Search

We present a lattice calculation of the Hadronic Vacuum Polarization (HVP) contribution of the strange and charm quarks to the anomalous magnetic moment of the muon in isospin symmetric QCD. We employ the gauge configurations generated by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ flavors of Wilson-clover twisted-mass quarks at five lattice spacings and at values of the quark mass parameters that are close and/or include the isospin symmetric QCD point of interest. After computing the small corrections necessary to precisely match this point, and carrying out an extrapolation to the continuum limit based on the data at lattice spacings $a \simeq 0.049, 0.057, 0.068, 0.080$~fm and spatial lattice sizes up to $L \simeq 7.6$~fm, we obtain $a_\mu^{\rm HVP}(s) = (53.57 \pm 0.63) \times 10^{-10}$ and $a_\mu^{\rm HVP}(c) = (14.56 \pm 0.13) \times 10^{-10}$, for the quark-connected strange and charm contributions, respectively. Our findings agree well with the corresponding results by other lattice groups., Comment: 33 pages, 18 figures, 3 tables

Astronomy is entering an unprecedented era of Big Data science, driven by missions like the ESA's Gaia telescope, which aims to map the Milky Way in three dimensions. Gaia's vast dataset presents a monumental challenge for traditional analysis methods. The sheer scale of this data exceeds the capabilities of manual exploration, necessitating the utilization of advanced computational techniques. In response to this challenge, we developed a novel approach leveraging deep learning to estimate the metallicity of fundamental mode (ab-type) RR Lyrae stars from their light curves in the Gaia optical G-band. Our study explores applying deep learning techniques, particularly advanced neural network architectures, in predicting photometric metallicity from time-series data. Our deep learning models demonstrated notable predictive performance, with a low mean absolute error (MAE) of 0.0565, the root mean square error (RMSE) achieved is 0.0765 and a high $R^2$ regression performance of 0.9401 measured by cross-validation. The weighted mean absolute error (wMAE) is 0.0563, while the weighted root mean square error (wRMSE) is 0.0763. These results showcase the effectiveness of our approach in accurately estimating metallicity values. Our work underscores the importance of deep learning in astronomical research, particularly with large datasets from missions like Gaia. By harnessing the power of deep learning methods, we can provide precision in analyzing vast datasets, contributing to more precise and comprehensive insights into complex astronomical phenomena., Comment: Sensors 2024, 24(16), 5203; (23 pages)

We use RR Lyrae stars identified by the Gaia third data release (DR3) to explore the outskirts of the Ursa Minor (UMi) dwarf spheroidal galaxy (dSph) and update the census of its variable star population. We adopted different tools based on the Gaia DR3 astrometric and photometric data (proper motions, Period-Wesenheit-Metallicity relations, spatial distribution, colour-magnitude diagram and stellar isochrone fitting) to discriminate between different types of variable stars, and to identify UMi members. We find a total of 129 RR Lyrae stars and Anomalous Cepheids (ACs) that belong to UMi. We report 47 new RR Lyrae stars (46 bona fide and 1 candidate) and 5 new ACs (4 bona fide and 1 candidate), including new possible members in the extreme periphery of the galaxy at a distance of $\sim$ 12 half-light radii. We reclassified 13 RR Lyrae stars identified by the Gaia DR3 Specific Object Study pipeline for Cepheids and RR Lyrae stars (SOS Cep$\&$RRL), using data from the literature and Gaia astrometry and photometry. Specifically, we assigned these 13 DR3 RR Lyrae stars to 10 Anomalous Cepheids and 3 double-mode RR Lyrae (RRd), respectively. From the average luminosity of the RR Lyrae stars we derive for UMi a distance modulus of $(m-M)_{0}=$ 19.23 $\pm$ 0.09 mag in excellent agreement with the literature. Finally, we investigated whether some of UMi's variable stars might be members of the ultra-faint stellar cluster Mu{\~n}oz~1, that lies at a projected distance of 45 arcmin from UMi's centre. Based on the properties of the variable stars (distances, colours and metallicities), we find unlikely that they belong to the cluster., Comment: 25 pages, 23 figures and 6 tables. Submitted to Astronomy & Astrophysics

