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We present a reformulation of QM/MM as a fully quantum mechanical theory of interacting subsystems, all treated at the level of density functional theory (DFT). For the MM subsystem, which lacks orbitals, we assign an ad hoc electron density and apply orbital-free DFT functionals to describe its quantum properties. The interaction between the QM and MM subsystems is also treated using orbital-free density functionals, accounting for Coulomb interactions, exchange, correlation, and Pauli repulsion. Consistency across QM and MM subsystems is ensured by employing data-driven, many-body MM force fields that faithfully represent DFT functionals. Applications to water-solvated systems demonstrate that this approach achieves unprecedented, very rapid convergence to chemical accuracy as the size of the QM subsystem increases. We validate the method with several pilot studies, including water bulk, water clusters (prism hexamer and pentamers), solvated glucose, a palladium aqua ion, and a wet monolayer of MoS$_2$.

We develop an excursion theory that describes the evolution of a Markov process indexed by a Levy tree away from a regular and instantaneous point $x$ of the state space. The theory builds upon a notion of local time at $x$ that was recently introduced in [37]. Despite the radically different setting, our results exhibit striking similarities to the classical excursion theory for $\mathbb{R}_+$-indexed Markov processes. We then show that the genealogy of the excursions can be encoded in a Levy tree called the tree coded by the local time. In particular, we recover by different methods the excursion theory of Abraham and Le Gall [2], which was developed for Brownian motion indexed by the Brownian tree., Comment: 64 pages. Comments are welcome

Heisenberg's uncertainty relation does not take into account that position and momentum are defined relative to a quantum reference frame (QRF). We introduce such a QRF as a covariant phase space observable to derive novel, frame-relative uncertainty relations and show that relative to such a frame, position and momentum appear compatible. We investigate the classical limit of the QRF, and demonstrate that in a Galilei-invariant setting, large frame mass corresponds to classical frame preparation. Finally, we give further conditions under which the standard uncertainty relations are recovered.

Processing Using Memory (PUM) accelerators have the potential to perform Deep Neural Network (DNN) inference by using arrays of memory cells as computation engines. Among various memory technologies, ReRAM crossbars show promising performance in computing dot-product operations in the analog domain. Nevertheless, the expensive writing procedure of ReRAM cells has led researchers to design accelerators whose crossbars have enough capacity to store the full DNN. Given the tremendous and continuous increase in DNN model sizes, this approach is unfeasible for some networks, or inefficient due to the huge hardware requirements. Those accelerators lack the flexibility to adapt to any given DNN model, facing an challenge. To address this issue we introduce ARAS, a cost-effective ReRAM-based accelerator that employs a smart scheduler to adapt different DNNs to the resource-limited hardware. ARAS also overlaps the computation of a layer with the weight writing of several layers to mitigate the high writing latency of ReRAM. Furthermore, ARAS introduces three optimizations aimed at reducing the energy overheads of writing in ReRAM. Our key optimization capitalizes on the observation that DNN weights can be re-encoded to augment their similarity between layers, increasing the amount of bitwise values that are equal or similar when overwriting ReRAM cells and, hence, reducing the amount of energy required to update the cells. Overall, ARAS greatly reduces the ReRAM writing activity. We evaluate ARAS on a popular set of DNNs. ARAS provides up to 2.2x speedup and 45% energy savings over a baseline PUM accelerator without any optimization. Compared to a TPU-like accelerator, ARAS provides up to 1.5x speedup and 61% energy savings., Comment: 13 pages, 17 figures

