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Understanding the confidence with which a machine learning model classifies an input datum is an important, and perhaps under-investigated, concept. In this paper, we propose a new calibration metric, the Entropic Calibration Difference (ECD). Based on existing research in the field of state estimation, specifically target tracking (TT), we show how ECD may be applied to binary classification machine learning models. We describe the relative importance of under- and over-confidence and how they are not conflated in the TT literature. Indeed, our metric distinguishes under- from over-confidence. We consider this important given that algorithms that are under-confident are likely to be 'safer' than algorithms that are over-confident, albeit at the expense of also being over-cautious and so statistically inefficient. We demonstrate how this new metric performs on real and simulated data and compare with other metrics for machine learning model probability calibration, including the Expected Calibration Error (ECE) and its signed counterpart, the Expected Signed Calibration Error (ESCE).

How we should design and interact with social artificial intelligence depends on the socio-relational role the AI is meant to emulate or occupy. In human society, relationships such as teacher-student, parent-child, neighbors, siblings, or employer-employee are governed by specific norms that prescribe or proscribe cooperative functions including hierarchy, care, transaction, and mating. These norms shape our judgments of what is appropriate for each partner. For example, workplace norms may allow a boss to give orders to an employee, but not vice versa, reflecting hierarchical and transactional expectations. As AI agents and chatbots powered by large language models are increasingly designed to serve roles analogous to human positions - such as assistant, mental health provider, tutor, or romantic partner - it is imperative to examine whether and how human relational norms should extend to human-AI interactions. Our analysis explores how differences between AI systems and humans, such as the absence of conscious experience and immunity to fatigue, may affect an AI's capacity to fulfill relationship-specific functions and adhere to corresponding norms. This analysis, which is a collaborative effort by philosophers, psychologists, relationship scientists, ethicists, legal experts, and AI researchers, carries important implications for AI systems design, user behavior, and regulation. While we accept that AI systems can offer significant benefits such as increased availability and consistency in certain socio-relational roles, they also risk fostering unhealthy dependencies or unrealistic expectations that could spill over into human-human relationships. We propose that understanding and thoughtfully shaping (or implementing) suitable human-AI relational norms will be crucial for ensuring that human-AI interactions are ethical, trustworthy, and favorable to human well-being., Comment: 76 pages, 2 figures

The Simons Observatory (SO) is a ground-based cosmic microwave background (CMB) survey experiment that currently consists of three 0.42m small-aperture telescopes (SATs) and one 6m large-aperture telescope (LAT), located at an elevation of 5200m in the Atacama Desert in Chile. At the LAT's focal plane, SO will install >62,000 transition-edge sensor detectors across 13 optics tubes (OTs) within the Large Aperture Telescope Receiver (LATR), the largest cryogenic camera ever built to observe the CMB. Here we report on the validation of the LATR in the laboratory and the subsequent dark testing and validation within the LAT. We show that the LATR meets cryogenic, optical, and detector specifications required for high-sensitivity measurements of the CMB. At the time of writing, the LATR is installed in the LAT with six OTs (corresponding to >31,000 detectors), and the LAT mirrors and remaining seven OTs are undergoing development.

I present a variant of the Buffon Needle method for determination of the value of the mathematical constant, pi. The original method is based on the random casting of a needle of length l onto a planked floor of plank width L. The described variant involves the random casting of an equilateral triangle with side length l onto a tiled floor consisting of square tiles of side width L. Source code for the computer simulation of this method is provided.

The problems of finding isomorphism classes of indecomposable modules with certain properties, or determining the indecomposable summands of a module, are ubiquitous in commutative algebra, group theory, representation theory, and other fields. The purpose of this work is to describe and prove correctness of a practical algorithm for computing indecomposable summands of finitely generated modules over a finitely generated k-algebra, for k a field of positive characteristic. Our algorithm works over multigraded rings, which enables the computation of indecomposable summands of coherent sheaves on subvarieties of toric varieties (in particular, for varieties embedded in projective space). We also present multiple examples, including some which present previously unknown phenomena regarding the behavior of summands of Frobenius pushforwards and syzygies over Artinian rings., Comment: 12 pages

