation at $\xi$, gives a formula for the restricted $K$-limit of the normal component of the normal derivative $\langle df_z(n_\xi),n_\eta\rangle$. Our principal tools are methods from Gromov hyperbolicity theory, a scaling in the normal direction, and the strong asymptoticity of complex geodesics. To obtain our main result we prove a conjecture by Abate on the Kobayashi type of a vector $v$, proving that it is equal to the reciprocal of the line type of $v$, and we give new extrinsic characterizations of both $K$-convergence and restricted convergence to a point $\xi\in \partial D$ in terms of the multitype at $\xi$.

A tracer sample in a gravitational potential, starting from a generic initial condition, phase-mixes towards a stationary state. This evolution is accompanied by an entropy increase, and the final state is characterized by a distribution function (DF) that depends only on integrals of motion (Jeans theorem). In terms of angle-action variables, the final state is uniform in angles (high entropy) and maximally clustered in actions (low entropy). We present a method exploring this fact to constrain a gravitational potential using a sample that is stationary in it. We estimate the entropy in the action space of trial potentials and recover the true potential by minimizing this entropy. This method avoids assuming a known DF, and may be applicable to other sets of integrals. We provide expressions for the entropy of DFs depending on energy, $f(E)$, energy and angular momentum, $f(E,L)$, or three actions, $f(\vec{J})$, and investigate the bias and fluctuations in their estimates. We show that the method correctly recovers the potential parameters for spherical and axisymmetric potentials. We also present a methodology to characterize the posterior probability distribution of the parameters with an Approximate Bayesian Computation, and indicate a pathway for application to observational data. Using $N=10^4$ tracers with $20\%$-uncertainties in the 6D coordinates, we recover the flattening parameter $q$ of an axisymmetric potential with $\sigma_q/q\sim 10\%$., Comment: 17 pages + appendix + references, 13 figs. Comments are very welcome!

An increasing number of unhardened commercial-off-the-shelf embedded devices are deployed under harsh operating conditions and in highly-dependable systems. Due to the mechanisms of hardware degradation that affect these devices, ageing detection and monitoring are crucial to prevent critical failures. In this paper, we empirically study the propagation delay of 298 naturally-aged FPGA devices that are deployed in the European XFEL particle accelerator. Based on in-field measurements, we find that operational devices show significantly slower switching frequencies than unused chips, and that increased gamma and neutron radiation doses correlate with increased hardware degradation. Furthermore, we demonstrate the feasibility of developing machine learning models that estimate the switching frequencies of the devices based on historical and environmental data., Comment: If you cite this paper, please use the DSD reference: Leandro Lanzieri, Lukasz Butkowski, Jiri Kral, Goerschwin Fey, Holger Schlarb, and Thomas C. Schmidt. Studying the Degradation of Propagation Delay on FPGAs at the European XFEL. In Proceedings of the 27th Euromicro Conference on Digital System Design (DSD), IEEE, 2024

The novelty of the current work is precisely to propose a statistical procedure to combine estimates of the modal parameters provided by any set of Operational Modal Analysis (OMA) algorithms so as to avoid preference for a particular one and also to derive an approximate joint probability distribution of the modal parameters, from which engineering statistics of interest such as mean value and variance are readily provided. The effectiveness of the proposed strategy is assessed considering measured data from an actual centrifugal compressor. The statistics obtained for both forward and backward modal parameters are finally compared against modal parameters identified during standard stability verification testing (SVT) of centrifugal compressors prior to shipment, using classical Experimental Modal Analysis (EMA) algorithms. The current work demonstrates that combination of OMA algorithms can provide quite accurate estimates for both the modal parameters and the associated uncertainties with low computational costs., Comment: 6 figures

The battle against the spread of misinformation on the Internet is a daunting task faced by modern society. Fake news content is primarily distributed through digital platforms, with websites dedicated to producing and disseminating such content playing a pivotal role in this complex ecosystem. Therefore, these websites are of great interest to misinformation researchers. However, obtaining a comprehensive list of websites labeled as producers and/or spreaders of misinformation can be challenging, particularly in developing countries. In this study, we propose a novel methodology for identifying websites responsible for creating and disseminating misinformation content, which are closely linked to users who share confirmed instances of fake news on social media. We validate our approach on Twitter by examining various execution modes and contexts. Our findings demonstrate the effectiveness of the proposed methodology in identifying misinformation websites, which can aid in gaining a better understanding of this phenomenon and enabling competent entities to tackle the problem in various areas of society., Comment: This is a preprint version of a submitted manuscript on the Brazilian Symposium on Multimedia and the Web (WebMedia)

