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The development of high-performance materials for microelectronics, energy storage, and extreme environments depends on our ability to describe and direct property-defining microstructural order. Our present understanding is typically derived from laborious manual analysis of imaging and spectroscopy data, which is difficult to scale, challenging to reproduce, and lacks the ability to reveal latent associations needed for mechanistic models. Here, we demonstrate a multi-modal machine learning (ML) approach to describe order from electron microscopy analysis of the complex oxide La$_{1-x}$Sr$_x$FeO$_3$. We construct a hybrid pipeline based on fully and semi-supervised classification, allowing us to evaluate both the characteristics of each data modality and the value each modality adds to the ensemble. We observe distinct differences in the performance of uni- and multi-modal models, from which we draw general lessons in describing crystal order using computer vision., Comment: 30 pages, 5 figures, 2 tables

We consider the problem of sampling a multimodal distribution with a Markov chain given a small number of samples from the stationary measure. Although mixing can be arbitrarily slow, we show that if the Markov chain has a $k$th order spectral gap, initialization from a set of $\tilde O(k/\varepsilon^2)$ samples from the stationary distribution will, with high probability over the samples, efficiently generate a sample whose conditional law is $\varepsilon$-close in TV distance to the stationary measure. In particular, this applies to mixtures of $k$ distributions satisfying a Poincar\'e inequality, with faster convergence when they satisfy a log-Sobolev inequality. Our bounds are stable to perturbations to the Markov chain, and in particular work for Langevin diffusion over $\mathbb R^d$ with score estimation error, as well as Glauber dynamics combined with approximation error from pseudolikelihood estimation. This justifies the success of data-based initialization for score matching methods despite slow mixing for the data distribution, and improves and generalizes the results of Koehler and Vuong (2023) to have linear, rather than exponential, dependence on $k$ and apply to arbitrary semigroups. As a consequence of our results, we show for the first time that a natural class of low-complexity Ising measures can be efficiently learned from samples.

Sufficiently capable models could subvert human oversight and decision-making in important contexts. For example, in the context of AI development, models could covertly sabotage efforts to evaluate their own dangerous capabilities, to monitor their behavior, or to make decisions about their deployment. We refer to this family of abilities as sabotage capabilities. We develop a set of related threat models and evaluations. These evaluations are designed to provide evidence that a given model, operating under a given set of mitigations, could not successfully sabotage a frontier model developer or other large organization's activities in any of these ways. We demonstrate these evaluations on Anthropic's Claude 3 Opus and Claude 3.5 Sonnet models. Our results suggest that for these models, minimal mitigations are currently sufficient to address sabotage risks, but that more realistic evaluations and stronger mitigations seem likely to be necessary soon as capabilities improve. We also survey related evaluations we tried and abandoned. Finally, we discuss the advantages of mitigation-aware capability evaluations, and of simulating large-scale deployments using small-scale statistics.

Hundreds of exoplanets between 1-1.8 times the size of the Earth have been discovered on close in orbits. However, these planets show such a diversity in densities that some appear to be made entirely of iron, while others appear to host gaseous envelopes. To test this diversity in composition, we update the masses of 5 rocky exoplanets (HD 93963 A b, Kepler-10 b, Kepler-100 b, Kepler-407 b, and TOI-1444 b) and present the confirmation of a new planet (TOI-1011) using 187 high precision RVs from Gemini/MAROON-X and Keck/KPF. Our updated planet masses suggest compositions closer to that of the Earth than previous literature values for all planets in our sample. In particular, we report that two previously identified ``super-Mercuries'' (Kepler-100 b and HD 93963 A b) have lower masses that suggest less iron-rich compositions. We then compare the ratio of iron to rock-building species to the abundance ratios of those elements in their host stars. These updated planet compositions do not suggest a steep relationship between planet and host star compositions, contradictory to previous results, and suggest that planets and host stars have similar abundance ratios., Comment: Submitted to AJ 09/30/2024

The use of guidance in diffusion models was originally motivated by the premise that the guidance-modified score is that of the data distribution tilted by a conditional likelihood raised to some power. In this work we clarify this misconception by rigorously proving that guidance fails to sample from the intended tilted distribution. Our main result is to give a fine-grained characterization of the dynamics of guidance in two cases, (1) mixtures of compactly supported distributions and (2) mixtures of Gaussians, which reflect salient properties of guidance that manifest on real-world data. In both cases, we prove that as the guidance parameter increases, the guided model samples more heavily from the boundary of the support of the conditional distribution. We also prove that for any nonzero level of score estimation error, sufficiently large guidance will result in sampling away from the support, theoretically justifying the empirical finding that large guidance results in distorted generations. In addition to verifying these results empirically in synthetic settings, we also show how our theoretical insights can offer useful prescriptions for practical deployment.