The widespread diffusion of compute-intensive edge-AI workloads and the stringent demands of modern autonomous systems require advanced heterogeneous embedded architectures. Such architectures must support high-performance and reliable execution of parallel tasks with different levels of criticality. Hardware-assisted virtualization is crucial for isolating applications concurrently executing these tasks under real-time constraints, but interrupt virtualization poses challenges in ensuring transparency to virtual guests while maintaining real-time system features, such as interrupt vectoring, nesting, and tail-chaining. Despite its rapid advancement to address virtualization needs for mixed-criticality systems, the RISC-V ecosystem still lacks interrupt controllers with integrated virtualization and real-time features, currently relying on non-deterministic, bus-mediated message-signaled interrupts (MSIs) for virtualization. To overcome this limitation, we present the design, implementation, and in-system assessment of vCLIC, a virtualization extension to the RISC-V CLIC fast interrupt controller. Our approach achieves 20x interrupt latency speed-up over the software emulation required for handling non-virtualization-aware systems, reduces response latency by 15% compared to existing MSI-based approaches, and is free from interference from the system bus, at an area cost of just 8kGE when synthesized in an advanced 16nm FinFet technology., Comment: 4 pages, 4 figures, accepted for presentation at the 42nd IEEE International Conference on Computer Design (ICCD 2024)

Mature radio galaxies such as M87 belong to a specific subclass of active galaxies (AGN) whose evolution in time endows them with five distinguishing characteristics, including (1) low excitation emission, (2) low star formation rates, (3) high bulge stellar-velocity dispersion, (4) bright stellar nuclei, and (5) weak or nonexistent merger signatures. We show how to understand these seemingly disparate characteristics as originating from the time evolution of powerful radio quasars and describe a new model prediction that tilted accretion disks in AGN are expected to occur in bright quasars but not in other subclasses of AGN. The picture we present should be understood as the most compelling evidence for counter-rotation as a key element in feedback from accreting black holes., Comment: 11 pages, 6 Figures, Published in the Universe journal

Many excited states in the hadron spectrum have large branching ratios to three-hadron final states. Understanding such particles from first principles QCD requires input from lattice QCD with one-, two-, and three-meson interpolators as well as a reliable three-body formalism relating finite-volume spectra at unphysical pion mass values to the scattering amplitudes at the physical point. In this work, we provide the first-ever calculation of the resonance parameters of the $\omega$ meson from lattice QCD, including an update of the formalism through matching to effective field theories. The main result of this pioneering study, the pole position of the $\omega$ meson at $\sqrt{s_\omega}= (778.0(11.2)-i\,3.0(5) )\,\mathrm{MeV}$, agrees reasonably well with experiment. In addition we provide an estimate of the $\omega-\rho$ mass difference as $29(15)\,\mathrm{MeV}$., Comment: 14 pages, 11 figures, 3 tables. v2: version published in PRL

We present new $P -\phi_{31}-{\rm [Fe/H]}$ and $P -\phi_{31}- A_2 - {\rm [Fe/H]}$ relations for fundamental-mode (RRab) and first-overtone mode (RRc) RR Lyrae stars (RRLs), respectively. The relations were calibrated based on pulsation periods and Fourier parameters of the RRL light curves in the Gaia $G$-band published in the Gaia Data Release 3 (DR3), and accurate spectroscopically measured metallicities available in the literature. We apply the feature selection algorithm to identify the most relevant parameters for the determination of metallicity. To fit the relations, we used the Bayesian approach, which allowed us to carefully take into account uncertainties in various parameters and the intrinsic scatter of the relations. The root mean squared errors of the predicted metallicity values in the training samples are 0.28 dex and 0.21 dex for RRab and RRc stars, respectively, comparable with the typical uncertainty of low/intermediate resolution spectroscopic metallicity measurements. We applied the new relations to measure individual metallicities and distances to $\sim$ 134,000 RRLs from the Gaia DR3 catalogue, as well as mean metallicities and distances to 38 Milky Way globular clusters. We also estimate the mean metallicity and distance to the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC): ${\rm [Fe/H]_{LMC} = -1.63\pm0.36}$ and $\mu_{\rm LMC}=18.55\pm0.18$~mag, ${\rm [Fe/H]_{SMC}=-1.86\pm0.36}$~dex and $\mu_{\rm SMC}=19.01\pm 0.17$~mag, respectively, in excellent agreement with previous measurements., Comment: 21 pages, 20 figure, submitted to MNRAS on May 13