We present ~ 126 new spectroscopically identified members of the GD-1 tidal stream obtained with the 5000-fiber Dark Energy Spectroscopic Instrument (DESI). We confirm the existence of a ``cocoon'' which is broad (FWHM~2.932deg~460pc) and kinematically hot (velocity dispersion, sigma~5-8km/s) component that surrounds a narrower (FWHM~0.353deg~55pc) and colder (sigma~ 2.2-2.6km/s) thin stream component (based on a median per star velocity precision of 2.7km/s). The cocoon extends over at least a ~ 20deg segment of the stream observed by DESI. The thin and cocoon components have similar mean values of [Fe/H]: -2.54+/- 0.04dex and -2.45+/-0.06dex suggestive of a common origin. The data are consistent with the following scenarios for the origin of the cocoon. The progenitor of the GD-1 stream was an accreted globular cluster (GC) and: (a) the cocoon was produced by pre-accretion tidal stripping of the GC while it was still inside its parent dwarf galaxy; (b) the cocoon is debris from the parent dwarf galaxy; (c) an initially thin GC tidal stream was heated by impacts from dark subhalos in the Milky Way; (d) an initially thin GC stream was heated by a massive Sagittarius dwarf galaxy; or a combination of some these. In the first two cases the velocity dispersion and mean metallicity are consistent with the parent dwarf galaxy having a halo mass of ~0^9\msun. Future DESI spectroscopy and detailed modeling may enable us to distinguish between these possible origins., Comment: Submitted to ApJ, 23 pages, 13 figures 4 tables

This paper presents the first public data release of the S-PLUS Ultra-Short Survey (USS), a photometric survey with short exposure times, covering approximately 9300 deg$^{2}$ of the Southern sky. The USS utilizes the Javalambre 12-band magnitude system, including narrow and medium-band and broad-band filters targeting prominent stellar spectral features. The primary objective of the USS is to identify bright, extremely metal-poor (EMP; [Fe/H] $\leq -3$) and ultra metal-poor (UMP; [Fe/H] $\leq -4$) stars for further analysis using medium- and high-resolution spectroscopy.}{This paper provides an overview of the survey observations, calibration method, data quality, and data products. Additionally, it presents the selection of EMP and UMP candidates.}{The data from the USS were reduced and calibrated using the same methods as presented in the S-PLUS DR2. An additional step was introduced, accounting for the offset between the observed magnitudes off the USS and the predicted magnitudes from the very low-resolution Gaia XP spectra.}{This first release contains data for 163 observed fields totaling $\sim$324 deg$^{2}$ along the Celestial Equator. The magnitudes obtained from the USS are well-calibrated, showing a difference of $\sim 15$ mmag compared to the predicted magnitudes by the GaiaXPy toolkit. By combining colors and magnitudes, 140 candidates for EMP or UMP have been identified for follow-up studies.}{The S-PLUS USS DR1 is an important milestone in the search for bright metal-poor stars, with magnitudes in the range 10 $ < r \leq 14$. The USS is an ongoing survey; in the near future, it will provide many more bright metal-poor candidate stars for spectroscopic follow-up., Comment: Accepted for publication in A&A. 17 pages 6 figures. Long table at the end of the paper

The use of generative AI in video game development is on the rise, and as the conversational and other capabilities of large language models continue to improve, we expect LLM-driven non-player characters (NPCs) to become widely deployed. In this paper, we seek to understand how human players collaborate with LLM-driven NPCs to accomplish in-game goals. We design a minigame within Minecraft where a player works with two GPT4-driven NPCs to complete a quest. We perform a user study in which 28 Minecraft players play this minigame and share their feedback. On analyzing the game logs and recordings, we find that several patterns of collaborative behavior emerge from the NPCs and the human players. We also report on the current limitations of language-only models that do not have rich game-state or visual understanding. We believe that this preliminary study and analysis will inform future game developers on how to better exploit these rapidly improving generative AI models for collaborative roles in games., Comment: Accepted at Wordplay workshop at ACL 2024

