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Solid-state quantum registers consisting of optically active electron spins with nearby nuclear spins are promising building blocks for future quantum technologies. For electron spin-1 registers, dynamical decoupling (DD) quantum gates have been developed that enable the precise control of multiple nuclear spin qubits. However, for the important class of electron spin-1/2 systems, this control method suffers from intrinsic selectivity limitations, resulting in reduced nuclear spin gate fidelities. Here we demonstrate improved control of single nuclear spins by an electron spin-1/2 using Dynamically Decoupled Radio Frequency (DDRF) gates. We make use of the electron spin-1/2 of a diamond tin-vacancy center, showing high-fidelity single-qubit gates, single-shot readout, and spin coherence beyond a millisecond. The DD control is used as a benchmark to observe and control a single carbon-13 nuclear spin. Using the DDRF control method, we demonstrate improved control on that spin. In addition, we find and control an additional nuclear spin that is insensitive to the DD control method. Using these DDRF gates, we show entanglement between the electron and the nuclear spin with 72(3)% state fidelity. Our extensive simulations indicate that DDRF gate fidelities well in excess are feasible. Finally, we employ time-resolved photon detection during readout to quantify the hyperfine coupling for the electron's optically excited state. Our work provides key insights into the challenges and opportunities for nuclear spin control in electron spin-1/2 systems, opening the door to multi-qubit experiments on these promising qubit platforms.

Stereoelectroencephalography (SEEG) is an invasive surgical procedure to record the electrical activities in cortical brain regions, aiming at identifying the Epileptogenic Zone (EZ) in patients with drug-resistant epilepsy. To improve the accuracy of the EZ definition, SEEG analysis can be supported by computational tools, among which the Epileptogenic Index (EI) represents the most common solution. However, the scientific community has still not found an agreement on which quantitative biomarkers can characterize the cortical sites within the EZ. In this work, we design a new algorithm, named Desynchronization Index (DI), to assist neurophysiologists in SEEG interpretation. Our algorithm estimates the effective connectivity between cortical sites and hypothesizes that the EZ is identified by those sites getting abnormally desynchronized from the network during the seizure generation. We test the proposed method over a SEEG dataset of 10 seizures, comparing its accuracy in terms of EZ definition against the EI algorithm and clinical ground truth. Our results indicate that the DI algorithm underscores specific connectivity dynamics that can hardly be identified with a pure visual analysis, increasing sensitivity in detecting epileptogenic cortical sites.

Superclusters are the largest-scale environments where a number of galaxy clusters interact with each other through minor/major mergers and grow via accretion along cosmic filaments. We focus on the A3528 complex in the core of the Shapley Supercluster. This system includes three clusters, A3528 (composed itself by two sub-clusters, namely A3528N and A3528S), A3532 and A3530, and presents a mildly active dynamical state. We study how minor mergers affect the evolution of radio galaxies and whether they are able to re-accelerate relativistic electrons in the ICM. We used observations from the uGMRT (Band 3, 4 and 5) and MeerKAT (L-band) telescopes to obtain images and spectral index maps over a wide frequency band and spatial resolutions. We compare these data with those from the SRG/eROSITA X-ray telescope. We detect faint diffuse radio emission associated with the radio galaxies. The BCGs in A3528S and A3532 show filaments of diffuse radio emission which extend for $\sim200-400$ kpc out of the radio galaxy. The spectral index of these filaments is extremely steep and almost constant ($\alpha\sim -2, -2.5$). Contrary to the radio tails in A3528N, the spectral properties of these radio filaments are not consistent with standard models of plasma ageing. We also detect roundish diffuse radio emission around the BCG in A3528S which could be classified as a radio mini-halo. The radio tail in this cluster appears longer that in earlier detections, being $\sim300$ kpc long at all frequencies. We linked the presence of extended radio emission in the form of filaments and threads in the A3528 complex with the effect of minor mergers. This is reinforced by the increasing X-ray fluctuations in correspondence with the radio extended emission in A3528S. Despite the less energy involved, our findings support the hypothesis that these events can re-energise plasma originating from radio galaxies., Comment: 28 pages, 23 figures and 5 tables; accepted for publication in Astronomy & Astrophysics