Mental health concerns are prevalent among college students, highlighting the need for effective interventions that promote self-awareness and holistic well-being. MindScape pioneers a novel approach to AI-powered journaling by integrating passively collected behavioral patterns such as conversational engagement, sleep, and location with Large Language Models (LLMs). This integration creates a highly personalized and context-aware journaling experience, enhancing self-awareness and well-being by embedding behavioral intelligence into AI. We present an 8-week exploratory study with 20 college students, demonstrating the MindScape app's efficacy in enhancing positive affect (7%), reducing negative affect (11%), loneliness (6%), and anxiety and depression, with a significant week-over-week decrease in PHQ-4 scores (-0.25 coefficient), alongside improvements in mindfulness (7%) and self-reflection (6%). The study highlights the advantages of contextual AI journaling, with participants particularly appreciating the tailored prompts and insights provided by the MindScape app. Our analysis also includes a comparison of responses to AI-driven contextual versus generic prompts, participant feedback insights, and proposed strategies for leveraging contextual AI journaling to improve well-being on college campuses. By showcasing the potential of contextual AI journaling to support mental health, we provide a foundation for further investigation into the effects of contextual AI journaling on mental health and well-being., Comment: arXiv admin note: text overlap with arXiv:2404.00487

We report the sky-projected spin-orbit angle $\lambda$ for HD 191939 b, the innermost planet in a 6 planet system, using Keck/KPF to detect the Rossiter-McLaughlin (RM) effect. Planet b is a sub-Neptune with radius 3.4 $\pm$ 0.8 R$_{\oplus}$ and mass 10.0 $\pm$ 0.7 M$_{\oplus}$ with an RM amplitude $<$1 ms$^{-1}$. We find the planet is consistent with a well-aligned orbit, measuring $\lambda= \, $ 3.7 $\pm$ 5.0 degrees. Additionally, we place new constraints on the mass and period of the distant super-Jupiter, planet f, finding it to be 2.88 $\pm$ 0.26 $M_J$ on a 2898 $\pm$ 152 day orbit. With these new orbital parameters, we perform a dynamical analysis of the system and constrain the mutual inclination of the non-transiting planet e to be smaller than 12 degrees relative to the plane shared by the inner three transiting planets. Additionally, the further planet f is inclined off this shared plane, the greater the amplitude of precession for the entire inner system, making it increasingly unlikely to measure an aligned orbit for planet b. Through this analysis, we show that this system's wide variety of planets are all well-aligned with the star and nearly co-planar, suggesting that the system formed dynamically cold and flat out of a well-aligned proto-planetary disk, similar to our own solar system., Comment: 11 pages, 4 figures, Accepted for publication in The Astronomical Journal

Generating realistic human motion is essential for many computer vision and graphics applications. The wide variety of human body shapes and sizes greatly impacts how people move. However, most existing motion models ignore these differences, relying on a standardized, average body. This leads to uniform motion across different body types, where movements don't match their physical characteristics, limiting diversity. To solve this, we introduce a new approach to develop a generative motion model based on body shape. We show that it's possible to train this model using unpaired data by applying cycle consistency, intuitive physics, and stability constraints, which capture the relationship between identity and movement. The resulting model generates diverse, physically plausible, and dynamically stable human motions that are both quantitatively and qualitatively more realistic than current state-of-the-art methods. More details are available on our project page https://CarstenEpic.github.io/humos/., Comment: Accepted in ECCV'24. Project page: https://CarstenEpic.github.io/humos/

Generalizing a formula of Stanley, we prove combinatorially that the probability that $1, 2, \dots, k$ are contained in the same cycle of a product of two random $n$-cycles is \[\frac{1}{k} + \frac{4 (-1)^n}{ \binom{2k}{k}} \sum_{\substack{1 \leq i \leq k-1 \\ i \not\equiv n \bmod 2}} \binom{2k-1}{k+i} \left(\frac{1}{n+i+1} - \frac{1}{n-i}\right).\], Comment: 23 pages, 12 figures

Retirement plans can create strong financial incentives that have important labor market implications, and many states have adopted alternative plan designs that significantly change these incentives. The authors use longitudinal data to investigate the impact of Washington State's 1996 introduction of a hybrid retirement plan on late-career attrition. The unique setup of Washington's plans allows them to provide empirical evidence on the influence of financial incentives created by statutory retirement eligibility thresholds. Findings show that despite facing very different financial incentives, teachers enrolled in the hybrid and traditional plans respond similarly to reaching a key retirement eligibility threshold. The authors hypothesize that teachers are anchoring to the eligibility thresholds, muting the influence of the financial incentives. They also provide evidence that, in the presence of bright-line eligibility thresholds that can anchor workers' separation behavior, commonly used structural models may overpredict workers' responsiveness to the financial incentives embedded in retirement plans. [This paper will be published in "ILR Review."]

