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Human Activity Recognition (HAR) is critical for applications in healthcare, fitness, and IoT, but deploying accurate models on resource-constrained devices remains challenging due to high energy and memory demands. This paper demonstrates the application of Differentiable Weightless Neural Networks (DWNs) to HAR, achieving competitive accuracies of 96.34% and 96.67% while consuming only 56nJ and 104nJ per sample, with an inference time of just 5ns per sample. The DWNs were implemented and evaluated on an FPGA, showcasing their practical feasibility for energy-efficient hardware deployment. DWNs achieve up to 926,000x energy savings and 260x memory reduction compared to state-of-the-art deep learning methods. These results position DWNs as a nano-machine learning nanoML model for HAR, setting a new benchmark in energy efficiency and compactness for edge and wearable devices, paving the way for ultra-efficient edge AI., Comment: Accepted as a full paper by the 2025 EDGE AI FOUNDATION Austin

We investigate the shape of a tin sheet formed from a droplet struck by a nanosecond laser pulse. Specifically, we examine the dynamics of the process as a function of laser beam properties, focusing on the outstanding riddle of curvature inversion: tin sheets produced in experiments and state-of-the-art extreme ultraviolet (EUV) nanolithography light sources curve in a direction opposite to previous theoretical predictions. We resolve this discrepancy by combining direct numerical simulations with experimental data, demonstrating that curvature inversion can be explained by an instantaneous pressure impulse with low kurtosis. Specifically, we parametrize a dimensionless pressure width, $W$, using a raised cosine function and successfully reproduce the experimentally observed curvature over a wide range of laser-to-droplet diameter ratios, $0.3 < d/D_0 < 0.8$. The simulation process described in this work has applications in the EUV nanolithography industry, where a laser pulse deforms a droplet into a sheet, which is subsequently ionized by a second pulse to produce EUV-emitting plasma., Comment: 16 pages, 10 figures

We study equivariant primitives of Eisenstein series for principal congruence subgroups and show that they are precisely the corresponding non-holomorphic Eisenstein series. We present closed formulas that naturally generalise existing results for the full modular group. We also focus on Eisenstein series of weight two in the case where the modular curve has genus zero. We show that in those cases the non-holomorphic Eisenstein series of weight two can be written as single-valued logarithms whose argument is a rational function of the Hauptmodul., Comment: 26 pages

Regression analysis is used for prediction and to understand the effect of independent variables on dependent variables. Symbolic regression (SR) automates the search for non-linear regression models, delivering a set of hypotheses that balances accuracy with the possibility to understand the phenomena. Many SR implementations return a Pareto front allowing the choice of the best trade-off. However, this hides alternatives that are close to non-domination, limiting these choices. Equality graphs (e-graphs) allow to represent large sets of expressions compactly by efficiently handling duplicated parts occurring in multiple expressions. E-graphs allow to store and query all SR solution candidates visited in one or multiple GP runs efficiently and open the possibility to analyse much larger sets of SR solution candidates. We introduce rEGGression, a tool using e-graphs to enable the exploration of a large set of symbolic expressions which provides querying, filtering, and pattern matching features creating an interactive experience to gain insights about SR models. The main highlight is its focus in the exploration of the building blocks found during the search that can help the experts to find insights about the studied phenomena.This is possible by exploiting the pattern matching capability of the e-graph data structure., Comment: 9 pages, 4 figures, 2 tables

The search for symbolic regression models with genetic programming (GP) has a tendency of revisiting expressions in their original or equivalent forms. Repeatedly evaluating equivalent expressions is inefficient, as it does not immediately lead to better solutions. However, evolutionary algorithms require diversity and should allow the accumulation of inactive building blocks that can play an important role at a later point. The equality graph is a data structure capable of compactly storing expressions and their equivalent forms allowing an efficient verification of whether an expression has been visited in any of their stored equivalent forms. We exploit the e-graph to adapt the subtree operators to reduce the chances of revisiting expressions. Our adaptation, called eggp, stores every visited expression in the e-graph, allowing us to filter out from the available selection of subtrees all the combinations that would create already visited expressions. Results show that, for small expressions, this approach improves the performance of a simple GP algorithm to compete with PySR and Operon without increasing computational cost. As a highlight, eggp was capable of reliably delivering short and at the same time accurate models for a selected set of benchmarks from SRBench and a set of real-world datasets., Comment: 10 pages, 5 figures, 5 tables