Vision Language Models (VLMs) often struggle with culture-specific knowledge, particularly in languages other than English and in underrepresented cultural contexts. To evaluate their understanding of such knowledge, we introduce WorldCuisines, a massive-scale benchmark for multilingual and multicultural, visually grounded language understanding. This benchmark includes a visual question answering (VQA) dataset with text-image pairs across 30 languages and dialects, spanning 9 language families and featuring over 1 million data points, making it the largest multicultural VQA benchmark to date. It includes tasks for identifying dish names and their origins. We provide evaluation datasets in two sizes (12k and 60k instances) alongside a training dataset (1 million instances). Our findings show that while VLMs perform better with correct location context, they struggle with adversarial contexts and predicting specific regional cuisines and languages. To support future research, we release a knowledge base with annotated food entries and images along with the VQA data., Comment: Preprint

Word frequency is a key variable in psycholinguistics, useful for modeling human familiarity with words even in the era of large language models (LLMs). Frequency in film subtitles has proved to be a particularly good approximation of everyday language exposure. For many languages, however, film subtitles are not easily available, or are overwhelmingly translated from English. We demonstrate that frequencies extracted from carefully processed YouTube subtitles provide an approximation comparable to, and often better than, the best currently available resources. Moreover, they are available for languages for which a high-quality subtitle or speech corpus does not exist. We use YouTube subtitles to construct frequency norms for five diverse languages, Chinese, English, Indonesian, Japanese, and Spanish, and evaluate their correlation with lexical decision time, word familiarity, and lexical complexity. In addition to being strongly correlated with two psycholinguistic variables, a simple linear regression on the new frequencies achieves a new high score on a lexical complexity prediction task in English and Japanese, surpassing both models trained on film subtitle frequencies and the LLM GPT-4. Our code, the frequency lists, fastText word embeddings, and statistical language models are freely available at https://github.com/naist-nlp/tubelex., Comment: Submitted for review to COLING 2025. 8 pages, 3 figures

Hybrid quantum-classical optimization techniques, which incorporate the pre-optimization of Variational Quantum Algorithms (VQAs) using Tensor Networks (TNs), have been shown to allow for the reduction of quantum computational resources. In the particular case of large optimization problems, commonly found in real-world use cases, this strategy is almost mandatory to reduce the otherwise unfathomable execution costs and improve the quality of the results. We identify the coherence entropy as a crucial metric in determining the suitability of quantum states as effective initialization candidates. Our findings are validated through extensive numerical tests for the Quantum Approximate Optimization Algorithm (QAOA), in which we find that the optimal initialization states are pure Gibbs states. Further, these results are explained with the inclusion of a simple and yet novel notion of expressivity adapted to classical optimization problems. Based on this finding, we propose a quantum-classical optimization protocol that significantly improves on previous approaches for such tasks, with specific focus on its effectiveness., Comment: 14 pages, 10 figures

Cell-free massive multiple-input multiple-output (CF-mMIMO) is a breakthrough technology for beyond-5G systems, designed to significantly boost the energy and spectral efficiencies of future mobile networks while ensuring a consistent quality of service for all users. Additionally, multicasting has gained considerable attention recently because physical-layer multicasting offers an efficient method for simultaneously serving multiple users with identical service demands by sharing radio resources. Typically, multicast services are delivered either via unicast transmissions or a single multicast transmission. This work, however, introduces a novel subgroup-centric multicast CF-mMIMO framework that divides users into several multicast subgroups based on the similarities in their spatial channel characteristics. This approach allows for efficient sharing of the pilot sequences used for channel estimation and the precoding filters used for data transmission. The proposed framework employs two scalable precoding strategies: centralized improved partial MMSE (IP-MMSE) and distributed conjugate beam-forming (CB). Numerical results show that for scenarios where users are uniformly distributed across the service area, unicast transmissions using centralized IP-MMSE precoding are optimal. However, in cases where users are spatially clustered, multicast subgrouping significantly improves the sum spectral efficiency (SE) of the multicast service compared to both unicast and single multicast transmission. Notably, in clustered scenarios, distributed CB precoding outperforms IP-MMSE in terms of per-user SE, making it the best solution for delivering multicast content., Comment: 6 pages, 5 figures, European Wireless 2024 Conference