Characterizing outer companions to hot Jupiters plays a crucial role in deciphering their origins. We present the discovery of a long-period giant planet, HD 118203 c ($m_{c}=11.79^{+0.69}_{-0.63}\ \mathrm{M_{J}}$, $a_{c}=6.28^{+0.10}_{-0.11}$ AU) exterior to a close-in eccentric hot Jupiter HD 118203 b ($P_{b}=6.135\ \mathrm{days}$, $m_{b}=2.14\pm{0.12}\ \mathrm{M_{J}}$, $r_{b}=1.14\pm{0.029}\ \mathrm{R_{J}}$, $e_{b}=0.31\pm{0.007}$) based on twenty-year radial velocities. Using Rossiter-McLaughlin (RM) observations from the Keck Planet Finder (KPF), we measured a low sky-projected spin-orbit angle $\lambda_{b}=-11^{\circ}.7^{+7.6}_{-10.0}$ for HD 118203 b and detected stellar oscillations in the host star, confirming its evolved status. Combining the RM observation with the stellar inclination measurement, we constrained the true spin-orbit angle of HD 118203 b as $\Psi_{b}<33^{\circ}.5\ (2\sigma)$, indicating the orbit normal of the hot Jupiter nearly aligned with the stellar spin axis. Furthermore, by combining radial velocities and Hipparcos-Gaia astrometric acceleration, we constrained the line-of-sight mutual inclination between the hot Jupiter and the outer planet to be $9^{\circ}.8^{+16.2}_{-9.3}$ at $2\sigma$ level. HD 118203 is one of first hot Jupiter systems where both the true spin-orbit angle of the hot Jupiter and the mutual inclination between inner and outer planets have been determined. Our results are consistent with a system-wide alignment, with low mutual inclinations between the outer giant planet, the inner hot Jupiter, and the host star. This alignment, along with the moderate eccentricity of HD 118203 c, implies that the system may have undergone coplanar high-eccentricity tidal migration. Under this framework, our dynamical analysis suggests an initial semi-major axis of 0.3 to 3.2 AU for the proto-hot Jupiter., Comment: 30 pages, 12 figures, accepted by AJ

The degree of alignment between a star's spin axis and the orbital plane of its planets (the stellar obliquity) is related to interesting and poorly understood processes that occur during planet formation and evolution. Hot Jupiters orbiting hot stars ($\gtrsim$6250 K) display a wide range of obliquities, while similar planets orbiting cool stars are preferentially aligned. Tidal dissipation is expected to be more rapid in stars with thick convective envelopes, potentially explaining this trend. Evolved stars provide an opportunity to test the damping hypothesis, particularly stars that were hot on the main sequence and have since cooled and developed deep convective envelopes. We present the first systematic study of the obliquities of hot Jupiters orbiting subgiants that recently developed convective envelopes using Rossiter-McLaughlin observations. Our sample includes two newly discovered systems in the Giants Transiting Giants Survey (TOI-6029 b, TOI-4379 b). We find that the orbits of hot Jupiters orbiting subgiants that have cooled below $\sim$6250 K are aligned or nearly aligned with the spin-axis of their host stars, indicating rapid tidal realignment after the emergence of a stellar convective envelope. We place an upper limit for the timescale of realignment for hot Jupiters orbiting subgiants at $\sim$500 Myr. Comparison with a simplified tidal evolution model shows that obliquity damping needs to be $\sim$4 orders of magnitude more efficient than orbital period decay to damp the obliquity without destroying the planet, which is consistent with recent predictions for tidal dissipation from inertial waves excited by hot Jupiters on misaligned orbits., Comment: 22 pages, 14 figures, 3 tables