We present the results of Chandra and XMM-Newton X-ray imaging and spatially-resolved spectroscopy, as well as new MUSTANG2 90~GHz observations of the thermal Sunyaev-Zeldovich effect from MACS J0717.5+3745, an intermediate redshift ($z=0.5458$) and exceptionally massive ($3.5 \pm 0.6\ times 10^{15}~\rm M_\odot$) Frontier Fields cluster experiencing multiple mergers and hosting an apparent X-ray bright large scale structure filament. Thermodynamical maps are produced from Chandra, XMM-Newton, and ROSAT data using a new method for modeling the astrophysical and instrumental backgrounds. The temperature peak of $24 \pm 4$ keV is also the pressure peak of the cluster and closely correlates spatially with the Sunyaev-Zeldovich peak from the MUSTANG2 data. The cluster center hosts shock fronts to the north and south, for which we report estimates for the shock Mach numbers of $M = 1.6 \pm 0.4$ and $M = 1.9 \pm 0.3$, respectively. Bayesian X-ray Analysis methods were used to disentangle different projected spectral signatures for the filament structure, with Akaike and Bayes criteria being used to select the most appropriate model to describe the various temperature components. We report an X-ray filament temperature of $3.1_{-0.3}^{+0.6}$ keV and a density $(3.78\pm0.05)\times10^{-4}\,{\rm cm^{-3}}$, corresponding to an overdensity of $\sim400$ relative to the critical density of the Universe. We estimate the hot gas mass of the filament to be $\sim6.1\times10^{12}~\rm M_\odot$, while its total projected weak lensing measured mass is $\sim(6.8\pm2.7)\times10^{13}~\rm M_\odot$, indicating a hot baryon fraction of 4--10\%., Comment: 19 pages, 10+1 figures, 7 tables

The performance of embodied agents has been shown to improve by increasing model parameters, dataset size, and compute. This has been demonstrated in domains from robotics to video games, when generative learning objectives on offline datasets (pre-training) are used to model an agent's behavior (imitation learning) or their environment (world modeling). This paper characterizes the role of scale in these tasks more precisely. Going beyond the simple intuition that `bigger is better', we show that the same types of power laws found in language modeling also arise in world modeling and imitation learning (e.g. between loss and optimal model size). However, the coefficients of these laws are heavily influenced by the tokenizer, task \& architecture -- this has important implications on the optimal sizing of models and data.

We present DisCo, a distributed algorithm for contact-rich, multi-robot tasks. DisCo is a distributed contact-implicit trajectory optimization algorithm, which allows a group of robots to optimize a time sequence of forces to objects and to their environment to accomplish tasks such as collaborative manipulation, robot team sports, and modular robot locomotion. We build our algorithm on a variant of the Alternating Direction Method of Multipliers (ADMM), where each robot computes its own contact forces and contact-switching events from a smaller single-robot, contact-implicit trajectory optimization problem, while cooperating with other robots through dual variables, enforcing constraints between robots. Each robot iterates between solving its local problem, and communicating over a wireless mesh network to enforce these consistency constraints with its neighbors, ultimately converging to a coordinated plan for the group. The local problems solved by each robot are significantly less challenging than a centralized problem with all robots' contact forces and switching events, improving the computational efficiency, while also preserving the privacy of some aspects of each robot's operation. We demonstrate the effectiveness of our algorithm in simulations of collaborative manipulation, multi-robot team sports scenarios, and in modular robot locomotion, where DisCo achieves $3$x higher success rates with a 2.5x to 5x faster computation time. Further, we provide results of hardware experiments on a modular truss robot, with three collaborating truss nodes planning individually while working together to produce a punctuated rolling-gate motion of the composite structure. Videos are available on the project page: https://disco-opt.github.io.

The high electron temperature in galaxy clusters ($>1\,$keV or $>10^7\,$K) leads to corrections at the level of a few percent in their thermal Sunyaev-Zeldovich effect signatures. Both the size and frequency dependence of these corrections, which are known as relativistic temperature corrections, depend upon the temperature of the objects. In this work we exploit this effect to measure the average temperature of a stack of Compton-$y$ selected clusters. Specifically, we apply the "spectroscopic method" and search for the temperature that best fits the clusters' signal measured at frequencies from 30 to 545 GHz by the Atacama Cosmology Telescope and Planck satellite. We measure the average temperature of clusters detected in the ACT maps to be $8.5\pm 2.4\,$keV, with an additional systematic error of comparable amplitude dominated by passband uncertainty. Upcoming surveys, such as the Simons Observatory and CMB-S4, have the potential to dramatically improve upon these measurements and thereby enable precision studies of cluster temperatures with millimeter observations. The key challenge for future observations will be mitigating instrumental systematic effects, which already limit this analysis., Comment: 21 pages with 17 figures