Automated speech analysis is a thriving approach to detect early markers of Alzheimer's disease (AD). Yet, recording conditions in most AD datasets are heterogeneous, with patients and controls often evaluated in different acoustic settings. While this is not a problem for analyses based on speech transcription or features obtained from manual alignment, it does cast serious doubts on the validity of acoustic features, which are strongly influenced by acquisition conditions. We examined this issue in the ADreSSo dataset, derived from the widely used Pitt corpus. We show that systems based on two acoustic features, MFCCs and Wav2vec 2.0 embeddings, can discriminate AD patients from controls with above-chance performance when using only the non-speech part of the audio signals. We replicated this finding in a separate dataset of Spanish speakers. Thus, in these datasets, the class can be partly predicted by recording conditions. Our results are a warning against the use of acoustic systems for identifying patients based on non-standardized recordings. We propose that acoustically heterogeneous datasets for dementia studies should be either (a) analyzed using only transcripts or other features derived from manual annotations, or (b) replaced by datasets collected with strictly controlled acoustic conditions., Comment: 5 pages, 1 figure, 1 table

Interest in quantum machine learning is increasingly growing due to its potential to offer more efficient solutions for problems that are difficult to tackle with classical methods. In this context, the research work presented here focuses on the use of quantum machine learning techniques for image classification tasks. We exploit a quantum extreme learning machine by taking advantage of its rich feature map provided by the quantum reservoir substrate. We systematically analyse different phases of the quantum extreme learning machine process, from the dataset preparation to the image final classification. In particular, we have tested different encodings, together with Principal Component Analysis, the use of Auto-Encoders, as well as the dynamics of the model through the use of different Hamiltonians for the quantum reservoir. Our results show that the introduction of a quantum reservoir systematically improves the accuracy of the classifier. Additionally, while different encodings can lead to significantly different performances, Hamiltonians with varying degrees of connectivity exhibit the same discrimination rate, provided they are interacting., Comment: 11 pages, 6 figures

Every massive particle behaves like a wave, according to quantum physics. Yet, this characteristic wave nature has only been observed in double-slit experiments with microscopic systems, such as atoms and molecules. The key aspect is that the wavefunction describing the motion of these systems extends coherently over a distance comparable to the slit separation, much larger than the size of the system itself. Preparing these states of more massive and complex objects remains an outstanding challenge. While the motion of solid-state oscillators can now be controlled at the level of single quanta, their coherence length remains comparable to the zero-point motion, limited to subatomic distances. Here, we prepare a delocalized state of a levitating solid-state nanosphere with coherence length exceeding the zero-point motion. We first cool its motion to the ground state. Then, by modulating the stiffness of the confinement potential, we achieve more than a threefold increment of the initial coherence length with minimal added noise. Optical levitation gives us the necessary control over the confinement that other mechanical platforms lack. Our work is a stepping stone towards the generation of delocalization scales comparable to the object size, a crucial regime for macroscopic quantum experiments, and towards quantum-enhanced force sensing with levitated particles.

It is well-known that functions over finite fields play a crucial role in designing substitution boxes (S-boxes) in modern block ciphers. In order to analyze the security of an S-box, recently, three new tables have been introduced: the Extended Boomerang Connectivity Table (EBCT), the Lower Boomerang Connectivity Table (LBCT), and the Upper Boomerang Connectivity Table (UBCT). In fact, these tables offer improved methods over the usual Boomerang Connectivity Table (BCT) for analyzing the security of S-boxes against boomerang-style attacks. Here, we put in context these new EBCT, LBCT, and UBCT concepts by connecting them to the DDT for a differentially $\delta$-uniform function and also determine the EBCT, LBCT, and UBCT entries of three classes of differentially $4$-uniform power permutations, namely, Gold, Kasami and Bracken-Leander. We also determine the Double Boomerang Connectivity Table (DBCT) entries of the Gold function. As byproducts of our approach, we obtain some previously published results quite easily.