We introduce the OATMEAL survey, an effort to measure the obliquities of stars with transiting brown dwarf companions. We observed a transit of the close-in ($P_{\rm orb} = 1.74 \,$ days) brown dwarf GPX-1 b using the Keck Planet Finder (KPF) spectrograph to measure the sky-projected angle between its orbital axis and the spin axis of its early F-type host star ($\lambda$). We measured $\lambda = 6.88 \pm 1.72 ^\circ$ (with additional unquantified systematic uncertainty), suggesting an orbit that is prograde and well aligned with the stellar equator. Hot Jupiters around early F stars are frequently found to have highly misaligned orbits, with polar and retrograde orbits being commonplace. It has been theorized that these misalignments stem from dynamical interactions, such as von Zeipel-Kozai-Lidov cycles, and are retained over long timescales due to weak tidal dissipation in stars with radiative envelopes. By comparing GPX-1 to similar systems under the frameworks of different tidal evolution theories, we argued that the rate of tidal dissipation is too slow to have re-aligned the system. This suggests that GPX-1 may have arrived at its close-in orbit via coplanar high-eccentricity migration or migration through an aligned protoplanetary disk. Our result for GPX-1 is one of few measurements of the obliquity of a star with a transiting brown dwarf. By enlarging the number of such measurements and comparing them with hot Jupiter systems, we will more clearly discern the differences between the mechanisms that dictate the formation and evolution of both classes of objects., Comment: 8 pages, 4 figures

Asteroseismology of dwarf stars cooler than the Sun is very challenging due to the low amplitudes and rapid timescales of oscillations. Here, we present the asteroseismic detection of solar-like oscillations at 4-minute timescales ($\nu_{\mathrm{max}}\sim4300\mu$Hz) in the nearby K-dwarf $\sigma$ Draconis using extreme precision Doppler velocity observations from the Keck Planet Finder and 20-second cadence photometry from NASA's Transiting Exoplanet Survey Satellite. The star is the coolest dwarf star to date with both velocity and luminosity observations of solar-like oscillations, having amplitudes of $5.9\pm0.8\,$cm$\,\text{s}^{-1}$ and $0.8\pm0.2$ ppm, respectively. These measured values are in excellent agreement with established luminosity-velocity amplitude relations for oscillations and provide further evidence that mode amplitudes for stars with $T_{\mathrm{eff}}<\,5500\,$K diminish in scale following a $(L/M)^{1.5}$ relation. By modeling the star's oscillation frequencies from photometric data, we measure an asteroseismic age of $4.5\pm0.9\,\rm{(ran)} \pm 1.2\,\rm{(sys)}$ Gyr. The observations demonstrate the capability of next-generation spectrographs and precise space-based photometry to extend observational asteroseismology to nearby cool dwarfs, which are benchmarks for stellar astrophysics and prime targets for directly imaging planets using future space-based telescopes., Comment: Accepted for publication in The Astrophysical Journal

We present the first spectroscopic transit results from the newly commissioned Keck Planet Finder on the Keck-I telescope at W. M. Keck Observatory. We observed a transit of KELT-18 b, an inflated ultra-hot Jupiter orbiting a hot star ($T_\text{eff} = 6670$ K) with a binary stellar companion. By modeling the perturbation to the measured cross correlation functions using the Reloaded Rossiter-McLaughlin technique, we derived a sky projected obliquity of $\lambda = -94.8 \pm 0.7$ deg ($\psi = 93.8_{-1.8}^{+1.6}$ deg for isotropic $i_\star$). The data are consistent with an extreme stellar differential rotation ($\alpha = 0.9$), though a more likely explanation is moderate center-to-limb variations of the emergent stellar spectrum. We see additional evidence for the latter from line widths increasing towards the limb. Using loose constraints on the stellar rotation period from observed variability in the available TESS photometry, we were able to constrain the stellar inclination and thus the true 3D stellar obliquity to $\psi = 91.7_{-1.8}^{+2.2}$ deg. KELT-18 b could have obtained its polar orbit through high-eccentricity migration initiated by Kozai-Lidov oscillations induced by the binary stellar companion KELT-18 B, as the two likely have a large mutual inclination as evidenced by Gaia astrometry. KELT-18 b adds another data point to the growing population of close-in polar planets, particularly around hot stars., Comment: 17 pages, 8 figures, submitted to AJ (in revision)