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 2,700 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai., Comment: 27 pages, 6 figures

We report limits on WIMP dark matter derived from three years of data collected by the COSINE-100 experiment with NaI(Tl) crystals, achieving an improved energy threshold of 0.7 keV. This lowered threshold enhances sensitivity in the sub-GeV mass range, extending the reach for direct detection of low-mass dark matter. Although no excess of WIMP-like events was observed, the increased sensitivity enabled a model-independent comparison between the expected WIMP signal rate-based on mass limits from our data-and DAMA's reported modulation amplitude. Our findings strongly disfavor the DAMA signal as originating from WIMP interactions, fully excluding DAMA/LIBRA 3$\sigma$ allowed regions and providing enhanced WIMP mass limits by an order of magnitude in the spin-independent model compared to previous results. In the spin-dependent model, cross-section upper limits were obtained in the mass range [0.1-5.0] GeV/c$^2$, with additional sensitivity to sub-GeV WIMPs through the inclusion of the Migdal effect. These results represent substantial progress in low-mass dark matter exploration and reinforce constraints on the longstanding DAMA claim.

As quantum devices continue to grow in size but remain affected by noise, it is crucial to determine when and how they can outperform classical computers on practical tasks. A central piece in this effort is to develop the most efficient classical simulation algorithms possible. Among the most promising approaches are Pauli backpropagation algorithms, which have already demonstrated their ability to efficiently simulate certain classes of parameterized quantum circuits-a leading contender for near-term quantum advantage-under random circuit assumptions and depolarizing noise. However, their efficiency was not previously established for more realistic non-unital noise models, such as amplitude damping, that better capture noise on existing hardware. Here, we close this gap by adapting Pauli backpropagation to non-unital noise, proving that it remains efficient even under these more challenging conditions. Our proof leverages a refined combinatorial analysis to handle the complexities introduced by non-unital channels, thus strengthening Pauli backpropagation as a powerful tool for simulating near-term quantum devices.

In this work we propose MirrorCBO, a consensus-based optimization (CBO) method which generalizes standard CBO in the same way that mirror descent generalizes gradient descent. For this we apply the CBO methodology to a swarm of dual particles and retain the primal particle positions by applying the inverse of the mirror map, which we parametrize as the subdifferential of a strongly convex function $\phi$. In this way, we combine the advantages of a derivative-free non-convex optimization algorithm with those of mirror descent. As a special case, the method extends CBO to optimization problems with convex constraints. Assuming bounds on the Bregman distance associated to $\phi$, we provide asymptotic convergence results for MirrorCBO with explicit exponential rate. Another key contribution is an exploratory numerical study of this new algorithm across different application settings, focusing on (i) sparsity-inducing optimization, and (ii) constrained optimization, demonstrating the competitive performance of MirrorCBO. We observe empirically that the method can also be used for optimization on (non-convex) submanifolds of Euclidean space, can be adapted to mirrored versions of other recent CBO variants, and that it inherits from mirror descent the capability to select desirable minimizers, like sparse ones. We also include an overview of recent CBO approaches for constrained optimization and compare their performance to MirrorCBO., Comment: 64 pages, 18 figures, 19 tables

The chapter supports educators and postgraduate students in understanding the role of simulation in software engineering research based on the authors' experience. This way, it includes a background positioning simulation-based studies in software engineering research, the proposition of learning objectives for teaching simulation as a research method, and presents our experience when teaching simulation concepts and practice. For educators, it further provides learning objectives when teaching simulation, considering the current state of the art in software engineering research and the necessary guidance and recommended learning activities to achieve these objectives. For students, it drives the learning path for those interested in learning this method but had no opportunity to engage in an entire course on simulation in the context of empirical research.