Self-similar Markov trees constitute a remarkable family of random compact real trees carrying a decoration function that is positive on the skeleton. As the terminology suggests, they are self-similar objects that further satisfy a Markov branching property. They are built from the combination of the recursive construction of real trees by gluing line segments with the seminal observation of Lamperti, which relates positive self-similar Markov processes and L\'evy processes via a time change. They carry natural length and harmonic measures, which can be used to perform explicit spinal decompositions. Self-similar Markov trees encompass a large variety of random real trees that have been studied over the last decades, such as the Brownian CRT, stable L\'evy trees, fragmentation trees, and growth-fragmentation trees. We establish general invariance principles for multi-type Galton--Watson trees with integer types and illustrate them with many combinatorial classes of random trees that have been studied in the literature, including (possibly dissipative) discrete fragmentation trees, peeling trees of Boltzmann (possibly $O(n)$-decorated) planar maps, or even the more recent fully parked trees., Comment: This is Part I of a research monograph. Part II will be available soon. Comments are very welcome

We propose a modular quantum computation architecture based on utilizing multipartite entanglement. Each module consists of a small-scale quantum computer comprising data, memory and entangling qubits. Entangling qubits are used to selectively couple different modules by harnessing some non-controllable, distance-dependent interaction, which is effectively controlled and enhanced via a proper adjusting of the internal state of the qubits. In this way, multipartite entangled states with different entanglement topologies can be shared between modules. These states are stored in memory qubits where they can be further processed so they can eventually be used to deterministically perform certain classes of gates or circuits between modules on demand, including parallel controlled-Z gates with arbitrary interaction patterns, multi-qubit gates or whole Clifford circuits, depending on their entanglement structure. The usage of different kinds of multipartite entanglement rather than Bell pairs allows for more efficient and flexible coupling between modules, leading to a scalable quantum computation architecture., Comment: (8 + 6) pages, 7 figures

We establish a new spatial Markov property of the Brownian half-plane. According to this property, if one removes a hull centered at a boundary point, the remaining space equipped with an intrinsic metric is still a Brownian half-plane, which is independent of the part that has been removed. This is an analog of the well-known peeling procedure for random planar maps. We also investigate several distributional properties of hulls centered at a boundary point, and we provide a new construction of the Brownian half-plane giving information about distances from a half-boundary., Comment: 28 pages, 2 figures

We introduce MultiPhys, a method designed for recovering multi-person motion from monocular videos. Our focus lies in capturing coherent spatial placement between pairs of individuals across varying degrees of engagement. MultiPhys, being physically aware, exhibits robustness to jittering and occlusions, and effectively eliminates penetration issues between the two individuals. We devise a pipeline in which the motion estimated by a kinematic-based method is fed into a physics simulator in an autoregressive manner. We introduce distinct components that enable our model to harness the simulator's properties without compromising the accuracy of the kinematic estimates. This results in final motion estimates that are both kinematically coherent and physically compliant. Extensive evaluations on three challenging datasets characterized by substantial inter-person interaction show that our method significantly reduces errors associated with penetration and foot skating, while performing competitively with the state-of-the-art on motion accuracy and smoothness. Results and code can be found on our project page (http://www.iri.upc.edu/people/nugrinovic/multiphys/).