The orbits of close-in exoplanets provide clues to their formation and evolutionary history. Many close-in exoplanets likely formed far out in their protoplanetary disks and migrated to their current orbits, perhaps via high-eccentricity migration (HEM), a process that can also excite obliquities. A handful of known exoplanets are perhaps caught in the act of HEM, as they are observed on highly eccentric orbits with tidal circularization timescales shorter than their ages. One such exoplanet is Kepler-1656 b, which is also the only known non-giant exoplanet (<100 $M_\oplus$) with an extreme eccentricity (e=0.84). We measured the sky-projected obliquity of Kepler-1656 b by observing the Rossiter-McLaughlin effect during a transit with the Keck Planet Finder. Our data are consistent with an aligned orbit, but are also consistent with moderate misalignment with $\lambda < 50$ deg at 95% confidence, with the most likely solution of $35^{+14.9}_{-21.6}$ deg. A low obliquity would be an unlikely outcome of most eccentricity-exciting scenarios, but we show that the properties of the outer companion in the system are consistent with the coplanar HEM mechanism. Alternatively, if the system is not relatively coplanar (<20 deg mutual inclination), Kepler-1656 b may be presently at a rare snapshot of long-lived eccentricity oscillations that do not induce migration. Kepler-1656 b is only the fourth exoplanet with e>0.8 to have its obliquity constrained; expanding this population will help establish the degree to which orbital misalignment accompanies migration. Future work that constrains the mutual inclinations of outer perturbers will be key for distinguishing plausible mechanisms., Comment: 11 pages, 5 figures, accepted to ApJL

TOI-6255~b (GJ 4256) is an Earth-sized planet (1.079$\pm0.065$ $R_\oplus$) with an orbital period of only 5.7 hours. With the newly commissioned Keck Planet Finder (KPF) and CARMENES spectrographs, we determined the planet's mass to be 1.44$\pm$0.14 $M_{\oplus}$. The planet is just outside the Roche limit, with $P_{\rm orb}/P_{\rm Roche}$ = 1.13 $\pm0.10$. The strong tidal force likely deforms the planet into a triaxial ellipsoid with a long axis that is $\sim$10\% longer than the short axis. Assuming a reduced stellar tidal quality factor $Q_\star^\prime \approx10^7$, we predict that tidal orbital decay will cause TOI-6255 to reach the Roche limit in roughly 400 Myr. Such tidal disruptions may produce the possible signatures of planet engulfment that have been on stars with anomalously high refractory elemental abundances compared to its conatal binary companion. TOI-6255 b is also a favorable target for searching for star-planet magnetic interactions, which might cause interior melting and hasten orbital decay. TOI-6255 b is a top target (Emission Spectroscopy Metric of about 24) for phase curve observations with the James Webb Space Telescope., Comment: 18 pages, 7 figures, 5 tables, accepted to AAS Journals. The first RV mass measurement from the Keck Planet Finder

The continuous random energy model (CREM) is a toy model of spin glasses on $\{0,1\}^N$ that, in the limit, exhibits an infinitely hierarchical correlation structure. We give two polynomial-time algorithms to approximately sample from the Gibbs distribution of the CREM in the high-temperature regime, based on a Markov chain and a sequential sampler. The running time depends algebraically on the desired TV distance and failure probability and exponentially in $(1/g')^{O(1)}$, where $g'$ is the gap to a certain inverse temperature threshold; this contrasts with previous results which only attain $o(N)$ accuracy in KL divergence. If the covariance function $A$ of the CREM is concave, the algorithms work up to the critical threshold $\beta_c$, which is the static phase transition point; moreover, for certain $A$, the algorithms work up to the known algorithmic threshold $\beta_G$ proposed in Addario-Berry and Maillard (2020) for non-trivial sampling guarantees. Our result depends on quantitative bounds for the fluctuation of the partition function and a new contiguity result of the ``tilted" CREM obtained from sampling, which is of independent interest. We also show that the spectral gap is exponentially small with high probability, suggesting that the algebraic dependence is unavoidable with a Markov chain approach.

Code linters play a crucial role in developing high-quality software systems by detecting potential problems (e.g., memory leaks) in the source code of systems. Despite their benefits, code linters are often language-specific, focused on certain types of issues, and prone to false positives in the interest of speed. This paper investigates whether large language models can be used to develop a more versatile code linter. Such a linter is expected to be language-independent, cover a variety of issue types, and maintain high speed. To achieve this, we collected a large dataset of code snippets and their associated issues. We then selected a language model and trained two classifiers based on the collected datasets. The first is a binary classifier that detects if the code has issues, and the second is a multi-label classifier that identifies the types of issues. Through extensive experimental studies, we demonstrated that the developed large language model-based linter can achieve an accuracy of 84.9% for the binary classifier and 83.6% for the multi-label classifier., Comment: 44 pages, 3 figures

Transformers have revolutionized machine learning across diverse domains, yet understanding their behavior remains crucial, particularly in high-stakes applications. This paper introduces the contextual counting task, a novel toy problem aimed at enhancing our understanding of Transformers in quantitative and scientific contexts. This task requires precise localization and computation within datasets, akin to object detection or region-based scientific analysis. We present theoretical and empirical analysis using both causal and non-causal Transformer architectures, investigating the influence of various positional encodings on performance and interpretability. In particular, we find that causal attention is much better suited for the task, and that no positional embeddings lead to the best accuracy, though rotary embeddings are competitive and easier to train. We also show that out of distribution performance is tightly linked to which tokens it uses as a bias term.

