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This report provides a summary of the full "First Look" report, which presents data on students in the United States in kindergarten through grade 12 in a physical or virtual school or are homeschooled for equivalent grades. The focus of the report is on parent and family involvement in the students' education during the 2022-2023 school year, as reported by the students' parents or guardians. It includes the percentage of students who participated in selected family activities. Demographic information about students and families is presented, including students' poverty status and parents' education and language spoken at home, as well as school characteristics, such as school size and school type. These data represent circumstances after the termination of most COVID-19 pandemic safety measures limiting in-person group activities. The data for this report come from the Parent and Family Involvement in Education (PFI) Survey, administered as part of the 2023 National Household Education Surveys Program (NHES:2023).

Cooling flows are common in galaxy clusters which have cool cores. The soft X-ray emission below 1 keV from the flows is mostly absorbed by cold dusty gas within the central cooling sites. Further evidence for this process is presented here through a more detailed analysis of the nearby Centaurus cluster and some additional clusters. Predictions of JWST near and mid-infrared spectra from cooling gas are presented. [NeVI] emission at 7.65 micron should be an important diagnostic of gas cooling between 6 and 1.5 times 10^5 K. The emerging overall picture of hidden cooling flows is explored. The efficiency of AGN feedback in reducing the total cooling rate in cool cores is shown to be above 50 percent for many clusters but is rarely above 90 per cent. The reduction is mostly in outer gas. Cooling dominates in elliptical galaxies and galaxy groups which have mass flow rates below about 15M/yr and in some massive clusters where rates can exceed 1000M/yr., Comment: 17 pages, 49 figures submitted to MNRAS

Today, we are open-sourcing our core speech recognition and diarization models for non-commercial use. We are releasing both a full production pipeline for developers as well as pared-down research models for experimentation. Rev hopes that these releases will spur research and innovation in the fast-moving domain of voice technology. The speech recognition models released today outperform all existing open source speech recognition models across a variety of long-form speech recognition domains.

We say that a semigroup of matrices has a submultiplicative spectrum if the spectrum of the product of any two elements of the semigroup is contained in the product of the two spectra in question (as sets). In this note we explore an approximate version of this condition., Comment: minor changes from version 2

In this paper, we use Clifford algebra $Cl_{2,0}$ to find the 2D orbit of Hydrogen electron under a Coulomb force and a perturbing circularly polarized electric field of light at angular frequency~$\omega$, which is turned on at time $t = 0$ via a unit step switch. Using a coordinate system co-rotating with the electron's unperturbed circular orbit at angular frequency $\omega_0$, we derive the complex nonlinear differential equation for the perturbation which is similar to but different from the Lorentz oscillator equation: (1) the acceleration terms are similar, (2) the damping term coefficient is not real but imaginary due to Coriolis force, (3) the term similar to spring force is not positive but negative, (3) there is a complex conjugate of the perturbation term which has no Lorentz analog but which makes the equation nonlinear, and (4) the angular frequency of the forcing term is not $\omega$ but $\omega - \omega_0$. By imposing that the position and velocity of the electron are continuous at time $t = 0$, we show that the orbit of the electron is a sum of five exponential Fourier terms with frequencies 0, $\omega_0$, $2\omega_0$, $(2\omega_0 - \omega)$, and $\omega$, which correspond to the eccentric, deferent, and three epicycles in Copernican astronomy. We show that at the three resonant light frequencies $0$, $\omega_0$, and $2\omega_0$, the electron's orbit is divergent, but approximates a Keplerian ellipse. At other light frequencies, the orbits are nondivergent with periods that are integer multiples of $\pi/\omega_0$ depending on the frequency ratio $\omega/\omega_0$. And as $\omega/\omega_0\rightarrow \pm\infty$, the orbit approaches the electron's unperturbed circular orbit., Comment: 50 pages, 200+ equations