Small business owners (SBOs), specially women, face several challenges in everyday life, especially when asking for microcredit loans from financial institutions. Usual difficulties include low credit scores, unbaked situations, outstanding debts, informal employment situations, inability to showcase their payable capacity, and lack of financial guarantor. Moreover, SBOs often need help applying for microcredit loans due to the lack of information on how to proceed. The task of asking for a loan is a complex practice, and asymmetric power relationships might emerge, but that benefits micro-entrepreneurs only sometimes. In this paper, we interviewed 20 women entrepreneurs living in a low-income community in Brazil. We wanted to unveil value tensions derived from this practice that might influence the design of AI technologies for the public. In doing so, we used a conversational system as a probe to understand the opportunities for empowering their practices with the support of AI multimedia conversational systems. We derived seven recommendations for designing AI systems for evaluating micro-business health in low-income communities.

The performance of a large language model (LLM) depends heavily on the quality and size of its pretraining dataset. However, the pretraining datasets for state-of-the-art open LLMs like Llama 3 and Mixtral are not publicly available and very little is known about how they were created. In this work, we introduce FineWeb, a 15-trillion token dataset derived from 96 Common Crawl snapshots that produces better-performing LLMs than other open pretraining datasets. To advance the understanding of how best to curate high-quality pretraining datasets, we carefully document and ablate all of the design choices used in FineWeb, including in-depth investigations of deduplication and filtering strategies. In addition, we introduce FineWeb-Edu, a 1.3-trillion token collection of educational text filtered from FineWeb. LLMs pretrained on FineWeb-Edu exhibit dramatically better performance on knowledge- and reasoning-intensive benchmarks like MMLU and ARC. Along with our datasets, we publicly release our data curation codebase and all of the models trained during our ablation experiments.

Automated software engineering has been greatly empowered by the recent advances in Large Language Models (LLMs) for programming. While current benchmarks have shown that LLMs can perform various software engineering tasks like human developers, the majority of their evaluations are limited to short and self-contained algorithmic tasks. Solving challenging and practical programming tasks requires the capability of utilizing diverse function calls as tools to efficiently implement functionalities like data analysis and web development. In addition, using multiple tools to solve a task needs compositional reasoning by accurately understanding complex instructions. Fulfilling both of these characteristics can pose a great challenge for LLMs. To assess how well LLMs can solve challenging and practical programming tasks, we introduce Bench, a benchmark that challenges LLMs to invoke multiple function calls as tools from 139 libraries and 7 domains for 1,140 fine-grained programming tasks. To evaluate LLMs rigorously, each programming task encompasses 5.6 test cases with an average branch coverage of 99%. In addition, we propose a natural-language-oriented variant of Bench, Benchi, that automatically transforms the original docstrings into short instructions only with essential information. Our extensive evaluation of 60 LLMs shows that LLMs are not yet capable of following complex instructions to use function calls precisely, with scores up to 60%, significantly lower than the human performance of 97%. The results underscore the need for further advancements in this area., Comment: 44 pages, 14 figures, 7 tables, built with love by the BigCode community :)

Complex networks, such as those in social, biological, and technological systems, often present challenges to the task of community detection. Our research introduces a novel rough clustering based consensus community framework (RC-CCD) for effective structure identification of network communities. The RC-CCD method employs rough set theory to handle uncertainties within data and utilizes a consensus clustering approach to aggregate multiple clustering results, enhancing the reliability and accuracy of community detection. This integration allows the RC-CCD to effectively manage overlapping communities, which are often present in complex networks. This approach excels at detecting overlapping communities, offering a detailed and accurate representation of network structures. Comprehensive testing on benchmark networks generated by the Lancichinetti-Fortunato-Radicchi method showcased the strength and adaptability of the new proposal to varying node degrees and community sizes. Cross-comparisons of RC-CCD versus other well known detection algorithms outcomes highlighted its stability and adaptability.