Gravitational waves from black-hole merging events have revealed a population of extra-galactic BHs residing in short-period binaries with masses that are higher than expected based on most stellar evolution models - and also higher than known stellar-origin black holes in our Galaxy. It has been proposed that those high-mass BHs are the remnants of massive metal-poor stars. Gaia astrometry is expected to uncover many Galactic wide-binary systems containing dormant BHs, which may not have been detected before. The study of this population will provide new information on the BH-mass distribution in binaries and shed light on their formation mechanisms and progenitors. As part of the validation efforts in preparation for the fourth Gaia data release (DR4), we analysed the preliminary astrometric binary solutions, obtained by the Gaia Non-Single Star pipeline, to verify their significance and to minimise false-detection rates in high-mass-function orbital solutions. The astrometric binary solution of one source, Gaia BH3, implies the presence of a 32.70 \pm 0.82 M\odot BH in a binary system with a period of 11.6 yr. Gaia radial velocities independently validate the astrometric orbit. Broad-band photometric and spectroscopic data show that the visible component is an old, very metal-poor giant of the Galactic halo, at a distance of 590 pc. The BH in the Gaia BH3 system is more massive than any other Galactic stellar-origin BH known thus far. The low metallicity of the star companion supports the scenario that metal-poor massive stars are progenitors of the high-mass BHs detected by gravitational-wave telescopes. The Galactic orbit of the system and its metallicity indicate that it might belong to the Sequoia halo substructure. Alternatively, and more plausibly, it could belong to the ED-2 stream, which likely originated from a globular cluster that had been disrupted by the Milky Way., Comment: 23 pages, accepted fro publication in A&A Letters. New version with small fixes

In this paper, we study different approaches for classifying emotions from speech using acoustic and text-based features. We propose to obtain contextualized word embeddings with BERT to represent the information contained in speech transcriptions and show that this results in better performance than using Glove embeddings. We also propose and compare different strategies to combine the audio and text modalities, evaluating them on IEMOCAP and MSP-PODCAST datasets. We find that fusing acoustic and text-based systems is beneficial on both datasets, though only subtle differences are observed across the evaluated fusion approaches. Finally, for IEMOCAP, we show the large effect that the criteria used to define the cross-validation folds have on results. In particular, the standard way of creating folds for this dataset results in a highly optimistic estimation of performance for the text-based system, suggesting that some previous works may overestimate the advantage of incorporating transcriptions., Comment: 5 pages. Accepted in ICASSP 2020

Orchard and tree-child networks share an important property with phylogenetic trees: they can be completely reduced to a single node by iteratively deleting cherries and reticulated cherries. As it is the case with phylogenetic trees, the number of ways in which this can be done gives information about the topology of the network. Here, we show that the problem of computing this number in tree-child networks is akin to that of finding the number of linear extensions of the poset induced by each network, and give an algorithm based on this reduction whose complexity is bounded in terms of the level of the network., Comment: 22 pages, 5 figures

This paper presents the design, objectives, experiences, and results of an international cooperation project funded by the European Commission in the context of the Erasmus Intensive Programme (IP, for short) designed to improve students' curricula. An IP is a short programme of study (minimum 2 weeks) that brings together university students and staff from at least three countries in order to encourage efficient and multinational teaching of specialist topics, which might otherwise not be taught at all. This project lasted for 6 years, covering two different editions, each one with three year duration. This project lasted for 6 years, covering two different editions, each one with three year duration. The first edition, named SAVRO (Simulation and Virtual Reality in Robotics for Industrial Assembly Processes) was held in the period 2008-2010, with the participation of three Universities, namely the Universitat Politecnica de Valencia (Spain), acting as IP coordinator, the Technische Universitat Kaiserslautern (Germany), and the Universita degli Studi di Salerno (Italy). The Universite de Reims Champagne-Ardenne (France) participated as a new partner in the subsequent edition (2011-2013) of the IP, renamed as HUMAIN (Human-Machine Interaction). Both editions of the teaching project were characterized by the same objectives and organizational aspects, aiming to provide educational initiatives based on active teaching through collaborative works between international institutions, involving industrial partners too. The aim of the paper is to illustrate the best practices that characterized the organization of our experience as well as to present some general recommendations and suggestions on how to devise computing academic curricula., Comment: 21 pages

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.