We prove bounds on the variance of a function $f$ under the empirical measure of the samples obtained by the Sequential Monte Carlo (SMC) algorithm, with time complexity depending on local rather than global Markov chain mixing dynamics. SMC is a Markov Chain Monte Carlo (MCMC) method, which starts by drawing $N$ particles from a known distribution, and then, through a sequence of distributions, re-weights and re-samples the particles, at each instance applying a Markov chain for smoothing. In principle, SMC tries to alleviate problems from multi-modality. However, most theoretical guarantees for SMC are obtained by assuming global mixing time bounds, which are only efficient in the uni-modal setting. We show that bounds can be obtained in the truly multi-modal setting, with mixing times that depend only on local MCMC dynamics.

The Transiting Exoplanet Survey Satellite (TESS) has discovered hundreds of new worlds, with TESS planet candidates now outnumbering the total number of confirmed planets from $\textit{Kepler}$. Owing to differences in survey design, TESS continues to provide planets that are better suited for subsequent follow-up studies, including mass measurement through radial velocity (RV) observations, compared to Kepler targets. In this work, we present the TESS-Keck Survey's (TKS) Mass Catalog: a uniform analysis of all TKS RV survey data which has resulted in mass constraints for 126 planets and candidate signals. This includes 58 mass measurements that have reached $\geq5\sigma$ precision. We confirm or validate 32 new planets from the TESS mission either by significant mass measurement (15) or statistical validation (17), and we find no evidence of likely false positives among our entire sample. This work also serves as a data release for all previously unpublished TKS survey data, including 9,204 RV measurements and associated activity indicators over our three year survey. We took the opportunity to assess the performance of our survey, and found that we achieved many of our goals including measuring the mass of 38 small ($<4R_{\oplus}$) planets, nearly achieving the TESS mission's basic science requirement. In addition, we evaluated the performance of the Automated Planet Finder (APF) as survey support and observed meaningful constraints on system parameters due to its more uniform phase coverage. Finally, we compared our measured masses to those predicted by commonly used mass-radius relations and investigated evidence of systematic bias., Comment: 51 pages (22 of text), 24 figures

We prove RE-completeness (and thus undecidability) of several 2D games in the Super Mario Bros. platform video game series: the New Super Mario Bros. series (original, Wii, U, and 2), and both Super Mario Maker games in all five game styles (Super Mario Bros. 1 and 3, Super Mario World, New Super Mario Bros. U, and Super Mario 3D World). These results hold even when we restrict to constant-size levels and screens, but they do require generalizing to allow arbitrarily many enemies at each location and onscreen, as well as allowing for exponentially large (or no) timer. Our New Super Mario Bros. constructions fit within one standard screen size. In our Super Mario Maker reductions, we work within the standard screen size and use the property that the game engine remembers offscreen objects that are global because they are supported by "global ground". To prove these Mario results, we build a new theory of counter gadgets in the motion-planning-through-gadgets framework, and provide a suite of simple gadgets for which reachability is RE-complete.

Large-scale cosmological simulations suggest that feedback from active galactic nuclei (AGN) plays a crucial role in galaxy evolution. In this study, we directly test this hypothesis utilising SDSS spectra of a sample of 48 low redshift (z<0.14) type 2 quasars (QSO2s). We characterised the kinematics of the warm ionised gas by performing a non-parametric analysis of the [OIII]$\lambda 5007$ emission line, as well as constrain the properties of the young stellar populations (YSP) of their host galaxies through spectral synthesis modelling. These analyses revealed that 85% of the QSO2s display gas velocity dispersions larger than that of the stellar component of their host galaxies, indicating the presence of AGN-driven outflows. Comparing the gas kinematics to the AGN properties, we found a positive correlation between gas velocity dispersion and 1.4 GHz radio luminosity but not with AGN bolometric luminosity or Eddington ratio, suggesting that, either the radio luminosity is the key factor in driving outflows or that the outflows themselves are shocking the ISM and producing synchrotron emission. We found that 98% of the sample host YSPs to varying degrees, with star formation rates (SFR) $0 \le SFR \le 92 \mbox{ M}_{\odot} \mbox{yr}^{-1}$, averaged over 100 Myr. We compared the gas kinematics and outflow properties to the SFRs to establish possible correlations which may suggest that the presence of the outflowing gas is impacting SF and find that none exists, leading to the conclusion that, on the scales probed by the SDSS fibre, AGN-driven outflows do not impact SF on the timescales probed in this study. However, we found a positive correlation between the light-weighted stellar ages of the QSO2s and the black hole mass, which may indicate that successive AGN episodes lead to the suppression of SF over the course of galaxy evolution., Comment: 15 pages including 12 Figures. Three additional appendices including 2 long Figures and 4 Tables. Accepted for publication in Astronomy and Astrophysics (A&A)