Efficient audio representations in a compressed continuous latent space are critical for generative audio modeling and Music Information Retrieval (MIR) tasks. However, some existing audio autoencoders have limitations, such as multi-stage training procedures, slow iterative sampling, or low reconstruction quality. We introduce Music2Latent, an audio autoencoder that overcomes these limitations by leveraging consistency models. Music2Latent encodes samples into a compressed continuous latent space in a single end-to-end training process while enabling high-fidelity single-step reconstruction. Key innovations include conditioning the consistency model on upsampled encoder outputs at all levels through cross connections, using frequency-wise self-attention to capture long-range frequency dependencies, and employing frequency-wise learned scaling to handle varying value distributions across frequencies at different noise levels. We demonstrate that Music2Latent outperforms existing continuous audio autoencoders in sound quality and reconstruction accuracy while achieving competitive performance on downstream MIR tasks using its latent representations. To our knowledge, this represents the first successful attempt at training an end-to-end consistency autoencoder model., Comment: Accepted to ISMIR 2024

A fraction of galaxy clusters harbor diffuse radio sources known as radio halos. The currently adopted scenario for their formation is based on second-order Fermi re-acceleration of seed electrons that is driven by merger-driven turbulence in the intra-cluster medium. This mechanism is expected to be inefficient, which implies that a significant fraction of halos should have very steep ($\alpha < -1.5$) energy spectra. We start investigating the potential and current limitations of the combination of the two surveys conducted by LOFAR, LoTSS (144 MHz) and LoLSS (54 MHz), to probe the origin of radio halos. We follow up the 20 radio halos detected in the DR1 of LoTSS, which covers the HETDEX field, with the LoLSS survey, and we study their spectral properties between 54 and 144 MHz. After the removal of compact sources, 9 halos were excluded due to unreliable halo flux density measurements at 54 MHz. Our main finding is that 7 out of 11 ($\sim$ 64%) exhibit an ultra-steep spectrum ($\alpha < -1.5$), which is a key prediction of turbulent re-acceleration models. We also note a tentative trend for more massive systems to host flatter halos, although the currently poor statistics does not allow for a deeper analysis. Our sample suffers from low angular resolution at 54 MHz, which limits the accuracy of the compact-sources subtraction. Nevertheless, this study is the first step towards providing compelling evidence for the existence of a large fraction of radio halos with very steep spectrum, which is a fundamental prediction of turbulent re-acceleration models. In this regard, the forthcoming second data release of LoLSS, along with the integration of LOFAR international stations and the instrumental upgrade to LOFAR2.0, will improve both the statistics and the low-frequency angular resolution, allowing to conclusively determine the origin of radio halos in galaxy clusters., Comment: A&A Letter; 11 pages, 12 figures

We present our work on developing and training scalable graph foundation models (GFM) using HydraGNN, a multi-headed graph convolutional neural network architecture. HydraGNN expands the boundaries of graph neural network (GNN) in both training scale and data diversity. It abstracts over message passing algorithms, allowing both reproduction of and comparison across algorithmic innovations that define convolution in GNNs. This work discusses a series of optimizations that have allowed scaling up the GFM training to tens of thousands of GPUs on datasets that consist of hundreds of millions of graphs. Our GFMs use multi-task learning (MTL) to simultaneously learn graph-level and node-level properties of atomistic structures, such as the total energy and atomic forces. Using over 150 million atomistic structures for training, we illustrate the performance of our approach along with the lessons learned on two United States Department of Energy (US-DOE) supercomputers, namely the Perlmutter petascale system at the National Energy Research Scientific Computing Center and the Frontier exascale system at Oak Ridge National Laboratory. The HydraGNN architecture enables the GFM to achieve near-linear strong scaling performance using more than 2,000 GPUs on Perlmutter and 16,000 GPUs on Frontier. Hyperparameter optimization (HPO) was performed on over 64,000 GPUs on Frontier to select GFM architectures with high accuracy. Early stopping was applied on each GFM architecture for energy awareness in performing such an extreme-scale task. The training of an ensemble of highest-ranked GFM architectures continued until convergence to establish uncertainty quantification (UQ) capabilities with ensemble learning. Our contribution opens the door for rapidly developing, training, and deploying GFMs using large-scale computational resources to enable AI-accelerated materials discovery and design., Comment: 16 pages, 13 figures

Recent advancements in deep generative models present new opportunities for music production but also pose challenges, such as high computational demands and limited audio quality. Moreover, current systems frequently rely solely on text input and typically focus on producing complete musical pieces, which is incompatible with existing workflows in music production. To address these issues, we introduce "Diff-A-Riff," a Latent Diffusion Model designed to generate high-quality instrumental accompaniments adaptable to any musical context. This model offers control through either audio references, text prompts, or both, and produces 48kHz pseudo-stereo audio while significantly reducing inference time and memory usage. We demonstrate the model's capabilities through objective metrics and subjective listening tests, with extensive examples available on the accompanying website: sonycslparis.github.io/diffariff-companion/, Comment: 8 pages, 2 figures, 3 tables