We present results from a high cadence multi-wavelength observational campaign of the enigmatic changing look AGN 1ES 1927+654 from May 2022- April 2024, coincident with an unprecedented radio flare (an increase in flux by a factor of $\sim 60$ over a few months) and the emergence of a spatially resolved jet at $0.1-0.3$ pc scales (Meyer et al. 2024). Companion work has also detected a recurrent quasi-periodic oscillation (QPO) in the $2-10$ keV band with an increasing frequency ($1-2$ mHz) over the same period (Masterson et al., 2025). During this time, the soft X-rays ($0.3-2$ keV) monotonically increased by a factor of $\sim 8$, while the UV emission remained near-steady with $<30\%$ variation and the $2-10$ keV flux showed variation by a factor $\lesssim 2$. The weak variation of the $2-10$ keV X-ray emission and the stability of the UV emission suggest that the magnetic energy density and accretion rate are relatively unchanged, and that the jet could be launched due to a reconfiguration of the magnetic field (toroidal to poloidal) close to the black hole. Advecting poloidal flux onto the event horizon would trigger the Blandford-Znajek (BZ) mechanism, leading to the onset of the jet. The concurrent softening of the coronal slope (from $\Gamma= 2.70\pm 0.04$ to $\Gamma=3.27\pm 0.04$), the appearance of a QPO, and low coronal temperature ($kT_{e}=8_{-3}^{+8}$ keV) during the radio outburst suggest that the poloidal field reconfiguration can significantly impact coronal properties and thus influence jet dynamics. These extraordinary findings in real time are crucial for coronal and jet plasma studies, particularly as our results are independent of coronal geometry., Comment: Submitted to ApJ after minor referee comments

The Transformation-Interaction-Rational is a representation for symbolic regression that limits the search space of functions to the ratio of two nonlinear functions each one defined as the linear regression of transformed variables. This representation has the main objective to bias the search towards simpler expressions while keeping the approximation power of standard approaches. The performance of using Genetic Programming with this representation was substantially better than with its predecessor (Interaction-Transformation) and ranked close to the state-of-the-art on a contemporary Symbolic Regression benchmark. On a closer look at these results, we observed that the performance could be further improved with an additional selective pressure for smaller expressions when the dataset contains just a few data points. The introduction of a penalization term applied to the fitness measure improved the results on these smaller datasets. One problem with this approach is that it introduces two additional hyperparameters: i) a criteria to when the penalization should be activated and, ii) the amount of penalization to the fitness function. In this paper, we extend Transformation-Interaction-Rational to support multi-objective optimization, specifically the NSGA-II algorithm, and apply that to the same benchmark. A detailed analysis of the results show that the use of multi-objective optimization benefits the overall performance on a subset of the benchmarks while keeping the results similar to the single-objective approach on the remainder of the datasets. Specifically to the small datasets, we observe a small (and statistically insignificant) improvement of the results suggesting that further strategies must be explored., Comment: 25 pages, 8 figures, 4 tables, Genetic Programming and Evolvable Machines, vol 24, no 2

We investigate the single-site von Neumann entropy along a harmonically confined superfluid chain, as described by the one-dimensional fermionic Hubbard model with strongly attractive interactions. We find that by increasing the confinement (or equivalently the particle filling) the system undergoes a quantum phase transition from a superfluid (SF) to a non-trivial topological insulator (TI) phase, which is characterized by an insulating bulk surrounded by highly entangled superfluid edges. These highly entangled states are found to be robust against perturbations and topologically protected by the particle-hole symmetry, which is locally preserved. We also find a semi-quantitative agreement between entanglement and superconducting order parameter profiles, confirming then that entanglement can be used as a topological marker and an order parameter in these systems. The charge gap not only confirms the SF-TI transition, but also shows that this transition is mediated by a metallic intermediate regime within the bulk. Using the gap we could depict a phase diagram for which the non-trivial topological insulator can be found in such harmonically confined attractive systems.

We investigate how the quantum friction experienced by a polarizable atom moving with constant velocity parallel to a planar interface is modified when the latter consists of chiral or nonreciprocal media, with special focus on topological insulators. We use macroscopic quantum electrodynamics to obtain the velocity-dependent Casimir-Polder frequency shift and decay rate. These results are a generalization to matter with time-reversal symmetry breaking. We illustrate our findings by examining the nonretarded and retarded limits for five examples: a perfectly conducting mirror, a perfectly reflecting nonreciprocal mirror, a three-dimensional topological insulator, a perfectly reflecting chiral mirror and an isotropic chiral medium. We find different asymptotic power laws for all these materials. Interestingly, we find two bridges between chirality and nonreciprocity through the frequency shift that arise as a consequence of the magnetoelectric coupling. Namely, the position-dependent Casimir-Polder frequency shift for the nonreciprocal case depend on a geometric magnetic field associated with photoionization of chiral molecules, the Casimir-Polder depending on the velocities for the chiral case have the optical rotatory strength as the atomic response while those for the nonreciprocal case depend on an analog of the optical rotatory strength., Comment: 19 pages, 1 figure, Submitted