We compute the exact value of the quantum chromatic numbers of Hadamard graphs of order $n=2^N$ for $N$ a multiple of $4$ using the upper bound derived by Avis, Hasegawa, Kikuchi, and Sasaki, as well as an application of the Hoffman-like lower bound of Elphick and Wocjan that was generalized by Ganesan for quantum graphs. As opposed to prior computations for the lower bound, our approach uses Ito's results on conjugacy class graphs allowing us to also find bounds on the quantum chromatic numbers of products of Hadamard graphs. In particular, we also compute the exact quantum chromatic number of the categorical product of Hadamard graphs., Comment: Added references for prior proofs of the quantum chromatic number of Hadamard graphs. Fixed several typos. Added new section with results on the quantum chromatic number of products of Hadamard graphs

Common measures of accuracy used to assess the performance of automatic speech recognition (ASR) systems, as well as human transcribers, conflate multiple sources of error. Stylistic differences, such as verbatim vs non-verbatim, can play a significant role in ASR performance evaluation when differences exist between training and test datasets. The problem is compounded for speech from underrepresented varieties, where the speech to orthography mapping is not as standardized. We categorize the kinds of stylistic differences between 6 transcription versions, 4 human- and 2 ASR-produced, of 10 hours of African American English (AAE) speech. Focusing on verbatim features and AAE morphosyntactic features, we investigate the interactions of these categories with how well transcripts can be compared via word error rate (WER). The results, and overall analysis, help clarify how ASR outputs are a function of the decisions made by the training data's human transcribers., Comment: Published in Interspeech 2024 Proceedings, 5 pages excluding references, 5 figures

We define the Cartesian, Categorical, and Lexicographic, and Strong products of quantum graphs. We provide bounds on the quantum chromatic number of these products in terms of the quantum chromatic number of the factors. To adequately describe bounds on the lexicographic product of quantum graphs, we provide a notion of a quantum $b$-fold chromatic number for quantum graphs.

The persistence of the DAMA/LIBRA (DAMA) modulation over the past two decades has been a source of great contention within the dark matter community. The DAMA collaboration reports a persistent, modulating event rate within their setup of NaI(Tl) scintillating crystals at the INFN Laboratori Nazionali del Gran Sasso (LNGS) underground laboratory. A recent work alluded that this signal could have arisen due to an analysis artefact, caused by DAMA not accounting for time variation of decaying background radioisotopes in their analysis procedure. In this work, we examine in detail this 'induced modulation' effect, arguing that a number of aspects of the DAMA signal are incompatible with an induced modulation arising from decays of background isotopes over the lifetime of the experiment. Using a toy model of the DAMA/LIBRA experiment, we explore the induced modulation effect under different variations of the activities of the relevant isotopes - namely, $^3$H and $^{210}$Pb - highlighting the various inconsistencies between the resultant toy datasets and the DAMA signal. We stress the importance of the SABRE experiment, whose goal is to unambiguously test for the presence of such a modulating signal in an experiment using the same target material and comparable levels of background.

We study the Factorization Paradox from the bottom up by adapting methods from perturbative renormalization. Just as quantum field theories are plagued with loop divergences that need to be cancelled systematically by introducing counterterms, gravitational path integrals are plagued by wormhole contributions that spoil the factorization of the holographic dual. These wormholes must be cancelled by some stringy effects in a UV complete, holographic theory of quantum gravity. In a simple model of two-dimensional topological gravity, we outline a gravitational analog of the recursive BPHZ procedure in order to systematically introduce ``counter-wormholes" which parametrize the unknown stringy effects that lead to factorization. Underlying this procedure is a Hopf algebra of symmetries which is analogous to the Connes--Kreimer Hopf algebra underlying perturbative renormalization. The group dual to this Hopf algebra acts to reorganize contributions from spacetimes with distinct topology, and can be seen as a gauge group relating various equivalent ways of constructing a factorizing gravitational path integral., Comment: 35 pages + appendix, 11 figures, 1 table