We consider quantum computer architectures where interactions are mediated between hot qubits that are not in their mechanical ground state. Such situations occur, e.g., when not cooling ideally, or when moving ions or atoms around. We introduce quantum gates between logically encoded systems that consist of multiple physical ones and show how the encoding can be used to make these gates resilient against such imperfections. We demonstrate that, in this way, one can improve gate fidelities by enlarging the logical system, and counteract the effect of unknown positions or position fluctuations of involved particles. We consider both a classical treatment of positions in terms of probability distributions, as well a quantum treatment using mechanical eigenmodes. We analyze different settings including a cool logical system mediating interactions between two hot systems, as well as two logical systems consisting of hot physical systems whose positions fluctuate collectively or individually. In all cases, we demonstrate a significant improvement of gate fidelities, which provides a platform-independent tool to mitigate thermal noise., Comment: (8+3) pages, 6 figures

The constant growth of DNNs makes them challenging to implement and run efficiently on traditional compute-centric architectures. Some accelerators have attempted to add more compute units and on-chip buffers to solve the memory wall problem without much success, and sometimes even worsening the issue since more compute units also require higher memory bandwidth. Prior works have proposed the design of memory-centric architectures based on the Near-Data Processing (NDP) paradigm. NDP seeks to break the memory wall by moving the computations closer to the memory hierarchy, reducing the data movements and their cost as much as possible. The 3D-stacked memory is especially appealing for DNN accelerators due to its high-density/low-energy storage and near-memory computation capabilities to perform the DNN operations massively in parallel. However, memory accesses remain as the main bottleneck for running modern DNNs efficiently. To improve the efficiency of DNN inference we present QeiHaN, a hardware accelerator that implements a 3D-stacked memory-centric weight storage scheme to take advantage of a logarithmic quantization of activations. In particular, since activations of FC and CONV layers of modern DNNs are commonly represented as powers of two with negative exponents, QeiHaN performs an implicit in-memory bit-shifting of the DNN weights to reduce memory activity. Only the meaningful bits of the weights required for the bit-shift operation are accessed. Overall, QeiHaN reduces memory accesses by 25\% compared to a standard memory organization. We evaluate QeiHaN on a popular set of DNNs. On average, QeiHaN provides $4.3x$ speedup and $3.5x$ energy savings over a Neurocube-like accelerator.

The Feistel Boomerang Connectivity Table and the related notion of $F$-Boomerang uniformity (also known as the second-order zero differential uniformity) has been recently introduced by Boukerrou et al.~\cite{Bouk}. These tools shall provide a major impetus in the analysis of the security of the Feistel network-based ciphers. In the same paper, a characterization of almost perfect nonlinear functions (APN) over fields of even characteristic in terms of second-order zero differential uniformity was also given. Here, we find a sufficient condition for an odd or even function over fields of odd characteristic to be an APN function, in terms of second-order zero differential uniformity. Moreover, we compute the second-order zero differential spectra of several APN or other low differential uniform functions, and show that our considered functions also have low second-order zero differential uniformity, though it may vary widely, unlike the case for even characteristic when it is always zero.

Gaia's readout window strategy is challenged by very dense fields in the sky. Therefore, in addition to standard Gaia observations, full Sky Mapper (SM) images were recorded for nine selected regions in the sky. A new software pipeline exploits these Service Interface Function (SIF) images of crowded fields (CFs), making use of the availability of the full two-dimensional (2D) information. This new pipeline produced half a million additional Gaia sources in the region of the omega Centauri ($\omega$ Cen) cluster, which are published with this Focused Product Release. We discuss the dedicated SIF CF data reduction pipeline, validate its data products, and introduce their Gaia archive table. Our aim is to improve the completeness of the {\it Gaia} source inventory in a very dense region in the sky, $\omega$ Cen. An adapted version of {\it Gaia}'s Source Detection and Image Parameter Determination software located sources in the 2D SIF CF images. We validated the results by comparing them to the public {\it Gaia} DR3 catalogue and external Hubble Space Telescope data. With this Focused Product Release, 526\,587 new sources have been added to the {\it Gaia} catalogue in $\omega$ Cen. Apart from positions and brightnesses, the additional catalogue contains parallaxes and proper motions, but no meaningful colour information. While SIF CF source parameters generally have a lower precision than nominal {\it Gaia} sources, in the cluster centre they increase the depth of the combined catalogue by three magnitudes and improve the source density by a factor of ten. This first SIF CF data publication already adds great value to the {\it Gaia} catalogue. It demonstrates what to expect for the fourth {\it Gaia} catalogue, which will contain additional sources for all nine SIF CF regions.