We report on the masses and hyperfine structure of ground and isomeric states in $^{114,116,118,120}$Ag isotopes, measured with the phase-imaging ion-cyclotron-resonance technique (PI-ICR) with the JYFLTRAP mass spectrometer and the collinear laser spectroscopy beamline at the Ion Guide Isotope Separator On-Line (IGISOL) facility, Jyv\"askyl\"a, Finland. We measured the masses and excitation energies, electromagnetic moments, and charge radii, and firmly established the nuclear spins of the long-lived states. A new isomer was discovered in $^{118}$Ag and the half-lives of $^{118}$Ag long-lived states were reevaluated. We unambiguously pinned down the level ordering of all long-lived states, placing the inversion of the $I = 0^-$ and $I = 4^+$ states at $A = 118$ $(N = 71)$. Lastly, we compared the electromagnetic moments of each state to empirical single-particle moments to identify the dominant configuration where possible., Comment: 11 pages paper (excl. references) + 3 pages of supplementary material

According to CMB measurements, baryonic matter constitutes about $5\%$ of the mass-energy density of the universe. A significant population of these baryons, for a long time referred to as `missing', resides in a low density, warm-hot intergalactic medium (WHIM) outside galaxy clusters, tracing the ``cosmic web'', a network of large scale dark matter filaments. Various studies have detected this inter-cluster gas, both by stacking and by observing individual filaments in compact, massive systems. In this paper, we study short filaments (< 10 Mpc) connecting massive clusters ($M_{500} \approx 3\times 10^{14} M_{\odot}$) detected by the Atacama Cosmology Telescope (ACT) using the scattering of CMB light off the ionised gas, a phenomenon known as the thermal Sunyaev-Zeldovich (tSZ) effect. The first part of this work is a search for suitable candidates for high resolution follow-up tSZ observations. We identify four cluster pairs with an intercluster signal above the noise floor (S/N $>$ 2), including two with a tentative $>2\sigma$ statistical significance for an intercluster bridge from the ACT data alone. In the second part of this work, starting from the same cluster sample, we directly stack on ${\sim}100$ cluster pairs and observe an excess SZ signal between the stacked clusters of $y=(7.2^{+2.3}_{-2.5})\times 10^{-7}$ with a significance of $3.3\sigma$. It is the first tSZ measurement of hot gas between clusters in this range of masses at moderate redshift ($\langle z\rangle\approx 0.5$). We compare this to the signal from simulated cluster pairs with similar redshifts and separations in the THE300 and MAGNETICUM Pathfinder cosmological simulations and find broad consistency. Additionally, we show that our measurement is consistent with scaling relations between filament parameters and mass of the embedded halos identified in simulations., Comment: 37 pages, 17 images

We measure the growth of cosmic density fluctuations on large scales and across the redshift range $0.3

The kinematic Sunyaev--Zel'dovich (kSZ) effect induces a non-zero density-density-temperature bispectrum, which we can use to reconstruct the large-scale velocity field from a combination of cosmic microwave background (CMB) and galaxy density measurements, in a procedure known as ``kSZ velocity reconstruction''. This method has been forecast to constrain large-scale modes with future galaxy and CMB surveys, improving their measurement beyond what is possible with the galaxy surveys alone. Such measurements will enable tighter constraints on large-scale signals such as primordial non-Gaussianity, deviations from homogeneity, and modified gravity. In this work, we demonstrate a statistically significant measurement of kSZ velocity reconstruction for the first time, by applying quadratic estimators to the combination of the ACT DR6 CMB+kSZ map and the DESI LRG galaxies (with photometric redshifts) in order to reconstruct the velocity field. We do so using a formalism appropriate for the 2-dimensional projected galaxy fields that we use, which naturally incorporates the curved-sky effects important on the largest scales. We find evidence for the signal by cross-correlating with an external estimate of the velocity field from the spectroscopic BOSS survey and rejecting the null (no-kSZ) hypothesis at $3.8\sigma$. Our work presents a first step towards the use of this observable for cosmological analyses., Comment: 16 pages (main)+5 pages (Appendix); 13 figures (main) + 8 figures (appendix)

We conduct a systematic search for astrophysical transients using data from the Atacama Cosmology Telescope (ACT). The data were taken from 2017 to 2022 in three frequency bands spanning 77 GHz to 277 GHz. In this paper we present a pipeline for transient detection using single observation maps where each pixel of a map contains one observation with an integration time of approximately four minutes. We find 34 transient events at 27 unique locations. All but two of the transients are associated with Galactic stars and exhibit a wide range of properties. We also detect an event coincident with the classical nova, YZ Ret and one event consistent with a flaring active galactic nucleus. We notably do not detect any reverse shock emission from gamma ray bursts, a non-detection which is in tension with current models., Comment: 23 pages, 10 figures, 10 tables. First and second author share equal contributions. Article and accompanying data submitted to ApJ. Data tables will be made available upon publication