The tilt-to-length coupling during the LISA Pathfinder mission has been numerically and analytically modeled for particular timespans. In this work, we investigate the long-term stability of the coupling coefficients of this noise. We show that they drifted slowly (by 1\,$\mu$m/rad and 6$\times10^{-6}$ in 100 days) and strongly correlated to temperature changes within the satellite (8\,$\mu$m/rad/K and 30$\times10^{-6}$/K). Based on analytical TTL coupling models, we attribute the temperature-driven coupling changes to rotations of the test masses and small distortions in the optical setup. Particularly, we show that LISA Pathfinder's optical baseplate was bent during the cooldown experiment, which started in late 2016 and lasted several months.

A precise characterization of the magnetic properties of LISA Pathfinder free falling test-masses is of special interest for future gravitational wave observatory in space. Magnetic forces have an important impact on the instrument sensitivity in the low frequency regime below the millihertz. In this paper we report on the magnetic injection experiments performed throughout LISA Pathfinder operations. We show how these experiments allowed a high precision estimate of the instrument magnetic parameters. The remanent magnetic moment was found to have a modulus of $(0.245\pm0.081)\,\rm{nAm}^2$, the x-component of the background magnetic field within the test masses position was measured to be $(414 \pm 74)$ nT and its gradient had a value of $(-7.4\pm 2.1)\,\mu$T/m. Finally, we also measured the test mass magnetic susceptibility to be $(-3.35\pm0.15)\times$10$^{-5}$ in the low frequency regime. All results are in agreement with on-ground estimates.

LISA Pathfinder was a mission designed to test key technologies required for gravitational wave detection in space. Magnetically driven forces play a key role in the instrument sensitivity in the low-frequency regime, which corresponds to the measurement band of interest for future space-borne gravitational wave observatories. Magnetic-induced forces couple to the test mass motion, introducing a contribution to the relative acceleration noise between the free falling test masses. In this Letter we present the first complete estimate of this term of the instrument performance model. Our results set the magnetic-induced acceleration noise during the February 2017 noise run of $\rm 0.25_{-0.08}^{+0.15}\,fm\,s^{-2}/\sqrt{Hz}$ at 1 mHz and $\rm 1.01_{-0.24}^{+0.73}\, fm\,s^{-2}/\sqrt{Hz}$ at 0.1 mHz. We also discuss how the non-stationarities of the interplanetary magnetic field can affect these values during extreme space weather conditions.

When making decisions under uncertainty, individuals often deviate from rational behavior, which can be evaluated across three dimensions: risk preference, probability weighting, and loss aversion. Given the widespread use of large language models (LLMs) in decision-making processes, it is crucial to assess whether their behavior aligns with human norms and ethical expectations or exhibits potential biases. Several empirical studies have investigated the rationality and social behavior performance of LLMs, yet their internal decision-making tendencies and capabilities remain inadequately understood. This paper proposes a framework, grounded in behavioral economics, to evaluate the decision-making behaviors of LLMs. Through a multiple-choice-list experiment, we estimate the degree of risk preference, probability weighting, and loss aversion in a context-free setting for three commercial LLMs: ChatGPT-4.0-Turbo, Claude-3-Opus, and Gemini-1.0-pro. Our results reveal that LLMs generally exhibit patterns similar to humans, such as risk aversion and loss aversion, with a tendency to overweight small probabilities. However, there are significant variations in the degree to which these behaviors are expressed across different LLMs. We also explore their behavior when embedded with socio-demographic features, uncovering significant disparities. For instance, when modeled with attributes of sexual minority groups or physical disabilities, Claude-3-Opus displays increased risk aversion, leading to more conservative choices. These findings underscore the need for careful consideration of the ethical implications and potential biases in deploying LLMs in decision-making scenarios. Therefore, this study advocates for developing standards and guidelines to ensure that LLMs operate within ethical boundaries while enhancing their utility in complex decision-making environments., Comment: Jingru Jia and Zehua Yuan have equal contribution