The paper discusses capital allocation using the Euler formula and focuses on the risk measures Value-at-Risk (VaR) and Expected shortfall (ES). Some new results connected to this capital allocation is known. Two examples illustrate that capital allocation with VaR is not monotonous which may be surprising since VaR is monotonous. A third example illustrates why the same risk measure should be used in capital allocation as in the evaluation of the total portfolio. We show how simulation may be used in order to estimate the expected Return on risk adjusted capital in the commitment period of an asset. Finally, we show how Markov chain Monte Carlo may be used in the estimation of the capital allocation., Comment: 12 pages, 3 figures, 4 tables, 15 references

We give a new algorithm for learning mixtures of $k$ Gaussians (with identity covariance in $\mathbb{R}^n$) to TV error $\varepsilon$, with quasi-polynomial ($O(n^{\text{poly log}\left(\frac{n+k}{\varepsilon}\right)})$) time and sample complexity, under a minimum weight assumption. Unlike previous approaches, most of which are algebraic in nature, our approach is analytic and relies on the framework of diffusion models. Diffusion models are a modern paradigm for generative modeling, which typically rely on learning the score function (gradient log-pdf) along a process transforming a pure noise distribution, in our case a Gaussian, to the data distribution. Despite their dazzling performance in tasks such as image generation, there are few end-to-end theoretical guarantees that they can efficiently learn nontrivial families of distributions; we give some of the first such guarantees. We proceed by deriving higher-order Gaussian noise sensitivity bounds for the score functions for a Gaussian mixture to show that that they can be inductively learned using piecewise polynomial regression (up to poly-logarithmic degree), and combine this with known convergence results for diffusion models. Our results extend to continuous mixtures of Gaussians where the mixing distribution is supported on a union of $k$ balls of constant radius. In particular, this applies to the case of Gaussian convolutions of distributions on low-dimensional manifolds, or more generally sets with small covering number.

We prove NP-hardness and #P-hardness of Tetris clearing (clearing an initial board using a given sequence of pieces) with the Super Rotation System (SRS), even when the pieces are limited to any two of the seven Tetris piece types. This result is the first advance on a question posed twenty years ago: which piece sets are easy vs. hard? All previous Tetris NP-hardness proofs used five of the seven piece types. We also prove ASP-completeness of Tetris clearing, using three piece types, as well as versions of 3-Partition and Numerical 3-Dimensional Matching where all input integers are distinct. Finally, we prove NP-hardness of Tetris survival and clearing under the "hard drops only" and "20G" modes, using two piece types, improving on a previous "hard drops only" result that used five piece types.

We prove PSPACE-hardness for fifteen games in the Super Mario Bros. 2D platforming video game series. Previously, only the original Super Mario Bros. was known to be PSPACE-hard (FUN 2016), though several of the games we study were known to be NP-hard (FUN 2014). Our reductions build door gadgets with open, close, and traverse traversals, in each case using mechanics unique to the game. While some of our door constructions are similar to those from FUN 2016, those for Super Mario Bros. 2, Super Mario Land 2, Super Mario World 2, and the New Super Mario Bros. series are quite different; notably, the Super Mario Bros. 2 door is extremely difficult. Doors remain elusive for just two 2D Mario games (Super Mario Land and Super Mario Run); we prove that these games are at least NP-hard.

Linear confinement with Casimir scaling of the string tension in confining gauge theories is a consequence of a certain property of the Polyakov loop related to random matrices. This mechanism does not depend on the details of the theories (neither the gauge group nor dimensions) and explains approximate Casimir scaling below string-breaking length. In this paper, we study 3d SU(2) pure Yang-Mills theory numerically and find the same random-matrix behavior for rectangular Wilson loops. We conjecture that this is a universal feature of strongly coupled confining gauge theories., Comment: 23 pages, 12 figures