Three-Dimensional Polarized Light Imaging (3D-PLI) and Computational Scattered Light Imaging (ComSLI) map dense nerve fibers in brain sections with micrometer resolution using visible light. 3D-PLI reconstructs single fiber orientations, while ComSLI captures multiple directions per pixel, offering deep insights into brain tissue structure. Here, we introduce the Scattering Polarimeter, a high-speed correlative microscope to leverage the strengths of both methods. Based on a M\"uller polarimeter, it incorporates variable retarders and a large-area light source for direct and oblique illumination, enabling rapid 3D-PLI and ComSLI measurements as well as measuring the M\"uller matrix per pixel. Applied to human and vervet monkey brain sections, the Scattering Polarimeter generates results comparable to state-of-the-art 3D-PLI and ComSLI setups and creates a multi-modal fiber direction map, integrating the robust fiber orientations obtained from 3D-PLI with fiber crossings from ComSLI. Furthermore, we discuss applications of the Scattering Polarimeter for unprecedented correlative and multi-modal brain imaging., Comment: 29 pages, 8 figures, all study data are available on https://doi.org/10.26165/JUELICH-DATA/CUXQYF

Liebmann's Theorem is a fundamental result stating that a compact connected convex surface in $\mathbb{R}^3$ with constant mean curvature (cmc) is a totally umbilical sphere. We extend this theorem to surfaces with boundary by showing that a locally convex, embedded compact connected cmc surface, bounded by a convex curve in a plane $P$, is contained in one of the halfspaces of $\mathbb{R}^3$ determined by $P$. This extension leads to the conclusion that spherical caps are the only examples of locally convex, embedded compact connected cmc surfaces with non-zero curvature, bounded by a circle., Comment: Comments are welcome

Personalized Federated Learning is essential in AI-driven ubiquitous systems, supporting the distributed development of models able to adapt to diverse and evolving user behaviors while safeguarding privacy. Despite addressing heterogeneous user data distributions in collaborative model training, existing methods often face limitations balancing personalization and generalization, oversimplifying user similarities, or relying heavily on global models. In this paper, we propose FedSub, a novel federated approach designed to enhance personalization through the use of class-aware prototypes and model subnetworks. Prototypes serve as compact representations of user data, clustered on the server to identify similarities based on specific label patterns. Concurrently, subnetworks -- model components necessary to process each class -- are extracted locally and fused by the server according to these clusters, producing highly tailored model updates for each user. This fine-grained, class-specific aggregation of clients' models allows FedSub to capture the unique characteristics of individual user data patterns. The effectiveness of FedSub is validated in three real-world scenarios characterized by high data heterogeneity, derived from human activity recognition and mobile health applications. Experimental evaluations demonstrate FedSub's performance improvements with respect to the state-of-the-art and significant advancements in personalization for ubiquitous systems based on personal mobile and wearable devices., Comment: Submitted to Proceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies (IMWUT)

We propose a framework for two-player infinite-dimensional games with cooperative or competitive structure. These games take the form of coupled partial differential equations in which players optimize over a space of measures, driven by either a gradient descent or gradient descent-ascent in Wasserstein-2 space. We characterize the properties of the Nash equilibrium of the system, and relate it to the steady state of the dynamics. In the min-max setting, we show, under sufficient convexity conditions, that solutions converge exponentially fast and with explicit rate to the unique Nash equilibrium. Similar results are obtained for the cooperative setting. We apply this framework to distribution shift induced by interactions among a strategic population of agents and an algorithm, proving additional convergence results in the timescale-separated setting. We illustrate the performance of our model on (i) real data from an economics study on Colombia census data, (ii) feature modification in loan applications, and (iii) performative prediction. The numerical experiments demonstrate the importance of distribution-level, rather than moment-level, modeling., Comment: arXiv admin note: text overlap with arXiv:2307.01166