Survival is poor for patients with metastatic cancer, and it is vital to examine new biomarkers that can improve patient prognostication and identify those who would benefit from more aggressive therapy. In metastatic prostate cancer, two new assays have become available: one that quantifies the number of cancer cells circulating in the peripheral blood, and the other a marker of the aggressiveness of the disease. It is critical to determine the magnitude of the effect of these biomarkers on the discrimination of a model-based risk score. To do so, most analysts frequently consider the discrimination of two separate survival models: one that includes both the new and standard factors and a second that includes the standard factors alone. However, this analysis is ultimately incorrect for many of the scale-transformation models ubiquitous in survival, as the reduced model is misspecified if the full model is specified correctly. To circumvent this issue, we developed a projection-based approach to estimate the impact of the two prostate cancer biomarkers. The results indicate that the new biomarkers can influence model discrimination and justify their inclusion in the risk model; however, the hunt remains for an applicable model to risk-stratify patients with metastatic prostate cancer.

High-redshift radio(-loud) galaxies (H$z$RGs) are massive galaxies with powerful radio-loud active galactic nuclei (AGNs) and serve as beacons for protocluster identification. However, the interplay between H$z$RGs and the large-scale environment remains unclear. To understand the connection between H$z$RGs and the surrounding obscured star formation, we investigated the overdensity and spatial distribution of submillimeter-bright galaxies (SMGs) in the field of 4C\,23.56, a well-known H$z$RG at $z=2.48$. We used SCUBA-2 data ($\sigma\,{\sim}\,0.6$\,mJy) to estimate the $850\,{\rm \mu m}$ source number counts and examine the radial and azimuthal overdensities of the $850\,{\rm \mu m}$ sources in the vicinity of the H$z$RG. The angular distribution of SMGs is inhomogeneous around the H$z$RG 4C\,23.56, with fewer sources oriented along the radio jet. We also find a significant overdensity of bright SMGs (${\rm S}_{850\rm\,\mu m}\geq5\,$mJy). Faint and bright SMGs exhibit different spatial distributions. The former are concentrated in the core region, while the latter prefer the outskirts of the H$z$RG field. High-resolution observations show that the seven brightest SMGs in our sample are intrinsically bright, suggesting that the overdensity of bright SMGs is less likely due to the source multiplicity., Comment: 19 pages, 17 figures, 5 tables, accepted to A&A

We present several illustrations from completed clinical trials on a statistical approach that allows us to gain useful insights regarding the time dependency of treatment effects. Our approach leans on a simple proposition: all non-proportional hazards (NPH) models are equivalent to a proportional hazards model. The nph2ph transform brings an NPH model into a PH form. We often find very simple approximations for this transform, enabling us to analyze complex NPH observations as though they had arisen under proportional hazards. Many techniques become available to us, and we use these to understand treatment effects better.

The Simons Observatory (SO) is a cosmic microwave background experiment composed of three 0.42 m Small Aperture Telescopes (SATs) and one 6 m Large Aperture Telescope (LAT) in the Atacama Desert of Chile. The Large Aperture Telescope Receiver (LATR) was integrated into the LAT in August 2023; however, because mirrors were not yet installed, the LATR optical chain was capped at the 4K stage. In this dark configuration we are able to characterize many elements of the instrument without contributions from atmospheric noise. Here we show this noise is below the required upper limit and its features are well described with a simple noise model. Maps produced using this noise model have properties that are in good agreement with the white noise levels of our dark data. Additionally, we show that our nominal scan strategy has a minimal effect on the noise when compared to the noise when the telescope is stationary

We present a stacked lensing analysis of 96 galaxy clusters selected by the thermal Sunyaev-Zel'dovich (SZ) effect in maps of the cosmic microwave background (CMB). We select foreground galaxy clusters with a $5\sigma$-level SZ threshold in CMB observations from the Atacama Cosmology Telescope, while we define background source galaxies for the lensing analysis with secure photometric redshift cuts in Year 3 data of the Subaru Hyper Suprime Cam survey. We detect the stacked lensing signal in the range of $0.1 < R\, [h^{-1}\mathrm{Mpc}] < 100$ in each of three cluster redshift bins, $0.092