We present an in-depth analysis of the LISA Pathfinder differential acceleration performance over the entire course of its science operations, spanning approximately 500 days. We find that: 1) the evolution of the Brownian noise that dominates the acceleration amplitude spectral density (ASD), for frequencies $f\gtrsim 1\,\text{mHz}$, is consistent with the decaying pressure due to the outgassing of a single gaseous species. 2) between $f=36\,\mu\text{Hz}$ and $1\,\text{mHz}$, the acceleration ASD shows a $1/f$ tail in excess of the Brownian noise of almost constant amplitude, with $\simeq 20\%$ fluctuations over a period of a few days, with no particular time pattern over the course of the mission; 3) at the lowest considered frequency of $f=18\,\mu\text{Hz}$, the ASD significantly deviates from the $1/f$ behavior, because of temperature fluctuations that appear to modulate a quasi-static pressure gradient, sustained by the asymmetries of the outgassing pattern. We also present the results of a projection of the observed acceleration noise on the potential sources for which we had either a direct correlation measurement, or a quantitative estimate from dedicated experiments. These sources account for approximately $40\%$ of the noise power in the $1/f$ tail. Finally, we analyze the possible sources of the remaining unexplained fraction, and identify the possible measures that may be taken to keep those under control in LISA.

High resolution X-ray spectra reveal hidden cooling flows depositing cold gas at the centres of massive nearby early-type galaxies with little sign of normal star formation. Optical observations are revealing that a bottom-heavy Initial Mass Function is common within the inner kpc of similar galaxies. We revive the possibility that a low-mass star formation mode is operating due to the high thermal pressure in the cooling flow, thus explaining the accumulation of low-mass stars. We further explore whether such a mode operated in early, high-redshift galaxies and has sporadically continued to the present day. The idea links observed distant galaxies with black holes which are ultramassive for their stellar mass, nearby red nuggets and massive early-type galaxies. Nearby elliptical galaxies may be red but they are not dead., Comment: 4 pages, 2 Figures, Accepted for publication in MNRAS

Data augmentations are widely used in training medical image deep learning models to increase the diversity and size of sparse datasets. However, commonly used augmentation techniques can result in loss of clinically relevant information from medical images, leading to incorrect predictions at inference time. We propose the Interactive Medical Image Learning (IMIL) framework, a novel approach for improving the training of medical image analysis algorithms that enables clinician-guided intermediate training data augmentations on misprediction outliers, focusing the algorithm on relevant visual information. To prevent the model from using irrelevant features during training, IMIL will 'blackout' clinician-designated irrelevant regions and replace the original images with the augmented samples. This ensures that for originally mispredicted samples, the algorithm subsequently attends only to relevant regions and correctly correlates them with the respective diagnosis. We validate the efficacy of IMIL using radiology residents and compare its performance to state-of-the-art data augmentations. A 4.2% improvement in accuracy over ResNet-50 was observed when using IMIL on only 4% of the training set. Our study demonstrates the utility of clinician-guided interactive training to achieve meaningful data augmentations for medical image analysis algorithms., Comment: CVPR 2024 Workshop on Domain adaptation, Explainability and Fairness in AI for Medical Image Analysis (DEF-AI-MIA)

With the STAR experiment at the BNL Relativisic Heavy Ion Collider, we characterize $\sqrt{s_\mathrm{NN}}$ = 200 GeV p+Au collisions by event activity (EA) measured within the pseudorapidity range $eta$ $in$ [-5, -3.4] in the Au-going direction and report correlations between this EA and hard- and soft- scale particle production at midrapidity ($\eta$ $\in$ [-1, 1]). At the soft scale, charged particle production in low-EA p+Au collisions is comparable to that in p+p collisions and increases monotonically with increasing EA. At the hard scale, we report measurements of high transverse momentum (pT) jets in events of different EAs. In contrast with the soft particle production, high-pT particle production and EA are found to be inversely related. To investigate whether this is a signal of jet quenching in high-EA events, we also report ratios of pT imbalance and azimuthal separation of dijets in high- and low-EA events. Within our measurement precision, no significant differences are observed, disfavoring the presence of jet quenching in the highest 30% EA p+Au collisions at $\sqrt{s_\mathrm{NN}}$ = 200 GeV., Comment: 12 page, 9 figures