The evolution of Active Galactic Nuclei (AGN) is closely connected to their host galaxies and surroundings. Via feedback processes, AGN can counteract the cooling of the intracluster medium (ICM) and suppress star formation in their host galaxies. Radio observations at low frequencies provide a glimpse into the history of AGN activity. The Virgo cluster is a substantial reservoir of nearby galaxies and provides an ideal laboratory for the study of AGN as well as their feedback mechanisms. The aim of our work is to characterise the AGN population within the Virgo cluster down to low radio luminosities, constrain the AGN duty cycle and investigate environmental feedback in cluster member galaxies. We analyse 144 MHz and 1.3 GHz radio observations of early-type galaxies from the ACS Virgo Cluster Survey (ACSVCS) taken with LOFAR and MeerKAT. We detect 12 of these galaxies at 144 MHz, 5 of which show clearly extended radio emission. The radio luminosity shows a strong dependence on the stellar mass of the host galaxy, in agreement with previous results. As a notable outlier, the massive elliptical galaxy NGC 4365 ($M_* = 2.2 \times 10^{11} M_\odot$) is not detected as a compact source in the LOFAR observations. Instead, it is surrounded by diffuse, low-surface brightness emission, which hints towards a past phase of stronger nuclear activity. Furthermore, we find a cavity in NGC 4472 (= M 49) inflated by the wide-angle tail only visible in the LOFAR data, which implies that the cavity was created by a past outburst. The corresponding cavity power is of the same order of magnitude as the jet power in the present duty cycle of the AGN., Comment: 17 pages, 10 figures

Composing poetry or lyrics involves several creative factors, but a challenging aspect of generation is the adherence to a more or less strict metric and rhyming pattern. To address this challenge specifically, previous work on the task has mainly focused on reverse language modeling, which brings the critical selection of each rhyming word to the forefront of each verse. On the other hand, reversing the word order requires that models be trained from scratch with this task-specific goal and cannot take advantage of transfer learning from a Pretrained Language Model (PLM). We propose a novel fine-tuning approach that prepends the rhyming word at the start of each lyric, which allows the critical rhyming decision to be made before the model commits to the content of the lyric (as during reverse language modeling), but maintains compatibility with the word order of regular PLMs as the lyric itself is still generated in left-to-right order. We conducted extensive experiments to compare this fine-tuning against the current state-of-the-art strategies for rhyming, finding that our approach generates more readable text and better rhyming capabilities. Furthermore, we furnish a high-quality dataset in English and 12 other languages, analyse the approach's feasibility in a multilingual context, provide extensive experimental results shedding light on good and bad practices for lyrics generation, and propose metrics to compare methods in the future., Comment: 18 pages, 1 figure

Recent low-frequency radio observations at 140 MHz discovered a 3 Mpc-long bridge of diffuse emission connecting the galaxy clusters Abell 0399 and Abell 0401. We present follow-up observations at 60 MHz to constrain the spectral index of the bridge, which so far has only been detected at 140 and 144 MHz. We analysed deep (~18 hours) LOw Frequency ARray (LOFAR) Low Band Antenna (LBA) data at 60 MHz to detect the bridge at very low frequencies. We then conducted a multi-frequency study with LOFAR HBA data at 144 MHz and uGMRT data at 400 MHz. Assuming second-order Fermi mechanisms for the re-acceleration of relativistic electrons driven by turbulence in the radio bridge regions, we compare the observed radio spectrum with theoretical synchrotron models. The bridge is detected in the 75'' resolution LOFAR image at 60 MHz and its emission fully connects the region between the two galaxy clusters. Between 60 MHz and 144 MHz we found an integrated spectral index value of -1.44 +\- 0.16 for the bridge emission. For the first time, we produced spectral index and related uncertainties maps for a radio bridge. We produce a radio spectrum, which show significant steepening between 144 and 400 MHz. This detection at low frequencies provides important information on the models of particle acceleration and magnetic field structure on very extended scales. The spectral index gives important clues to the origin of inter-cluster diffuse emission. The steepening of the spectrum above 144 MHz can be explained in a turbulent re-acceleration framework, assuming that the acceleration timescales are longer than ~200 Myr., Comment: Letter to the Editor: 7 pages, 4 figures, 2 tables; accepted for publication in Astronomy & Astrophysics (A&A)