The Hubble constant ($H_0$), a crucial parameter in cosmology, quantifies the expansion rate of the universe so its precise measurement is important to understand the fundamental dynamics of our evolving universe. One of the major limitations of measuring $H_0$ using time-delay cosmography is the presence of the mass-sheet degeneracy (MSD) in the lens mass modeling. We propose and quantitatively assess the use of galaxy-galaxy shear measurements to break the MSD in the strong lensing mass modeling. We use stacked galaxy-galaxy lensing profiles and corresponding covariance matrices from Huang et al. (2022) to constrain the MSD in lens mass modeling with a highly flexible mass profile. Our analyses show that if ideally all galaxy-galaxy lensing measurements from the Hyper Suprime-Cam (HSC) survey can be used to constrain the MSD, we can achieve $\sim 10\%$ precision on the MSD constraint. We forecast that galaxy-galaxy lensing measurements from LSST-like surveys can in general constrain the MSD with $\sim 1-3\%$ precision. Furthermore, if we push weak lensing measurements to a lower angular scale of $\sim 0.04$ $\rm Mpc$, a survey like LSST can provide $\sim 1\%$ precision on the MSD constraint, enabling a measurement of $H_0$ at the $1\%$ level. We demonstrate that galaxy-galaxy weak lensing can robustly constrain the MSD independent of stellar kinematics of the deflector, with wide-field survey data alone., Comment: 11 pages, 8 figures, MNRAS in press

MindScape aims to study the benefits of integrating time series behavioral patterns (e.g., conversational engagement, sleep, location) with Large Language Models (LLMs) to create a new form of contextual AI journaling, promoting self-reflection and well-being. We argue that integrating behavioral sensing in LLMs will likely lead to a new frontier in AI. In this Late-Breaking Work paper, we discuss the MindScape contextual journal App design that uses LLMs and behavioral sensing to generate contextual and personalized journaling prompts crafted to encourage self-reflection and emotional development. We also discuss the MindScape study of college students based on a preliminary user study and our upcoming study to assess the effectiveness of contextual AI journaling in promoting better well-being on college campuses. MindScape represents a new application class that embeds behavioral intelligence in AI.

Mathematical and statistical models underlie many of the world's most important fisheries management decisions. Since the 19th century, difficulty calibrating and fitting such models has been used to justify the selection of simple, stationary, single-species models to aid tactical fisheries management decisions. Whereas these justifications are reasonable, it is imperative that we quantify the value of different levels of model complexity for supporting fisheries management, especially given a changing climate, where old methodologies may no longer perform as well as in the past. Here we argue that cost-benefit analysis is an ideal lens to assess the value of model complexity in fisheries management. While some studies have reported the benefits of model complexity in fisheries, modeling costs are rarely considered. In the absence of cost data in the literature, we report, as a starting point, relative costs of single-species stock assessment and marine ecosystem models from two Australian organizations. We found that costs varied by two orders of magnitude, and that ecosystem model costs increased with model complexity. Using these costs, we walk through a hypothetical example of cost-benefit analysis. The demonstration is intended to catalyze the reporting of modeling costs and benefits.

The ultra luminous infrared galaxy (ULIRG) F13451+1232 is an excellent example of a galaxy merger in the early stages of active galactic nucleus (AGN) activity, a phase in which AGN-driven outflows are expected to be particularly important. However, previous observations have determined that the mass outflow rates of the warm ionised and neutral gas phases in F13451+1232 are relatively modest, and there has been no robust detection of molecular outflows. Using high spatial resolution ALMA CO(1-0) observations, we detect a kiloparsec-scale circumnuclear disk, as well as extended ($r\sim440$ pc), intermediate-velocity (300<|$v$|<400 km s$^{-1}$) cold molecular gas emission that cannot be explained by rotational disk motions. If interpreted as AGN-driven outflows, the mass outflow rates associated with this intermediate-velocity gas are relatively modest ($\dot{M}_\mathrm{out}=22$-$27$ M$_\odot$ yr$^{-1}$); however, we also detect a compact ($r_\mathrm{out}$<120 pc), high velocity (400<$v$<680 km s$^{-1}$) cold molecular outflow near the primary nucleus of F13451+1232, which carries an order of magnitude more mass ($\dot{M}_\mathrm{out}\sim230$ M$_\odot$ yr$^{-1}$) than (and several times the kinetic power of) the previously-detected warmer phases. Moreover, the similar spatial scales of this compact outflow and the radio structure indicate that it is likely accelerated by the small-scale ($r\sim130$ pc) AGN jet in the primary nucleus of F13451+1232. Considering the compactness of the nuclear outflow and intermediate-velocity non-rotating gas that we detect, we argue that high spatial-resolution observations are necessary to properly quantify the properties of AGN-driven outflows and their impacts on host galaxies., Comment: 11 pages, 7 figures, 1 table; accepted for publication in MNRAS