It is of great interest to understand the thermalization of open quantum many-body systems, and how quantum computers are able to efficiently simulate that process. A recently introduced disispative evolution, inspired by existing models of open system thermalization, has been shown to be efficiently implementable on a quantum computer. Here, we prove that, at high enough temperatures, this evolution reaches the Gibbs state in time scaling logarithmically with system size. The result holds for Hamiltonians that satisfy the Lieb-Robinson bound, such as local Hamiltonians on a lattice, and includes long-range systems. To the best of our knowledge, these are the first results rigorously establishing the rapid mixing property of high-temperature quantum Gibbs samplers, which is known to give the fastest possible speed for thermalization in the many-body setting. We then employ our result to the problem of estimating partition functions at high temperature, showing an improved performance over previous classical and quantum algorithms., Comment: 5+10 pages. Comments welcome

In this work, we initiate the study of Hamiltonian learning for positive temperature bosonic Gaussian states, the quantum generalization of the widely studied problem of learning Gaussian graphical models. We obtain efficient protocols, both in sample and computational complexity, for the task of inferring the parameters of their underlying quadratic Hamiltonian under the assumption of bounded temperature, squeezing, displacement and maximal degree of the interaction graph. Our protocol only requires heterodyne measurements, which are often experimentally feasible, and has a sample complexity that scales logarithmically with the number of modes. Furthermore, we show that it is possible to learn the underlying interaction graph in a similar setting and sample complexity. Taken together, our results put the status of the quantum Hamiltonian learning problem for continuous variable systems in a much more advanced state when compared to spins, where state-of-the-art results are either unavailable or quantitatively inferior to ours. In addition, we use our techniques to obtain the first results on learning Gaussian states in trace distance with a quadratic scaling in precision and polynomial in the number of modes, albeit imposing certain restrictions on the Gaussian states. Our main technical innovations are several continuity bounds for the covariance and Hamiltonian matrix of a Gaussian state, which are of independent interest, combined with what we call the local inversion technique. In essence, the local inversion technique allows us to reliably infer the Hamiltonian of a Gaussian state by only estimating in parallel submatrices of the covariance matrix whose size scales with the desired precision, but not the number of modes. This way we bypass the need to obtain precise global estimates of the covariance matrix, controlling the sample complexity., Comment: 43 pages, 1 figure. Corrections to Lemma 4.1. Main results are unchanged

We aim at characterizing the X-ray-to-optical/near-infrared broad-band emission of luminous QSOs in the first Gyr of cosmic evolution to understand whether they exhibit differences compared to the lower-\textit{z} QSO population. Our goal is also to provide for these objects a reliable and uniform catalog of SED fitting derivable properties such as bolometric and monochromatic luminosities, Eddington ratios, dust extinction, strength of the hot dust emission. We characterize the X-ray/UV emission of each QSO using average SEDs from luminous Type 1 sources and calculate bolometric and monochromatic luminosities. Finally we construct a mean SED extending from the X-rays to the NIR bands. We find that the UV-optical emission of these QSOs can be modelled with templates of $z\sim$2 luminous QSOs. We observe that the bolometric luminosities derived adopting some bolometric corrections at 3000 \AA\ ($BC_{3000\text{\AA}}$) largely used in the literature are slightly overestimated by 0.13 dex as they also include reprocessed IR emission. We estimate a revised value, i.e. $BC_{3000\text{\AA}}=3.3 $ which can be used for deriving $L_\text{bol}$ in \textit{z} $\geq$ 6 QSOs. A sub-sample of 11 QSOs is provided with rest-frame NIR photometry, showing a broad range of hot dust emission strength, with two sources exhibiting low levels of emission. Despite potential observational biases arising from non-uniform photometric coverage and selection biases, we produce a X-ray-to-NIR mean SED for QSOs at \textit{z} $\gtrsim$ 6, revealing a good match with templates of lower-redshift, luminous QSOs up to the UV-optical range, with a slightly enhanced contribution from hot dust in the NIR., Comment: All photometric data and the derived properties (luminosities, spectral slopes) are available on Zenodo at https://zenodo.org/records/14867157 in machine-readable format. The repository also includes the mean SED template for QSOs at the Epoch of Reionization, as shown in Figure 13 of the paper