Intent inferral on a hand orthosis for stroke patients is challenging due to the difficulty of data collection from impaired subjects. Additionally, EMG signals exhibit significant variations across different conditions, sessions, and subjects, making it hard for classifiers to generalize. Traditional approaches require a large labeled dataset from the new condition, session, or subject to train intent classifiers; however, this data collection process is burdensome and time-consuming. In this paper, we propose ChatEMG, an autoregressive generative model that can generate synthetic EMG signals conditioned on prompts (i.e., a given sequence of EMG signals). ChatEMG enables us to collect only a small dataset from the new condition, session, or subject and expand it with synthetic samples conditioned on prompts from this new context. ChatEMG leverages a vast repository of previous data via generative training while still remaining context-specific via prompting. Our experiments show that these synthetic samples are classifier-agnostic and can improve intent inferral accuracy for different types of classifiers. We demonstrate that our complete approach can be integrated into a single patient session, including the use of the classifier for functional orthosis-assisted tasks. To the best of our knowledge, this is the first time an intent classifier trained partially on synthetic data has been deployed for functional control of an orthosis by a stroke survivor. Videos and additional information can be found at https://jxu.ai/chatemg., Comment: 8 pages

We present the first on-sky results from an ultra-low-readout-noise Skipper CCD focal plane prototype for the SOAR Integral Field Spectrograph (SIFS). The Skipper CCD focal plane consists of four 6k x 1k, 15 $\mu$m pixel, fully-depleted, p-channel devices that have been thinned to ~250 $\mu$m, backside processed, and treated with an anti-reflective coating. These Skipper CCDs were configured for astronomical spectroscopy, i.e., single-sample readout noise < 4.3 e- rms/pixel, the ability to achieve multi-sample readout noise $\ll$ 1 e- rms/pixel, full-well capacities ~40,000-65,000 e-, low dark current and charge transfer inefficiency (~2 x 10$^{-4}$ e-/pixel/s and 3.44 x 10$^{-7}$, respectively), and an absolute quantum efficiency of $\gtrsim$ 80% between 450 nm and 980 nm ($\gtrsim$ 90% between 600 nm and 900 nm). We optimized the readout sequence timing to achieve sub-electron noise (~0.5 e- rms/pixel) in a region of 2k x 4k pixels and photon-counting noise (~0.22 e- rms/pixel) in a region of 220 x 4k pixels, each with a readout time of $\lesssim$ 17 min. We observed two quasars (HB89 1159+123 and QSO J1621-0042) at redshift z ~ 3.5, two high-redshift galaxy clusters (CL J1001+0220 and SPT-CL J2040-4451), an emission line galaxy at z = 0.3239, a candidate member star of the Bo\"{o}tes II ultra-faint dwarf galaxy, and five CALSPEC spectrophotometric standard stars (HD074000, HD60753, HD106252, HD101452, HD200654). We present charge-quantized, photon-counting observations of the quasar HB89 1159+123 and show the detector sensitivity increase for faint spectral features. We demonstrate signal-to-noise performance improvements for SIFS observations in the low-background, readout-noise-dominated regime. We outline scientific studies that will leverage the SIFS-Skipper CCD data and new detector architectures that utilize the Skipper floating gate amplifier with faster readout times., Comment: 20 pages, 13 figures, 1 table; Proc. SPIE

PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.

Aerodynamic noise is a limitation for further exploitation of wind energy resources. As this type of noise is caused by the interaction of turbulent flow with the airframe, a detailed resolution of the flow is necessary to obtain an accurate prediction of the far-field noise. Computational fluid dynamic (CFD) solvers simulate the flow field but only at a high computational cost, which is much increased when the acoustic field is resolved. Therefore, wind turbine noise predictions using numerical approaches remain a challenge. This paper presents a methodology that couples (relatively fast) wind turbine CFD simulations using actuator lines with a fast turn-around noise prediction method. The flow field is simulated using actuator lines and large eddy simulations. The noise prediction method is based on the Amiet-Schlinker's theory for rotatory noise sources, considering leading- and trailing-edge noise as unique noise sources. A 2D panel code (XFOIL) calculates the sectional forces and boundary layer quantities. The resulting methodology for the noise prediction method is of high fidelity since the wind turbine geometry is accounted for in both flow and acoustics predictions. Results are compared with field measurements of a full-scale wind turbine for two operational conditions, validating the results of this research., Comment: 13 pages, 12 figures