Recent advances in cosmological observations have provided an unprecedented opportunity to investigate the distribution of baryons relative to the underlying matter. In this work, we robustly show that the gas is much more extended than the dark matter at 40$\sigma$ and the amount of baryonic feedback at $z \lesssim 1$ strongly disfavors low-feedback models such as that of state-of-the-art hydrodynamical simulation IllustrisTNG compared with high-feedback models such as that of the original Illustris simulation. This has important implications for bridging the gap between theory and observations and understanding galaxy formation and evolution. Furthermore, a better grasp of the baryon-dark matter link is critical to future cosmological analyses, which are currently impeded by our limited knowledge of baryonic feedback. Here, we measure the kinematic Sunyaev-Zel'dovich (kSZ) effect from the Atacama Cosmology Telescope (ACT), stacked on the luminous red galaxy (LRG) sample of the Dark Energy Spectroscopic Instrument (DESI) imaging survey. This is the first analysis to use photometric redshifts for reconstructing galaxy velocities. Due to the large number of galaxies comprising the DESI imaging survey, this is the highest signal-to-noise stacked kSZ measurement to date: we detect the signal at 13$\sigma$ and find that the gas is more spread out than the dark matter at $\sim$40$\sigma$. Our work opens up the possibility to recalibrate large hydrodynamical simulations using the kSZ effect. In addition, our findings point towards a way of alleviating inconsistencies between weak lensing surveys and cosmic microwave background (CMB) experiments such as the `low $S_8$' tension, and shed light on long-standing enigmas in astrophysics such as the `missing baryon' problem., Comment: 20 pages, 8 figures, submitting to PRL

Recent work has demonstrated both benefits and limitations from using supervised approaches (without temporal-difference learning) for offline reinforcement learning. While off-policy reinforcement learning provides a promising approach for improving performance beyond supervised approaches, we observe that training is often inefficient and unstable due to temporal difference bootstrapping. In this paper we propose a best-of-both approach by first learning the behavior policy and critic with supervised learning, before improving with off-policy reinforcement learning. Specifically, we demonstrate improved efficiency by pre-training with a supervised Monte-Carlo value-error, making use of commonly neglected downstream information from the provided offline trajectories. We find that we are able to more than halve the training time of the considered offline algorithms on standard benchmarks, and surprisingly also achieve greater stability. We further build on the importance of having consistent policy and value functions to propose novel hybrid algorithms, TD3+BC+CQL and EDAC+BC, that regularize both the actor and the critic towards the behavior policy. This helps to more reliably improve on the behavior policy when learning from limited human demonstrations. Code is available at https://github.com/AdamJelley/EfficientOfflineRL

Training agents to behave as desired in complex 3D environments from high-dimensional sensory information is challenging. Imitation learning from diverse human behavior provides a scalable approach for training an agent with a sensible behavioral prior, but such an agent may not perform the specific behaviors of interest when deployed. To address this issue, we draw an analogy between the undesirable behaviors of imitation learning agents and the unhelpful responses of unaligned large language models (LLMs). We then investigate how the procedure for aligning LLMs can be applied to aligning agents in a 3D environment from pixels. For our analysis, we utilize an academically illustrative part of a modern console game in which the human behavior distribution is multi-modal, but we want our agent to imitate a single mode of this behavior. We demonstrate that we can align our agent to consistently perform the desired mode, while providing insights and advice for successfully applying this approach to training agents. Project webpage at https://adamjelley.github.io/aligning-agents-like-llms .

The Simons Observatory is a new ground-based cosmic microwave background experiment, which is currently being commissioned in Chile's Atacama Desert. During its survey, the observatory's small aperture telescopes will map 10% of the sky in bands centered at frequencies ranging from 27 to 280 GHz to constrain cosmic inflation models, and its large aperture telescope will map 40% of the sky in the same bands to constrain cosmological parameters and use weak lensing to study large-scale structure. To achieve these science goals, the Simons Observatory is deploying these telescopes' receivers with 60,000 state-of-the-art superconducting transition-edge sensor bolometers for its first five year survey. Reading out this unprecedented number of cryogenic sensors, however, required the development of a novel readout system. The SMuRF electronics were developed to enable high-density readout of superconducting sensors using cryogenic microwave SQUID multiplexing technology. The commissioning of the SMuRF systems at the Simons Observatory is the largest deployment to date of microwave multiplexing technology for transition-edge sensors. In this paper, we show that a significant fraction of the systems deployed so far to the Simons Observatory's large aperture telescope meet baseline specifications for detector yield and readout noise in this early phase of commissioning., Comment: 10 pages, 5 figures, 1 table. To be presented at SPIE Astronomical Telescopes + Instrumentation 2024