Radio jets are present in a diverse sample of AGN. However, the mechanisms of jet powering are not fully understood, and it is yet unclear to what extent they obey mass-invariant scaling relations, similar to those found for the triggering and fuelling of X-ray selected AGN. We study the incidence of eROSITA/eFEDS X-ray and LOFAR radio AGN as a function of several stellar mass normalised AGN power indicators. A new sample of radio AGN from the LOFAR-eFEDS survey is defined and we publicly release this catalogue, including host galaxy counterparts from the Legacy Survey DR9, LOFAR radio morphologies and host galaxy properties from the complete, spectroscopic (z<0.4) GAMA09 survey. The fraction of GAMA09 galaxies hosting radio, X-ray and both radio and X-ray AGN are calculated as a function of the specific black hole kinetic ($\lambda_{\rm Jet}$) and radiative ($\lambda_{\rm Edd}$) power. The incidence of eFEDS X-ray AGN as a function of $\lambda_{\rm Edd}$ shows the same mass-invariance as found in past studies. Meanwhile, radio AGN, regardless of their morphology, are more likely to be hosted in more massive galaxies, at all $\lambda_{\rm Jet}$. Across the stellar mass range, the compact radio AGN incidence follows the same power-law distribution, showing that it is not only high mass galaxies that host high power radio AGN and vice versa. On the other hand, the incidence of compact and complex radio AGN is boosted at the highest jet powers, diverging from a simple power-law. Interestingly, this increased incidence cannot be explained by more powerful radio AGN lying in more dense environments which could naturally boost their radio luminosity. Overall, we show that statistical incidence studies are a powerful method to probe disk-jet coupling for different AGN accretion modes, although future work on a more reliable determination of jet power for diverse samples of radio AGN is needed., Comment: 30 pages, 32 figures, accepted for publication in A&A

The ability to automatically generate music that appropriately matches an arbitrary input track is a challenging task. We present a novel controllable system for generating single stems to accompany musical mixes of arbitrary length. At the core of our method are audio autoencoders that efficiently compress audio waveform samples into invertible latent representations, and a conditional latent diffusion model that takes as input the latent encoding of a mix and generates the latent encoding of a corresponding stem. To provide control over the timbre of generated samples, we introduce a technique to ground the latent space to a user-provided reference style during diffusion sampling. For further improving audio quality, we adapt classifier-free guidance to avoid distortions at high guidance strengths when generating an unbounded latent space. We train our model on a dataset of pairs of mixes and matching bass stems. Quantitative experiments demonstrate that, given an input mix, the proposed system can generate basslines with user-specified timbres. Our controllable conditional audio generation framework represents a significant step forward in creating generative AI tools to assist musicians in music production., Comment: ICASSP 2024

The eROSITA telescope array aboard the Spektrum Roentgen Gamma (SRG) satellite began surveying the sky in December 2019, with the aim of producing all-sky X-ray source lists and sky maps of an unprecedented depth. Here we present catalogues of both point-like and extended sources using the data acquired in the first six months of survey operations (eRASS1; completed June 2020) over the half sky whose proprietary data rights lie with the German eROSITA Consortium. We describe the observation process, the data analysis pipelines, and the characteristics of the X-ray sources. With nearly 930000 entries detected in the most sensitive 0.2-2.3 keV energy range, the eRASS1 main catalogue presented here increases the number of known X-ray sources in the published literature by more than 60%, and provides a comprehensive inventory of all classes of X-ray celestial objects, covering a wide range of physical processes. A smaller catalogue of 5466 sources detected in the less sensitive but harder 2.3-5 keV band is the result of the first true imaging survey of the entire sky above 2 keV. We show that the number counts of X-ray sources in eRASS1 are consistent with those derived over narrower fields by past X-ray surveys of a similar depth, and we explore the number counts variation as a function of the location in the sky. Adopting a uniform all-sky flux limit (at 50% completeness) of F_{0.5-2 keV} > 5 \times 10^{-14}$ erg\,s$^{-1}$\,cm$^{-2}$, we estimate that the eROSITA all-sky survey resolves into individual sources about 20% of the cosmic X-ray background in the 1-2 keV range. The catalogues presented here form part of the first data release (DR1) of the SRG/eROSITA all-sky survey. Beyond the X-ray catalogues, DR1 contains all detected and calibrated event files, source products (light curves and spectra), and all-sky maps. Illustrative examples of these are provided., Comment: 39 pages, 23 figures. Accepted for publication in A&A. Accompanying eROSITA-DE Data Release 1