Transformers are set to become ubiquitous with applications ranging from chatbots and educational assistants to visual recognition and remote sensing. However, their increasing computational and memory demands is resulting in growing energy consumption. Building models with fast and energy-efficient inference is imperative to enable a variety of transformer-based applications. Look Up Table (LUT) based Weightless Neural Networks are faster than the conventional neural networks as their inference only involves a few lookup operations. Recently, an approach for learning LUT networks directly via an Extended Finite Difference method was proposed. We build on this idea, extending it for performing the functions of the Multi Layer Perceptron (MLP) layers in transformer models and integrating them with transformers to propose Quasi Weightless Transformers (QuWeiT). This allows for a computational and energy-efficient inference solution for transformer-based models. On I-ViT-T, we achieve a comparable accuracy of 95.64% on CIFAR-10 dataset while replacing approximately 55% of all the multiplications in the entire model and achieving a 2.2x energy efficiency. We also observe similar savings on experiments with the nanoGPT framework.

In this paper we show that the number of radial positive solutions of the following critical problem $$ \Delta_p u(x) + \lambda K(|x|) \,u(x) \, |u(x)|^{q-2} =0\,,$$ $$ u(x)>0 \quad |x|<1,$$ $$ u(x)=0 \quad |x|=1,$$ where $q= \frac{np}{n-p}$, $\frac{2n}{n+2} \le p \le 2$ and $x \in \mathbb{R}^n$, undergoes a bifurcation phenomenon. Namely, the problem admits one solution for any $\lambda>0$ if $K$ is steep enough at $0$, while it admits no solutions for $\lambda$ small and two solutions for $\lambda$ large if $K$ is too flat at $0$. The existence of the second solution is new, even in the classical Laplace case. The proofs use Fowler transformation and dynamical systems tools., Comment: 41 pages, 5 figures

This article is devoted to the study of a $2$-dimensional piecewise smooth (but possibly) discontinuous dynamical system, subject to a non-autonomous perturbation; we assume that the unperturbed system admits a homoclinic trajectory $\vec{\gamma}(t)$. Our aim is to analyze the dynamics in a neighborhood of $\vec{\gamma}(t)$ as the perturbation is turned on, by defining a Poincar\'e map and evaluating fly time and space displacement of trajectories performing a loop close to $\vec{\gamma}(t)$. Besides their intrinsic mathematical interest, these results can be thought of as a first step in the analysis of several interesting problems, such as the stability of a homoclinic trajectory of a non-autonomous ODE and a possible extension of Melnikov chaos to a discontinuous setting., Comment: 62 pages, 11 figures

Let $\mathbb{F}$ be a field and $\mathsf{G}$ a group. This work is inspired in the following problem: "{\it given a division (simple) $\mathsf{G}$-graded $\mathbb{F}$-algebra, is there any other division (simple) $\mathsf{G}$-graded $\mathbb{F}$-algebra such that the former can be $\mathsf{G}$-imbedded in the latter?}". In this work, we answer this question affirmatively for $\mathbb{F}$ algebraically closed, $\mathsf{G}$ finite abelian, and associative algebras of finite dimension. To prove this, we apply concepts and properties of Group Cohomology. We show $\mathcal{H}^2(H, \mathbb{F}^*)=\mathsf{res}^\mathsf{G}_H \left(\mathcal{H}^2(\mathsf{G}, \mathbb{F}^*)\right)$, where $H$ is a subgroup of $\mathsf{G}$ and $\mathsf{res}^\mathsf{G}_H$ is the restriction homomorphism. Posteriorly, we prove that, given any $H_1,H_2\leq\mathsf{G}$ and $\sigma_i\in\mathcal{Z}^2(H_i,\mathbb{F}^*)$, $i=1,2$, are equivalent: i) $\mathbb{F}^{\sigma_1}[H_1] \stackrel{\mathsf{G}}{\hookrightarrow} \mathbb{F}^{\sigma_2}[H_2]$; ii) $H_1\leq H_2$ and $[\sigma_1]=[\sigma_2]_{H_1}$; iii) $\mathsf{T}^{\mathsf{G}}(\mathbb{F}^{\sigma_2}[H_2])\subseteq \mathsf{T}^{\mathsf{G}}(\mathbb{F}^{\sigma_1}[H_1])$, where $\mathsf{T}^{\mathsf{G}}(\mathbb{F}^{\sigma_i}[H_i])$ is the $\mathsf{G}$T-ideal of graded identities of $\mathbb{F}^{\sigma_i}[H_i]$. Furthermore, we prove that, given $\mathfrak{A}$ and $\mathfrak{B}$ two finite dimensional simple $\mathsf{G}$-graded $\mathbb{F}$-algebras, if $\mathbb{F}$ is algebraically closed, $\mathsf{char}(\mathbb{F}) = 0$ or $\mathsf{char} (\mathbb{F})$ is coprime with the order of each finite subgroup of $\mathsf{G}$, and any subgroup of $\mathsf{G}$ is normal, then $\mathsf{T}^{\mathsf{G}}(\mathfrak{A})\subseteq \mathsf{T}^{\mathsf{G}}(\mathfrak{B})$ iff $\mathfrak{B} \stackrel{\mathsf{G}}{\hookrightarrow} \mathfrak{A}$.