The rapid advancement and exploration of open-hardware RISC-V platforms are driving significant changes in sectors like autonomous vehicles, smart-city infrastructure, and medical devices. OpenTitan stands out as a groundbreaking open-source RISC-V design with a comprehensive security toolkit as a standalone system-on-chip (SoC). OpenTitan includes Earl Grey, a fully implemented and silicon-proven SoC, and Darjeeling, announced but not yet fully implemented. Earl Grey targets standalone SoC implementations, while Darjeeling is for integrable implementations. The literature lacks a silicon-ready embedded implementation of an open-source Root of Trust, despite lowRISC's efforts on Darjeeling. We address the limitations of existing implementations by optimizing data transfer latency between memory and cryptographic accelerators to prevent under-utilization and ensure efficient task acceleration. Our contributions include a comprehensive methodology for integrating custom extensions and IPs into the Earl Grey architecture, architectural enhancements for system-level integration, support for varied boot modes, and improved data movement across the platform. These advancements facilitate deploying OpenTitan in broader SoCs, even without specific technology-dependent IPs, providing a deployment-ready research vehicle for the community. We integrated the extended Earl Grey architecture into a reference architecture in a 22nm FDX technology node, benchmarking the enhanced architecture's performance. The results show significant improvements in cryptographic processing speed, achieving up to 2.7x speedup for SHA-256/HMAC and 1.6x for AES accelerators compared to the baseline Earl Grey architecture.

We prove two forms of uncertainty principle for the Schr\"odinger group generated by the Ornstein-Uhlenbeck operator. As a consequence, we derive a related (in fact, equivalent) result for the imaginary harmonic oscillator., Comment: Several typos have been corrected

The ongoing revolution in application domains targeting autonomous navigation, first and foremost automotive "zonalization", has increased the importance of certain off-chip communication interfaces, particularly Ethernet. The latter will play an essential role in next-generation vehicle architectures as the backbone connecting simultaneously and instantaneously the zonal/domain controllers. There is thereby an incumbent need to introduce a performant Ethernet controller in the open-source HW community, to be used as a proxy for architectural explorations and prototyping of mixed-criticality systems (MCSs). Driven by this trend, in this work, we propose a fully open-source, DMA-enhanced, technology-agnostic Gigabit Ethernet architecture that overcomes the limitations of existing open-source architectures, such as Lowrisc's Ethernet, often tied to FPGA implementation, performance-bound by sub-optimal design choices such as large memory buffers, and in general not mature enough to bridge the gap between academia and industry. Besides the area advantage, the proposed design increases packet transmission speed up to almost 3x compared to Lowrisc's and is validated through implementation and FPGA prototyping into two open-source, heterogeneous MCSs., Comment: 4 pages,4 figures, 21st ACM International Conference on Computing Frontiers Workshops and Special Sessions

We introduce a class of (possibly) degenerate dispersive equations with a drift. We prove that, under the H\"ormander hypoellipticity condition, the relevant Cauchy problem can be uniquely solved in the Schwartz class, and the solution operator can be uniquely extended to a strongly continuous semigroup $\{\mathcal T(t)\}_{t\ge 0}$ in $L^2(\Rm)$. Finally, we prove that for $t>0$ the operator $\mathcal T(t)$ satisfies a sharp form of dispersive estimate in $L^p$, for any $1\le p\le 2$, and an uncertainty principle.

We establish a new sharp estimate of the order of vanishing of solutions to parabolic equations with variable coefficients. For real-analytic leading coefficients, we prove a localised estimate of the nodal set, at a given time-level, that generalises the celebrated one of Donnelly and Fefferman. We also establish Landis type results for global solutions.