Context. Strongly lensed quasars are fundamental sources for cosmology. The Gaia space mission covers the entire sky with the unprecedented resolution of $0.18$" in the optical, making it an ideal instrument to search for gravitational lenses down to the limiting magnitude of 21. Nevertheless, the previous Gaia Data Releases are known to be incomplete for small angular separations such as those expected for most lenses. Aims. We present the Data Processing and Analysis Consortium GravLens pipeline, which was built to analyse all Gaia detections around quasars and to cluster them into sources, thus producing a catalogue of secondary sources around each quasar. We analysed the resulting catalogue to produce scores that indicate source configurations that are compatible with strongly lensed quasars. Methods. GravLens uses the DBSCAN unsupervised clustering algorithm to detect sources around quasars. The resulting catalogue of multiplets is then analysed with several methods to identify potential gravitational lenses. We developed and applied an outlier scoring method, a comparison between the average BP and RP spectra of the components, and we also used an extremely randomised tree algorithm. These methods produce scores to identify the most probable configurations and to establish a list of lens candidates. Results. We analysed the environment of 3 760 032 quasars. A total of 4 760 920 sources, including the quasars, were found within 6" of the quasar positions. This list is given in the Gaia archive. In 87\% of cases, the quasar remains a single source, and in 501 385 cases neighbouring sources were detected. We propose a list of 381 lensed candidates, of which we identified 49 as the most promising. Beyond these candidates, the associate tables in this Focused Product Release allow the entire community to explore the unique Gaia data for strong lensing studies further., Comment: 35 pages, 60 figures, accepted for publication by Astronomy and Astrophysics

The third Gaia Data Release (DR3) provided photometric time series of more than 2 million long-period variable (LPV) candidates. Anticipating the publication of full radial-velocity (RV) in DR4, this Focused Product Release (FPR) provides RV time series for a selection of LPVs with high-quality observations. We describe the production and content of the Gaia catalog of LPV RV time series, and the methods used to compute variability parameters published in the Gaia FPR. Starting from the DR3 LPVs catalog, we applied filters to construct a sample of sources with high-quality RV measurements. We modeled their RV and photometric time series to derive their periods and amplitudes, and further refined the sample by requiring compatibility between the RV period and at least one of the $G$, $G_{\rm BP}$, or $G_{\rm RP}$ photometric periods. The catalog includes RV time series and variability parameters for 9\,614 sources in the magnitude range $6\lesssim G/{\rm mag}\lesssim 14$, including a flagged top-quality subsample of 6\,093 stars whose RV periods are fully compatible with the values derived from the $G$, $G_{\rm BP}$, and $G_{\rm RP}$ photometric time series. The RV time series contain a mean of 24 measurements per source taken unevenly over a duration of about three years. We identify the great most sources (88%) as genuine LPVs, with about half of them showing a pulsation period and the other half displaying a long secondary period. The remaining 12% consists of candidate ellipsoidal binaries. Quality checks against RVs available in the literature show excellent agreement. We provide illustrative examples and cautionary remarks. The publication of RV time series for almost 10\,000 LPVs constitutes, by far, the largest such database available to date in the literature. The availability of simultaneous photometric measurements gives a unique added value to the Gaia catalog (abridged), Comment: 36 pages, 38 figures