We seek to identify genes involved in Parkinson's Disease (PD) by combining information across different experiment types. Each experiment, taken individually, may contain too little information to distinguish some important genes from incidental ones. However, when experiments are combined using the proposed statistical framework, additional power emerges. The fundamental building block of the family of statistical models that we propose is a hierarchical three-group mixture of distributions. Each gene is modeled probabilistically as belonging to either a null group that is unassociated with PD, a deleterious group, or a beneficial group. This three-group formalism has two key features. By apportioning prior probability of group assignments with a Dirichlet distribution, the resultant posterior group probabilities automatically account for the multiplicity inherent in analyzing many genes simultaneously. By building models for experimental outcomes conditionally on the group labels, any number of data modalities may be combined in a single coherent probability model, allowing information sharing across experiment types. These two features result in parsimonious inference with few false positives, while simultaneously enhancing power to detect signals. Simulations show that our three-groups approach performs at least as well as commonly-used tools for GWAS and RNA-seq, and in some cases it performs better. We apply our proposed approach to publicly-available GWAS and RNA-seq datasets, discovering novel genes that are potential therapeutic targets., Comment: 26 pages, 6 figures, 4 tables

Nonstabilizerness or `magic' is a key resource for quantum computing and a necessary condition for quantum advantage. Non-Clifford operations turn stabilizer states into resourceful states, where the amount of nonstabilizerness is quantified by resource measures such as stabilizer R\'enyi entropies (SREs). Here, we show that SREs saturate their maximum value at a critical number of non-Clifford operations. Close to the critical point SREs show universal behavior. Remarkably, the derivative of the SRE crosses at the same point independent of the number of qubits and can be rescaled onto a single curve. We find that the critical point depends non-trivially on R\'enyi index $\alpha$. For random Clifford circuits doped with T-gates, the critical T-gate density scales independently of $\alpha$. In contrast, for random Hamiltonian evolution, the critical time scales linearly with qubit number for $\alpha>1$, while is a constant for $\alpha<1$. This highlights that $\alpha$-SREs reveal fundamentally different aspects of nonstabilizerness depending on $\alpha$: $\alpha$-SREs with $\alpha<1$ relate to Clifford simulation complexity, while $\alpha>1$ probe the distance to the closest stabilizer state and approximate state certification cost via Pauli measurements. As technical contributions, we observe that the Pauli spectrum of random evolution can be approximated by two highly concentrated peaks which allows us to compute its SRE. Further, we introduce a class of random evolution that can be expressed as random Clifford circuits and rotations, where we provide its exact SRE. Our results opens up new approaches to characterize the complexity of quantum systems., Comment: 14 pages, 9 figures

We conjecture that whenever $M$ is a metric space of density at most continuum, then the space of Lipschitz functions is $w^*$-separable. We prove the conjecture for several classes of metric spaces including all the Banach spaces with a projectional skeleton, Banach spaces with a $w^*$-separable dual unit ball and locally separable complete metric spaces.

Given a frequency $\lambda=(\lambda_n)$, we consider the Hardy spaces $ \mathcal{H}_p^\lambda$ of $\lambda$-Dirichlet series $ D = \sum_n a_n e^{-\lambda_n s}$ and study the asymptotic behavior of the upper and lower democracy functions of its canonical basis $\mathcal B=\{e^{-\lambda_ns}\}$. For the ordinary case, $\mathcal B=\{n^{-s}\}$, we give the correct asymptotic behavior of all such functions, while in the general case we give sharp lower and upper bounds for all possible behaviors. Moreover, for $p>2$ we present examples showing that any intermediate behavior (between the extreme bounds) can occur. We also study how different properties of the frequency $\lambda$ lead to particular behaviors of the corresponding fundamental functions. Finally, we apply our results to analyze greedy-type properties of $\mathcal B=\{e^{-\lambda_ns}\}$ for some particular $\lambda$'s.