In the last decade, we have witnessed exponential growth in the complexity of control systems for safety-critical applications (automotive, robots, industrial automation) and their transition to heterogeneous mixed-criticality systems (MCSs). The growth of the RISC-V ecosystem is creating a major opportunity to develop open-source, vendor-neutral reference platforms for safety-critical computing. We present SentryCore, a reliable, real-time, self-contained, open-source mega-IP for advanced control functions that can be seamlessly integrated into Systems-on-Chip, e.g., for automotive applications, through industry-standard Advanced eXtensible Interface 4 (AXI4). SentryCore features three embedded RISC-V processor cores in lockstep with error-correcting code (ECC) protected data memory for reliable execution of any safety-critical application. Context switching is accelerated to under 110 clock cycles via a RISC-V core-local interrupt controller (CLIC) and dedicated hardware extensions, while a timer-based direct memory access (DMA) engine streamlines sensor data readout during periodic control loops. SentryCore was implemented in Intel's 16nm process node and tested with FreeRTOS, ThreadX, and RTIC software support., Comment: 2 pages, accepted at the RISC-V Summit Europe 2024

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

The counter-rotation between black holes and accretion disk configuration was introduced over a decade ago to elucidate the nature of the radio loud/radio-quiet dichotomy and the jet-disk connection, but has since been applied to a plethora of observations across space and time. We briefly review the paradigm in which counter-rotation is key for the triggering of radio galaxies and its observational support, then apply it to a series of observations concerning FR0 radio galaxies. FR0 radio galaxies appear to be radio galaxies in transition, with low-spinning black holes and thus weaker but tilted jets with respect to an earlier radio quasar phase. As a result, FR0 radio galaxies are prescribed to be in an earlier phase of star formation suppression in radio galaxies, compared to a later phase that is unlikely to be less than tens of millions of years in the future if they have enough accretion fuel to evolve into more powerful FRI radio galaxies. FR0 radio galaxies will have a greater or lesser star formation suppression feedback effect depending on how long they live. Tilted jets also enhance stellar velocities in the bulge. Because FR0 jet lengths are of the same order of magnitude as the radius of the stellar bulge, FR0 jets are prescribed to have begun, more or less recently depending on their age, to affect stellar velocity dispersions as well. As a result, they will be associated with dispersion values that tend to be larger than for characteristically non-jetted active galaxies, but smaller than giant radio galaxies such as M87 that have experienced a long-term tilted and more powerful FRI jet. With these ideas it is possible to make a coarse-grained prediction for the slope of the M-{\sigma} plane for FR0 radio galaxies with values between 4 and 8., Comment: 13 pages, 4 Figures, Accepted for publication in the Journal of High Energy Astrophysics

As robots shift from industrial to human-centered spaces, adopting mobile manipulators, which expand workspace capabilities, becomes crucial. In these settings, seamless interaction with humans necessitates compliant control. Two common methods for safe interaction, admittance, and impedance control, require force or torque sensors, often absent in lower-cost or lightweight robots. This paper presents an adaption of impedance control that can be used on current-controlled robots without the use of force or torque sensors and its application for compliant control of a mobile manipulator. A calibration method is designed that enables estimation of the actuators' current/torque ratios and frictions, used by the adapted impedance controller, and that can handle model errors. The calibration method and the performance of the designed controller are experimentally validated using the Kinova GEN3 Lite arm. Results show that the calibration method is consistent and that the designed controller for the arm is compliant while also being able to track targets with five-millimeter precision when no interaction is present. Additionally, this paper presents two operational modes for interacting with the mobile manipulator: one for guiding the robot around the workspace through interacting with the arm and another for executing a tracking task, both maintaining compliance to external forces. These operational modes were tested in real-world experiments, affirming their practical applicability and effectiveness., Comment: 8 pages, 13 figures, under review for IROS 2024

When a robotic system is redundant with respect to a given task, the remaining degrees of freedom can be used to satisfy additional objectives. With current robotic systems having more and more degrees of freedom, this can lead to an entire hierarchy of tasks that need to be solved according to given priorities. In this paper, the first compliant control strategy is presented that allows to consider an arbitrary number of equality and inequality tasks, while still preserving the natural inertia of the robot. The approach is therefore a generalization of a passivity-based controller to the case of an arbitrary number of equality and inequality tasks. The key idea of the method is to use a Weighted Hierarchical Quadratic Problem to extract the set of active tasks and use the latter to perform a coordinate transformation that inertially decouples the tasks. Thereby unifying the line of research focusing on optimization-based and passivity-based multi-task controllers. The method is validated in simulation.