One of the main open questions in the field of luminous ($L_{\rm bol}>10^{47}\,\rm erg\,s^{-1}$) quasars (QSOs) at $z \gtrsim 6$ is the rapid formation ($< 1\,$Gyr) of their supermassive black holes (SMBHs). For this work we analysed the relation between the X-ray properties and other properties describing the physics and growth of both the accretion disc and the SMBH in QSOs at the Epoch of Reionization (EoR). The sample consists of 21 $z>6$ QSOs, which includes 16 sources from the rapidly grown QSOs from the HYPERION sample and five other luminous QSOs with available high-quality archival X-ray data. We discovered a strong and statistically significant ($>3\sigma$) relation between the X-ray continuum photon index ($\Gamma$) and the $\rm C\,IV$ disc wind velocity ($v_{\rm C\,IV}$) in $z>6$ luminous QSOs, whereby the higher the $v_{\rm C\,IV}$, the steeper the $\Gamma$. This relation suggests a link between the disc-corona configuration and the kinematics of disc winds. Furthermore, we find evidence at $>2-3\sigma$ level that $\Gamma$ and $v_{\rm C\,IV}$ are correlated to the growth rate history of the SMBH. Although additional data are needed to confirm it, this result may suggest that, in luminous $z>6$ QSOs, the SMBH predominantly grows via fast accretion rather than via initial high seed BH mass., Comment: Accepted for publication in Astronomy & Astrophysics

We introduce the Differentiable Weightless Neural Network (DWN), a model based on interconnected lookup tables. Training of DWNs is enabled by a novel Extended Finite Difference technique for approximate differentiation of binary values. We propose Learnable Mapping, Learnable Reduction, and Spectral Regularization to further improve the accuracy and efficiency of these models. We evaluate DWNs in three edge computing contexts: (1) an FPGA-based hardware accelerator, where they demonstrate superior latency, throughput, energy efficiency, and model area compared to state-of-the-art solutions, (2) a low-power microcontroller, where they achieve preferable accuracy to XGBoost while subject to stringent memory constraints, and (3) ultra-low-cost chips, where they consistently outperform small models in both accuracy and projected hardware area. DWNs also compare favorably against leading approaches for tabular datasets, with higher average rank. Overall, our work positions DWNs as a pioneering solution for edge-compatible high-throughput neural networks.

We propose a convex controller synthesis framework for a large class of constrained linear systems, including those described by (deterministic and stochastic) partial differential equations and integral equations, commonly used in fluid dynamics, thermo-mechanical systems, quantum control, or transportation networks. Most existing control techniques rely on a (finite-dimensional) discrete description of the system, via ordinary differential equations. Here, we work instead with more general (infinite-dimensional) Hilbert spaces. This enables the discretization to be applied after the optimization (optimize-then-discretize). Using output-feedback SLS, we formulate the controller synthesis as a convex optimization problem. Structural constraints like sensor and communication delays, and locality constraints, are incorporated while preserving convexity, allowing parallel implementation and extending key SLS properties to infinite dimensions. The proposed approach and its benefits are demonstrated on a linear Boltzmann equation.