We reassess the problem of symmetry restoration induced by observers' acceleration within the context of interacting quantum field theories in Minkowski spacetime. We argue that the imposition of a frame-independent renormalization condition negates any observed symmetry restoration by a Rindler observer. Technically, we compute the one-loop effective potential of a $\lambda\varphi^4$ theory for an accelerated observer, employing a distinct methodology from prior investigations. Emphasizing the intricacies of the model's renormalization, the analysis offers novel insights into the interplay between acceleration and spontaneous symmetry breaking in quantum field theory., Comment: 16 pages, 1 figure

We present the analysis of new, deep $Chandra$ observations (130~ks) of the galaxy cluster Abell~2495. This object is known for the presence of a triple offset between the peaks of the intracluster medium (ICM), the brightest cluster galaxy (BCG), and the warm gas glowing in H$\alpha$ line. The new $Chandra$ data confirm that the X-ray emission peak is located at a distance of $\sim$6.2 kpc from the BCG, and at $\sim$3.9 kpc from the H$\alpha$ emission peak. Moreover, we identify two generations of X-ray cavities in the ICM, likely inflated by the central radio galaxy activity. Through a detailed morphological and spectral analysis we determine that the power of the AGN outbursts ($P_{cav} = 4.7\pm1.3\times10^{43}$~erg~s$^{-1}$) is enough to counterbalance the radiative losses from ICM cooling ($L_{cool} = 5.7\pm0.1\times10^{43}$~erg~s$^{-1}$). This indicates that, despite a fragmented cooling core, Abell~2495 still harbors an effective feedback cycle. We argue that the offsets are most likely caused by sloshing of the ICM, supported by the presence of spiral structures and a probable cold front in the gas at $\sim$58 kpc east of the center. Ultimately, we find that the outburst interval between the two generations of X-ray cavities is of the order of the dynamical sloshing timescale, as already hinted from the previous $Chandra$ snapshot. We thus speculate that sloshing may be able to regulate the timescales of AGN feedback in Abell~2495, by periodically fuelling the central AGN.

We present the discovery of a very extended (550 kpc) and low-surface-brightness ($ 3.3 \mu \mathrm{Jy} \, arcsec^{-2} $ at 144 MHz) radio emission region in Abell 1318. These properties are consistent with its characterisation as an active galactic nucleus (AGN) remnant radio plasma, based on its morphology and radio spectral properties. We performed a broad-band (54 - 1400 MHz) radio spectral index and curvature analysis using LOFAR, uGMRT, and WSRT-APERTIF data. We also derived the radiative age of the detected emission, estimating a maximum age of 250 Myr. The morphology of the source is remarkably intriguing, with two larger, oval-shaped components and a thinner, elongated, and filamentary structure in between, plausibly reminiscent of two aged lobes and a jet. Based on archival {\it Swift} as well as SDSS data we performed an X-ray and optical characterisation of the system, whose virial mass was estimated to be $ \sim 7.4 \times 10^{13} \, \mathrm{M} _{\odot}$. This places A1318 in the galaxy group regime. Interestingly, the radio source does not have a clear optical counterpart embedded in it, thus, we propose that it is most likely an unusual AGN remnant of previous episode(s) of activity of the AGN hosted by the brightest group galaxy ($ \sim 2.6 \times 10^{12} \, \mathrm{M} _{\odot}$), which is located at a projected distance of $\sim$170 kpc in the current epoch. This relatively high offset may be a result of IGrM sloshing sourced by a minor merger. The filamentary morphology of the source may suggest that the remnant plasma has been perturbed by the system dynamics, however, only future deeper X-ray observations will be able to address this question., Comment: 16 pages, 9 figures, accepted by A&A; edited some affiliations

Music source separation is focused on extracting distinct sonic elements from composite tracks. Historically, many methods have been grounded in supervised learning, necessitating labeled data, which is occasionally constrained in its diversity. More recent methods have delved into N-shot techniques that utilize one or more audio samples to aid in the separation. However, a challenge with some of these methods is the necessity for an audio query during inference, making them less suited for genres with varied timbres and effects. This paper offers a proof-of-concept for a self-supervised music source separation system that eliminates the need for audio queries at inference time. In the training phase, while it adopts a query-based approach, we introduce a modification by substituting the continuous embedding of query audios with Vector Quantized (VQ) representations. Trained end-to-end with up to N classes as determined by the VQ's codebook size, the model seeks to effectively categorise instrument classes. During inference, the input is partitioned into N sources, with some potentially left unutilized based on the mix's instrument makeup. This methodology suggests an alternative avenue for considering source separation across diverse music genres. We provide examples and additional results online., Comment: 4 pages, 2 figures, 1 table; Accepted at the 37th Conference on Neural Information Processing Systems (2023), Machine Learning for Audio Workshop