We present a lattice determination of the inclusive decay rate of the process $\tau\mapsto X_{us} \nu_\tau$ in which the $\tau$ lepton decays into a generic hadronic state $X_{us}$ with $\bar u s$ flavour quantum numbers. Our results have been obtained in $n_f=2+1+1$ iso-symmetric QCD with full non-perturbative accuracy, without any OPE approximation and, except for the presently missing long-distance isospin-breaking corrections, include a solid estimate of all sources of theoretical uncertainties. This has been possible by using the Hansen-Lupo-Tantalo method [1] that we have already successfully applied in [2] to compute the inclusive decay rate of the process $\tau\mapsto X_{ud} \nu_\tau$ in the $\bar u d$ flavour channel. By combining our first-principles theoretical results with the presently-available experimental data we extract the CKM matrix element $\vert V_{us}\vert$, the Cabibbo angle, with a $0.9$\% accuracy, dominated by the experimental error., Comment: 9 pages, 5 figures, 1 table. Version accepted by PRL, expanded technical discussion moved to an appendix, results unchanged

We study the gradient flow of an energy with mixed homogeneity which is at the interface of Finsler and sub-Riemannian geometry, Comment: A new section has been added (Section 3). The original file has been accordingly revised

We introduce a class of nonlinear partial differential equations in a product space which are at the interface of Finsler and sub-Riemannian geometry. To such equations we associate a non-isotropic Minkowski gauge $\Theta$ for which we introduce a suitable notion of Legendre transform $\Theta^0$. We compute the action of the relevant nonlinear PDEs on ``radial" functions, i.e., functions of $\Theta^0$, and by exploiting it we are able to compute explicit fundamental solutions of such PDEs.

We establish an optimal asymptotic on rings for a subelliptic Helmholtz equation with mixed homogeneities.

The increasing demand for heterogeneous functionality in the automotive industry and the evolution of chip manufacturing processes have led to the transition from federated to integrated critical real-time embedded systems (CRTESs). This leads to higher integration challenges of conventional timing predictability techniques due to access contention on shared resources, which can be resolved by providing system-level observability and controllability in hardware. We focus on the interconnect as a shared resource and propose AXI-REALM, a lightweight, modular, and technology-independent real-time extension to industry-standard AXI4 interconnects, available open-source. AXI-REALM uses a credit-based mechanism to distribute and control the bandwidth in a multi-subordinate system on periodic time windows, proactively prevents denial of service from malicious actors in the system, and tracks each manager's access and interference statistics for optimal budget and period selection. We provide detailed performance and implementation cost assessment in a 12nm node and an end-to-end functional case study implementing AXI-REALM into an open-source Linux-capable RISC-V SoC. In a system with a general-purpose core and a hardware accelerator's DMA engine causing interference on the interconnect, AXI-REALM achieves fair bandwidth distribution among managers, allowing the core to recover 68.2 % of its performance compared to the case without contention. Moreover, near-ideal performance (above 95 %) can be achieved by distributing the available bandwidth in favor of the core, improving the worst-case memory access latency from 264 to below eight cycles. Our approach minimizes buffering compared to other solutions and introduces only 2.45 % area overhead compared to the original SoC., Comment: 6 pages, 6 figures, accepted as a regular paper at DATE24

In his seminal 1943 paper F. Rellich proved that, in the complement of a cavity $\Omega = \{x\in \mathbb R^n\mid |x|>R_0\}$, there exist no nontrivial solution $f$ of the Helmholtz equation $\Delta f = - \lambda f$, when $\lambda>0$, such that $\int_{\Omega} |f|^2 dx < \infty$. In this note we generalise this result by showing that if $\int_{\Omega} |f|^p dx < \infty$ for some $0 \frac{2n}{n-1}$, eigenfunctions do exist in $\Omega$.

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