A new burn control scheme for tokamaks is described where the total fusion power is controlled by adjusting the plasma volume fraction that is packed into power dense regions. In an example spherical tokamak burning plasma, by modifying the plasma edge squareness the total fusion power is doubled at almost constant total plasma volume and fusion power density. Therefore, increased plasma squareness could be extremely beneficial to a fusion reactor and squareness control could be desirable for power load balancing. Experiments have observed the impact of increased edge squareness on modified core plasma volume, highlighting the practical relevance of this approach., Comment: 7 pages, 7 figures

CYGNUS is a proposed global network of large-scale gas time projection chambers (TPCs) with the capability of directionally detecting nuclear and electron recoils at $\gtrsim$keV energies. The primary focus of CYGNUS so far has been the detection of dark matter, with directional sensitivity providing a means of circumventing the so-called neutrino fog. However, the excellent background rejection and electron/nuclear recoil discrimination provided by directionality could turn the solar neutrino background into an interesting signal in its own right. For example, directionality would facilitate the simultaneous spectroscopy of multiple different flux sources. Here, we evaluate the possibility of measuring solar neutrinos using the same network of gas TPCs built from $10$ m$^3$-scale modules operating under conditions that enable simultaneous sensitivity to both dark matter and neutrinos. We focus in particular on electron recoils, which provide access to low-energy neutrino fluxes like $pp$, $pep$, $^7$Be, and CNO. An appreciable event rate is already detectable in experiments consisting of a single $10$ m$^3$ module, assuming standard fill gases such as CF$_4$ mixed with helium at atmospheric pressure. With total volumes around 1000 m$^3$ or higher, the TPC network could be complementary to dedicated neutrino observatories, whilst entering the dark-matter neutrino fog via the nuclear recoil channel. We evaluate the required directional performance and background conditions to observe, discriminate, and perform spectroscopy on neutrino events. We find that, under reasonable projections for planned technology that will enable 10--30-degree angular resolution and $\sim 10$\% fractional energy resolution, CYGNUS could be a competitive directional neutrino experiment., Comment: 23 pages, 14 figures

[OII] emission maps obtained with the Keck Cosmic Web Imager (KCWI) are presented for four galaxies centered in cooling X-ray cluster atmospheres. Nebular emission extending tens of kpc is found in systems covering a broad range of atmospheric cooling rates, cluster masses, and dynamical states. Abell 262's central galaxy hosts a kpc-scale disk. The nebular gas in RXJ0820.9+0752 is offset and redshifted with respect to the central galaxy by $10-20$ kpc and 150 km s$^{-1}$, respectively. The nebular gases in PKS 0745-191 and Abell 1835 are being churned to higher velocity dispersion by X-ray bubbles and jets. The churned gas is enveloped by larger scale, lower velocity dispersion (quiescent) nebular emission. The mean line-of-sight speeds of the churned gas, quiescent gas, and the central galaxy each differ by up to $\sim 150$ km s$^{-1}$; nebular speeds upward of $800$ km s$^{-1}$ are found. Gases with outwardly-rising speeds upward of several hundred km s$^{-1}$ are consistent with being advected behind and being lifted by the rising bubbles. The peculiar motion between the galaxy, nebular gas, and perhaps the hot atmosphere from which it presumably condensed is affecting the bubble dynamics, and may strongly affect thermally unstable cooling, the dispersal of jet energy, and the angular momentum of gas accreting onto the galaxies and their nuclear black holes., Comment: 36 pages, 26 figures, Accepted for publication in ApJ