Color-centers integrated with nanophotonic devices have emerged as a compelling platform for quantum science and technology. Here we integrate tin-vacancy centers in a diamond waveguide and investigate the interaction with light at the single-photon level. We observe single-emitter induced extinction of the transmitted light up to 25% and measure the nonlinear effect on the photon statistics. Furthermore, we demonstrate fully tunable interference between the reflected single-photon field and laser light back-scattered at the fiber end and show the corresponding controlled change between bunched and anti-bunched photon statistics in the reflected field.

Diamond Tin-Vacancy centers have emerged as a promising platform for quantum information science and technology. A key challenge for their use in more complex quantum experiments and scalable applications is the ability to prepare the center in the desired charge state with the optical transition at a pre-defined frequency. Here we report on heralding such successful preparation using a combination of laser excitation, photon detection, and real-time logic. We first show that fluorescence photon counts collected during an optimized resonant probe pulse strongly correlate with the subsequent charge state and optical transition frequency, enabling real-time heralding of the desired state through threshold photon counting. We then implement and apply this heralding technique to photoluminescence excitation measurements, coherent optical driving, and an optical Ramsey experiment, finding strongly improved optical coherence with increasing threshold. Finally, we demonstrate that the prepared optical frequency follows the probe laser across the inhomogeneous linewidth, enabling tuning of the transition frequency over multiple homogeneous linewidths.

Efficient coupling of optically active qubits to optical cavities is a key challenge for solid-state-based quantum optics experiments and future quantum technologies. Here we present a quantum photonic interface based on a single Tin-Vacancy center in a micrometer-thin diamond membrane coupled to a tunable open microcavity. We use the full tunability of the microcavity to selectively address individual Tin-Vacancy centers within the cavity mode volume. Purcell enhancement of the Tin-Vacancy center optical transition is evidenced both by optical excited state lifetime reduction and by optical linewidth broadening. As the emitter selectively reflects the single-photon component of the incident light, the coupled emitter-cavity system exhibits strong quantum nonlinear behavior. On resonance, we observe a transmission dip of 50 % for low incident photon number per Purcell-reduced excited state lifetime, while the dip disappears as the emitter is saturated with higher photon number. Moreover, we demonstrate that the emitter strongly modifies the photon statistics of the transmitted light by observing photon bunching. This work establishes a versatile and tunable platform for advanced quantum optics experiments and proof-of-principle demonstrations towards quantum networking with solid-state qubits., Comment: 15 pages, 12 figures

Generating entanglement between distant quantum systems is at the core of quantum networking. In recent years, numerous theoretical protocols for remote entanglement generation have been proposed, of which many have been experimentally realized. Here, we provide a modular theoretical framework to elucidate the general mechanisms of photon-mediated entanglement generation between single spins in atomic or solid-state systems. Our framework categorizes existing protocols at various levels of abstraction and allows for combining the elements of different schemes in new ways. These abstraction layers make it possible to readily compare protocols for different quantum hardware. To enable the practical evaluation of protocols tailored to specific experimental parameters, we have devised numerical simulations based on the framework with our codes available online.

In the upcoming decade, deep learning may revolutionize the natural sciences, enhancing our capacity to model and predict natural occurrences. This could herald a new era of scientific exploration, bringing significant advancements across sectors from drug development to renewable energy. To answer this call, we present DeepSpeed4Science initiative (deepspeed4science.ai) which aims to build unique capabilities through AI system technology innovations to help domain experts to unlock today's biggest science mysteries. By leveraging DeepSpeed's current technology pillars (training, inference and compression) as base technology enablers, DeepSpeed4Science will create a new set of AI system technologies tailored for accelerating scientific discoveries by addressing their unique complexity beyond the common technical approaches used for accelerating generic large language models (LLMs). In this paper, we showcase the early progress we made with DeepSpeed4Science in addressing two of the critical system challenges in structural biology research.