In the first part of the paper, we define the concept of a $G$-table of a $G$-(co)algebra and we compute the $G$-table of some $G$-(co)algebras (here a $G$-algebra is an algebra on which $G$ acts, semisimply, by algebra automorphisms). The $G$-table of a $G$-(co)algebra $A$ is a set of scalars that provides very precise and concise information about both the algebra structure and the $G$-module structure of $A$. In particular, the ordinary multiplication table of $A$ can be derived from the $G$-table of $A$. From the $G$-table of a $G$-algebra $A$ we define a plain algebra $P(A)$ associated to it and we present some basic functoriality results about $P$. Obtaining the $G$-table of a given $G$-algebra $A$ requires a considerable amount of work but, the result, is a very powerful tool as shown in the second part of the paper. Here we compute the $SL(2)$-tables of the Poisson algebra structure of the even-degree part of the cohomology associated to the cotangent bundle of the 3-dimensional Heisenberg Lie group with Lie algebra $h$, that is $H_E(h)=H_E^{\bullet}(h,\bigwedge^{\bullet}h)$. This Poisson $SL(2)$-algebra has dimension 18. From these $SL(2)$-tables we deduce that the underlying Lie algebra of $H_E(h)$ is isomorphic to $gl(3)\ltimes gl(3)_{ab}$ with the first factor acting on the second (abelian) one by the adjoint representation. We find it remarkable that the Lie algebra structure on $H_{E}(h)$ contains a semisimple Lie subalgebra (in this case $sl(3)$) strictly larger than the Levi factor of $\text{Der}(h)$, which in this case is $sl(2)\subset H^{1}(h,h)$. This means that the Levi factor of the Lie algebra $H_{E}(h)$ has nontrivial elements outside $H^{1}(h,h)$. Finally, this leads us to find a family of commutative Poisson algebras whose underlying Lie structure is $gl(n)\ltimes gl(n)_{ab}$ (arbitrary $n$) such that, for $n=3$, is isomorphic to $H_E(h)$.

We present an exact $n$-qubit computational-basis amplitude encoder of real- or complex-valued data vectors of $d=\binom{n}{k}$ components into a subspace of fixed Hamming weight $k$. This represents a polynomial space compression. The circuit is optimal in that it expresses an arbitrary data vector using only $d-1$ (controlled) Reconfigurable Beam Splitter (RBS) gates and is constructed by an efficient classical algorithm that sequentially generates all bitstrings of weight $k$ and identifies all gate parameters. An explicit compilation into CNOTs and single-qubit gates is presented, with the total CNOT-gate count of $\mathcal{O}(k\, d)$ provided in analytical form. In addition, we show how to load data in the binary basis by sequentially stacking encoders of different Hamming weights using $\mathcal{O}(d\,\log(d))$ CNOT gates. Moreover, using generalized RBS gates that mix states of different Hamming weights, we extend the construction to efficiently encode arbitrary sparse vectors. Finally, we perform an experimental proof-of-principle demonstration of our scheme on a commercial trapped-ion quantum computer. We successfully upload a $q$-Gaussian probability distribution in the non-log-concave regime with $n = 6$ and $k = 2$. We also showcase how the effect of hardware noise can be alleviated by quantum error mitigation. Our results constitute a versatile framework for quantum data compression with various potential applications in fields such as quantum chemistry, quantum machine learning, and constrained combinatorial optimizations., Comment: 13 pages, 7 figures, 4 tables; Revised text + new experimental data

Scale has become a main ingredient in obtaining strong machine learning models. As a result, understanding a model's scaling properties is key to effectively designing both the right training setup as well as future generations of architectures. In this work, we argue that scale and training research has been needlessly complex due to reliance on the cosine schedule, which prevents training across different lengths for the same model size. We investigate the training behavior of a direct alternative - constant learning rate and cooldowns - and find that it scales predictably and reliably similar to cosine. Additionally, we show that stochastic weight averaging yields improved performance along the training trajectory, without additional training costs, across different scales. Importantly, with these findings we demonstrate that scaling experiments can be performed with significantly reduced compute and GPU hours by utilizing fewer but reusable training runs. Our code is available at https://github.com/epfml/schedules-and-scaling.