Given any non-central interior point $o$ of the unit disc $D$, the diameter $L$ through $o$ is the union of two linear arcs emanating from $o$ which meet $\partial D$ orthogonally, the shorter of them stable and the longer unstable (under these boundary conditions). In each of the two half discs bounded by $L$, we construct a convex eternal solution to curve shortening flow which fixes $o$ and meets $\partial D$ orthogonally, and evolves out of the unstable critical arc at $t=-\infty$ and into the stable one at $t=+\infty$. We then prove that these two (congruent) solutions are the only non-flat convex ancient solutions to the curve shortening flow satisfying the specified boundary conditions. We obtain analogous conclusions in the "degenerate" case $o\in\partial D$ as well, although in this case the solution contracts to the point $o$ at a finite time with asymptotic shape that of a half Grim Reaper, thus providing an interesting example for which an embedded flow develops a collapsing singularity.

For training an encoder network to perform amortized variational inference, the Kullback-Leibler (KL) divergence from the exact posterior to its approximation, known as the inclusive or forward KL, is an increasingly popular choice of variational objective due to the mass-covering property of its minimizer. However, minimizing this objective is challenging. A popular existing approach, Reweighted Wake-Sleep (RWS), suffers from heavily biased gradients and a circular pathology that results in highly concentrated variational distributions. As an alternative, we propose SMC-Wake, a procedure for fitting an amortized variational approximation that uses likelihood-tempered sequential Monte Carlo samplers to estimate the gradient of the inclusive KL divergence. We propose three gradient estimators, all of which are asymptotically unbiased in the number of iterations and two of which are strongly consistent. Our method interleaves stochastic gradient updates, SMC samplers, and iterative improvement to an estimate of the normalizing constant to reduce bias from self-normalization. In experiments with both simulated and real datasets, SMC-Wake fits variational distributions that approximate the posterior more accurately than existing methods., Comment: Accepted to the International Conference on Artificial Intelligence and Statistics (AISTATS 2024)

The Lightning Launch Commit Criteria (LLCC) are a set of complex rules to avoid natural and rocket-triggered lightning strikes to in-flight space launch vehicles. The LLCC are the leading source of scrubs and delays to space launches from Cape Canaveral Air Force Station (CCAFS) and NASA Kennedy Space Center (KSC). An LLCC climatology would be useful for designing launch concept of operations, mission planning, long-range forecasting, training, and setting LLCC improvement priorities. Unfortunately, an LLCC climatology has not been available for CCAFS/KSC. Attempts have been made to develop such a climatology, but they have not been entirely successful. The main shortfall has been the lack of a long continuous record of LLCC evaluations. Even though CCAFS/KSC is the world's busiest spaceport, the record of LLCC evaluations is not detailed enough to create the climatology. As a potential solution, the research in this study developed a proxy climatology of LLCC violations by using the long continuous record of surface electric field mills at CCAFS/KSC., Comment: 27 pages, 10 figures, 1 table

We present new ALMA observations of CO, CN, CS, HCN and HCO$^{+}$ absorption seen against the bright and compact radio continuum sources of eight massive galaxies. Combined with archival observations, they reveal two distinct populations of molecular clouds, which we identify by combining CO emission and absorption profiles to unambiguously reveal each cloud's direction of motion and likely location. In galaxy disks, we see clouds with low velocity dispersions, low line of sight velocities and a lack of any systemic inflow or outflow. In galactic cores, we find high velocity dispersion clouds inflowing at up to 550 km/s. This provides observational evidence in favour of cold accretion onto galactic centres, which likely contributes to the fuelling of active galactic nuclei. We also see a wide range in the CO(2-1)/CO(1-0) ratios of the absorption lines. This is likely the combined effect of hierarchical substructure within the molecular clouds and continuum sources which vary in size with frequency., Comment: Submitted to MNRAS