Nonlinearities in the dispersion relations associated with different interactions designs, boundary conditions and the existence of a physical cut-off scale can alter the quantum vacuum energy of a nonrelativistic system nontrivially. As a material realization of this, we consider a 1D-periodic rotating, interacting non-relativistic setup. The quantum vacuum energy of such a system is expected to comprise two contributions: a fluctuation-induced quantum contribution and a repulsive centrifugal-like term. We analyze the problem in detail within a complex Schoedinger quantum field theory with a quartic interaction potential and perform the calculations non-perturbatively in the interaction strength by exploiting the nonlinear structure of the associated nonlinear Schroedinger equation. Calculations are done in both zeta-regularization, as well as by introducing a cut-off scale. We find a generic, regularization-independent behavior, where the competition between the interaction and rotation can be balanced at some critical ring-size, where the quantum vacuum energy has a maxima and the force changes sign. The inclusion of a cut-off smoothes out the vacuum energy at small distance but leaves unaltered the long distance behavior. We discuss how this behavior can be tested with ultracold-atoms., Comment: 10 pages, 3 figures

Given a collection $\{ G_i\}_{i=1}^d$ of finite groups and a ring $R$, we have previously introduced and studied certain foundational properties of the join ring $\mathcal{J}_{G_1, G_2, \ldots, G_d}(R)$. This ring bridges two extreme worlds: matrix rings $M_n(R)$ on one end, and group rings $R[G]$ on the other. The construction of this ring was motivated by various problems in graph theory, network theory, nonlinear dynamics, and neuroscience. In this paper, we continue our investigations of this ring, focusing more on its arithmetic properties. We begin by constructing a generalized augmentation map that gives a structural decomposition of this ring. This decomposition allows us to compute the zeta function of the join of group rings. We show that the join of group rings is a natural home for studying the concept of simultaneous primitive roots for a given set of primes. This concept is related to the order of the unit group of the join of group rings. Finally, we characterize the join of group rings over finite fields with the property that the order of every unit divides a fixed number. Remarkably, Mersenne and Fermat primes unexpectedly emerge within the context of this exploration., Comment: 21 pages

In this paper we propose a definition of regularity suited for polar spaces of infinite rank and we investigate to which extent properties of regular polar spaces of finite rank can be generalized to polar spaces of infinite rank., Comment: 44 pages

In this paper we consider a family of projective embeddings of the geometry $\Gamma = A_{n,\{1,n\}}(F)$ of point-hyperplanes flags of the projective geometry $\Sigma = PG(n,F)$. The natural embedding $\varepsilon_{mathrm{nat}}$ is one of them. It maps every point-hyperplane flag $(p,H)$ of $\Sigma$ onto the vector-line $\langle x\otimes\xi\rangle$, where $x$ is a representative vector of $p$ and $\xi$ is a linear functional describing $H$. The other embeddings have been discovered by Thas and Van Maldeghem (2000) for the case $n = 2$ and later generalized to any $n$ by De Schepper, Schillewaert and Van Maldeghem (2023). They are obtained as twistings of $\varepsilon_{\mathrm{nat}}$ by non-trivial automorphisms of $F$. Explicitly, for $\sigma\in Aut(F)\setminus\{\mathrm{id}_F\}$, the twisting $\varepsilon_\sigma$ of $\varepsilon_{\mathrm{nat}}$ by $\sigma$ maps $(p,H)$ onto $\langle x\sigma\otimes \xi\rangle$. We shall prove that, when $|Aut(F)| > 1$ a geometric hyperplane $\cal H$ of $\Gamma$ arises from $\varepsilon_{\mathrm{nat}}$ and one of its twistings or from two distinct twistings of $\varepsilon_{\mathrm{nat}}$ if and only if ${\cal H} = \{(p,H)\in \Gamma \mid p\in A \mbox{ or } a \in H\}$ for a possibly non-incident point-hyperplane pair $(a,A)$ of $\Sigma$. We call these hyperplanes quasi-singular hyperplanes. With the help of this result we shall prove that if $|Aut(F)| > 1$ then $\Gamma$ admits no absolutely universal embedding., Comment: 25 pages

Let $A$ and $B$ designate $n\times n$ matrices with coefficients in a field $F$. In this paper, we completely answer the following question: For $A$ fixed, what are the possible characteristic polynomials of $A+B$, where $B$ ranges over matrices of rank $\le m$?, Comment: To appear in Operators and Matrices