Let $X$ be a smooth variety over a field of characteristic $p$. It is a natural question whether the Frobenius pushforwards $F_*^e\mathcal O_X$ of the structure sheaf are tilting bundles. We show if $X$ is a smooth del Pezzo surface of degree $\leq 3$ or a Fano threefold with $\mathrm{vol}(K_X)<24$ over a field of characteristic $p$, then $\mathrm{Ext}^i(F_*^e\mathcal O_X,F^e_*\mathcal O_X)\neq 0$ and thus $F_*^e\mathcal O_X$ is not tilting., Comment: 8 pages, comments welcome

In this paper we study $d$-dependent random graphs -- introduced by Brody and Sanchez -- which are the family of random graph distributions where each edge is present with probability $p$, and each edge is independent of all but at most $d$ other edges. For this random graph model, we analyze degree sequences, jumbledness, connectivity, and subgraph containment. Our results mirror those of the classical Erd\H{o}s--R\'enyi random graph, which are recovered by specializing our problem to $d=0$, although we show that in many regards our setting is appreciably more nuanced. We survey what is known for this model and conclude with a variety of open questions., Comment: 12 pages

The Simons Observatory will map the temperature and polarization over half of the sky, at millimeter wavelengths in six spectral bands from the Atacama Desert in Chile. These data will provide new insights into the genesis, content, and history of our Universe; the astrophysics of galaxies and galaxy clusters; objects in our solar system; and time-varying astrophysical phenomena. This ambitious new instrument suite, initially comprising three 0.5 m small-aperture telescopes and one 6 m large aperture telescope, is designed using a common combination of new technologies and new implementations to realize an observatory significantly more capable than the previous generation. In this paper, we present the pre-deployment performance of the first mid-frequency "optics tube" which will be fielded on the large aperture telescope with sensitivity to the 90 and 150 GHz spectral bands. This optics tube contains lenses, filters, detectors, and readout components, all of which operate at cryogenic temperatures. It is one of seven that form the core of the large aperture telescope receiver in its initial deployment. We describe this optics tube, including details of comprehensive testing methods, new techniques for beam and passband characterization, and its measured performance. The performance metrics include beams, optical efficiency, passbands, and forecasts for the on-sky performance of the system. We forecast a sensitivity that exceeds the requirements of the large aperture telescope with greater than 30% margin in each spectral band, and predict that the instrument will realize diffraction-limited performance and the expected detector passbands.

We demonstrate efficient sub-thermal cooling of the modified cyclotron mode of a single trapped antiproton and reach particle temperatures $T_+=E_+/k_\text{B}$ below $200\,$mK in preparation times shorter than $500\,$s. This corresponds to the fastest resistive single-particle cyclotron cooling to sub-thermal temperatures ever demonstrated. By cooling trapped particles to such low energies, we demonstrate the detection of antiproton spin transitions with an error-rate $<0.000025$, more than three orders of magnitude better than in previous best experiments. This method will have enormous impact on multi-Penning-trap experiments that measure magnetic moments with single nuclear spins for tests of matter/antimatter symmetry, high-precision mass-spectrometry, and measurements of electron $g$-factors bound to highly-charged ions that test quantum electrodynamics.

Collinear laser spectroscopy measurements were performed on $^{68-74}$Ge isotopes ($Z = 32$) at ISOLDE-CERN, by probing the $4s^2 4p^2 \, ^3\!P_1 \rightarrow 4s^2 4p 5s \, ^3\!P_1^o$ atomic transition (269~nm) of germanium. Nuclear charge radii are determined via the measured isotope shifts, revealing a larger local variation than the neighboring isotopic chains. Nuclear density functional theory with the Fayans functionals Fy($\Delta r$,HFB) and Fy(IVP), and the SV-min Skyrme describes the experimental data for the differential charge radii $\delta\langle r^{2} \rangle$ and charge radii $R_{\rm c}$ within the theoretical uncertainties. The observed large variation in the charge radii of germanium isotopes is better accounted for by theoretical models incorporating ground state quadrupole correlations. This suggests that the polarization effects due to pairing and deformation contribute to the observed large odd-even staggering in the charge radii of the Ge isotopic chain., Comment: 6 pages,5 figures