The purpose of this feasibility study was to examine the potential impact of reading digital interactive e-books on essential skills that support reading comprehension with third-fifth grade students. Students read two e-Books that taught word learning and comprehension monitoring strategies in the service of learning difficult vocabulary and targeted science concepts about hurricanes. We investigated whether specific comprehension strategies including word learning and strategies that supported general reading comprehension, summarization, and question generation, show promise of effectiveness in building vocabulary knowledge and comprehension skills in the e-Books. Students were assigned to read one of three versions of each of the e-Books, each version implemented one strategy. The books employed a choose-your-adventure format with embedded comprehension questions that provided students with immediate feedback on their responses. Paired samples t-tests were run to examine pre-to-post differences in learning the targeted vocabulary and science concepts taught in both e-Books. For both e-Books, students demonstrated significant gains in word learning and on the targeted hurricane concepts. Additionally, Hierarchical Linear Modeling (HLM) revealed that no one strategy was more associated with larger gains than the other. Performance on the embedded questions in the books was also associated with greater posttest outcomes for both e-Books. This work discusses important considerations for implementation and future development of e-books that can enhance student engagement and improve reading comprehension.

Non-invertible symmetries in quantum field theory (QFT) generalize the familiar product rule of groups to a more general fusion rule. In many cases, gauged versions of these symmetries can be regarded as dual descriptions of invertible gauge symmetries. One may ask: are there any other types of non-invertible gauge symmetries? In theories with gravity we find a new form of non-invertible gauge symmetry that emerges in the limit of fundamental, tensionless strings. These stringy non-invertible gauge symmetries appear in standard examples such as non-abelian orbifolds. Moving away from the tensionless limit always breaks these symmetries. We also find that both the conventional form of non-invertible gauge symmetries and these stringy generalizations are realized in AdS/CFT. Although generically broken, approximate non-invertible symmetries have implications for Swampland constraints: in certain cases they can be used to prove the existence of towers of states related to the Distance Conjecture, and can sometimes explain the existence of slightly sub-extremal states which fill in the gaps in the sublattice Weak Gravity Conjecture., Comment: 56 pages, 11 figures

Electrostatic force actuation is a key component of the system of geodesic reference test masses (TM) for the LISA orbiting gravitational wave observatory and in particular for performance at low frequencies, below 1 mHz, where the observatory sensitivity is limited by stray force noise. The system needs to apply forces of order 10$^{-9}$ N while limiting fluctuations in the measurement band to levels approaching 10$^{-15}$ N/Hz$^{1/2}$. We present here the LISA actuation system design, based on audio-frequency voltage carrier signals, and results of its in-flight performance test with the LISA Pathfinder test mission. In LISA, TM force actuation is used to align the otherwise free-falling TM to the spacecraft-mounted optical metrology system, without any forcing along the critical gravitational wave-sensitive interferometry axes. In LISA Pathfinder, on the other hand, the actuation was used also to stabilize the TM along the critical $x$ axis joining the two TM, with the commanded actuation force entering directly into the mission's main differential acceleration science observable. The mission allowed demonstration of the full compatibility of the electrostatic actuation system with the LISA observatory requirements, including dedicated measurement campaigns to amplify, isolate, and quantify the two main force noise contributions from the actuation system, from actuator gain noise and from low frequency ``in band'' voltage fluctuations. These campaigns have shown actuation force noise to be a relevant, but not dominant, noise source in LISA Pathfinder and have allowed performance projections for the conditions expected in the LISA mission.

We introduce a diagrammatic monoidal category, the spin Brauer category, that plays the same role for the spin and pin groups as the Brauer category does for the orthogonal groups. In particular, there is a full functor from the spin Brauer category to the category of finite-dimensional modules for the spin and pin groups. This functor becomes essentially surjective after passing to the Karoubi envelope, and its kernel is the tensor ideal of negligible morphisms. In this way, the spin Brauer category can be thought of as an interpolating category for the spin and pin groups. We also define an affine version of the spin Brauer category, which acts on categories of modules for the pin and spin groups via translation functors., Comment: 46 pages. v2: Changed order of Sections 7 and 8, other improvements and corrections throughout