In this paper we investigate hyperplanes of the point-line geometry $\mathit{A}_{n,\{1,n\}}(\mathbb{F})$ of point-hyerplane flags of the projective geometry $\mathrm{PG}(n,\mathbb{F})$. Renouncing a complete classification, which is not yet within our reach, we describe the hyperplanes which arise from the natural embedding of $\mathit{A}_{n,\{1,n\}}(\mathbb{F})$, that is the embedding which yields the adjoint representation of $\mathrm{SL}(n+1,\mathbb{F})$. The information we shall collect on these hyperplanes will allow us to prove that all hyperplanes of $\mathit{A}_{n,\{1,n\}}(\mathbb{F})$ are maximal subspaces of $\mathit{A}_{n,\{1,n\}}(\mathbb{F})$. Hyperplanes of $\mathit{A}_{n,\{1,n\}}(\mathbb{F})$ can also be contructed starting from suitable line-spreads of $\mathrm{PG}(n,\mathbb{F})$ (provided that $\mathrm{PG}(n,\mathbb{F})$ admits line-spreads, of course). Explicitly, let $\mathfrak{S}$ be a line-spread of $\mathrm{PG}(n,\mathbb{K})$ satisfying certain conditions to be stated in this paper (which hold for all line-spreads obtained via the most popular constructions). The set of point-hyperplane flags $(p,\mathit{H})$ of $\mathrm{PG}(n,\mathbb{F})$ such that $\mathit{H}$ contains the member of $\mathfrak{S}$ through the point $p$ is a hyperplane of $\mathit{A}_{n,\{1,n\}}(\mathbb{F})$. We call these hyperplanes {\em hyperplanes of spread type}. Many of them arise from the natural embedding. We don't know if this is the case for all of them., Comment: 21 pages

Cosmological simulations predict the presence of warm hot thermal gas in the cosmic filaments that connect galaxy clusters. This gas is thought to constitute an important part of the missing baryons in the Universe. In addition to the thermal gas, cosmic filaments could contain a population of relativistic particles and magnetic fields. A detection of magnetic fields in filaments can constrain early magnetogenesis in the cosmos. So far, the resulting diffuse synchrotron emission has only been indirectly detected. We present our search for thermal and non-thermal diffuse emission from inter-cluster regions of 106 paired galaxy clusters by stacking the $0.6-2.3$~keV X-ray and 144~MHz radio data obtained with the eROSITA telescope on board the Spectrum-Roentgen-Gamma (SRG) observatory and LOw Frequency ARray (LOFAR), respectively. The stacked data do not show the presence of X-ray and radio diffuse emission in the inter-cluster regions. This could be due to the sensitivity of the data sets and/or the limited number of cluster pairs used in this study. Assuming a constant radio emissivity in the filaments, we find that the mean radio emissivity is not higher than $1.2\times10^{-44}\,{\rm erg \, s^{-1} \, cm^{-3} \, Hz^{-1}}$. Under equipartition conditions, our upper limit on the mean emissivity translates to an upper limit of $\sim75\,{\rm nG}$ for the mean magnetic field strength in the filaments, depending on the spectral index and the minimum energy cutoff. We discuss the constraint for the magnetic field strength in the context of the models for the formation of magnetic fields in cosmic filaments., Comment: Accepted for publication on MNRAS on June 5, 2023

Many galaxy clusters show diffuse cluster-scale emission in the form of radio halos, showing that magnetic fields and relativistic electrons are mixed in with the intra-cluster medium (ICM). There is general agreement that the origin of radio halos is connected to turbulence, generated during cluster mergers. Statistical studies of large samples of galaxy clusters in the radio band have the potential to unveil the connection between the properties of radio halos and the mass and dynamics of the host clusters. Previous studies have been limited to massive clusters and based on a small number of radio halos. The aim of this paper is to investigate the scaling relation between the radio power of radio halos and the mass of the host clusters at low frequencies and down to lower cluster masses. We analysed the clusters from the second catalogue of Planck Sunyaev Zel'dovich sources that lie within the 5634 sq deg covered by the second Data Release of the LOFAR Two-meter Sky Survey. We derived the correlation between the radio power and the mass of the host clusters and we investigated the distribution of clusters without radio halos with respect to the correlation. We use X-ray observations to classify the dynamical state of clusters and investigate its role on the power of radio halos. We found a correlation between the power of radio halos at 150 MHz and the mass of the host clusters down to 3e14 Msun. This correlation has a large scatter, part of which can be attributed to the different dynamical states of host clusters. We used two statistical test to show that the distribution of clusters with and without (upper limits) radio halos in the mass-radio power diagram is not compatible with a single correlation and that it is also not compatible with clusters being uniformly distributed below an upper envelope constituted by the correlation., Comment: 12 pages, 7 figures, submitted to A&A