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Noble gas and liquid detectors rely on high chemical purity for successful operation. While gaseous purification has emerged as a reliable method of producing high-purity noble fluids, the requirement for large mass flows drives the development of liquid-phase purification. We constructed a medium-scale liquid argon (LAr) purification system based on a copper catalyst and 4 A molecular sieve capable of purifying 1 t of commercial LAr 5.0 to a long effective triplet lifetime of $\tau_3 \sim 1.3 \mu$s. We further demonstrate that a quenched effective triplet lifetime of $\tau_3 \sim 1 \mu$s, due to contamination by air, can be recovered in loop-mode purification to $\tau_3 \sim 1.3 \mu$s after > 20 volume exchanges., Comment: 8 pages, 2 figures, contribution to LIDINE2023 v2: Added discussion of N2-trapping capability of purifier. Fixed typos, improved text/figure style, and added a reference

The COVID-19 pandemic has severely disrupted the retail landscape and has accelerated the adoption of innovative technologies. A striking example relates to the proliferation of online grocery orders and the technology deployed to facilitate such logistics. In fact, for many retailers, this disruption was a wake-up call after which they started recognizing the power of data analytics and artificial intelligence (AI). In this article, we discuss the opportunities that AI can offer to retailers in the new normal retail landscape. Some of the techniques described have been applied at scale to adapt previously deployed AI models, whereas in other instances, fresh solutions needed to be developed to help retailers cope with recent disruptions, such as unexpected panic buying, retraining predictive models, and leveraging online-offline synergies.

WASP-107b is a warm ($\sim$740 K) transiting planet with a Neptune-like mass of $\sim$30.5 $M_{\oplus}$ and Jupiter-like radius of $\sim$0.94 $R_{\rm J}$, whose extended atmosphere is eroding. Previous observations showed evidence for water vapour and a thick high-altitude condensate layer in WASP-107b's atmosphere. Recently, photochemically produced sulphur dioxide (SO$_2$) was detected in the atmosphere of a hot ($\sim$1,200 K) Saturn-mass planet from transmission spectroscopy near 4.05 $\mu$m, but for temperatures below $\sim$1,000 K sulphur is predicted to preferably form sulphur allotropes instead of SO$_2$. Here we report the 9$\sigma$-detection of two fundamental vibration bands of SO$_2$, at 7.35 $\mu$m and 8.69 $\mu$m, in the transmission spectrum of WASP-107b using the Mid-Infrared Instrument (MIRI) of the JWST. This discovery establishes WASP-107b as the second irradiated exoplanet with confirmed photochemistry, extending the temperature range of exoplanets exhibiting detected photochemistry from $\sim$1,200 K down to $\sim$740 K. Additionally, our spectral analysis reveals the presence of silicate clouds, which are strongly favoured ($\sim$7$\sigma$) over simpler cloud setups. Furthermore, water is detected ($\sim$12$\sigma$), but methane is not. These findings provide evidence of disequilibrium chemistry and indicate a dynamically active atmosphere with a super-solar metallicity.

The bispectrum is an important statistics helpful for measuring the primordial non-Gaussianity parameter $f_{\mathrm{NL}}$ to less than order unity in error, which would allow us to distinguish between single and multi-field inflation models. The Spectro-Photometer for the History of the Universe, Epoch of Reionization and Ices Explorer (SPHEREx) mission is particularly well-suited for making this measurement with its $\sim$100-band all-sky observations in the near-infrared. Consequently, the SPHEREx data will contain galaxies with spectroscopic-like redshift measurements as well as those with much larger errors. In this paper, we evaluate the impact of photometric redshift errors on $f_{\mathrm{NL}}$ constraints in the context of an updated multi-tracer forecast for SPHEREx, finding that the azimuthal averages of the first three even bispectrum multipoles are no longer sufficient for capturing most of the information (as opposed to the case of spectroscopic surveys shown in the literature). The final SPHEREx result with all five galaxy samples and six redshift bins is however not severely impacted because the total result is dominated by the samples with the best redshift errors, while the worse samples serve to reduce cosmic variance. Our fiducial result of $\sigma_{f_{\mathrm{NL}}} = 0.7$ from bispectrum alone is increased by $18\%$ and $3\%$ when using $l_{\mathrm{max}}=0$ and 2 respectively. We also explore the impact on parameter constraints when varying the fiducial redshift errors, as well as using subsets of multi-tracer combinations or triangles with different squeezing factors. Note that the fiducial result here is not the final SPHEREx capability, which is still on target for being $\sigma_{f_{\mathrm{NL}}} = 0.5$ once the power spectrum will be included., Comment: 15 pages, 3 figures

Active galactic nuclei (AGN) play an integral role in galaxy formation and evolution by influencing galaxies and their environments through radio jet feedback. Historically, interpreting observations of radio galaxies and quantifying radio jet feedback has been challenging due to degeneracies between their physical parameters. In particular, it is well-established that different combinations of jet kinetic power and environment density can yield indistinguishable radio continuum properties, including apparent size and Stokes I luminosity. We present an approach to breaking this degeneracy by probing the line-of-sight environment with Faraday rotation. We study this effect in simulations of three-dimensional relativistic magnetohydrodynamic AGN jets in idealised environments with turbulent magnetic fields. We generate synthetic Stokes I emission and Faraday rotation measure (RM) maps, which enable us to distinguish between our simulated sources. We find enhanced RMs near the jet head and lobe edges and an RM reversal across the jet axis. We show that increasing the environment density and the average cluster magnetic field strength broadens the distribution of Faraday rotation measure values. We study the depolarisation properties of our sources, finding that the hotspot regions depolarise at lower frequencies than the lobes. We quantify the effect of depolarisation on the RM distribution, finding that the frequency at which the source is too depolarised to measure the RM distribution accurately is a probe of environmental properties. This technique offers a range of new opportunities for upcoming surveys, including probing radio galaxy environments and determining more accurate estimates of the AGN feedback budget., Comment: 17 pages, 11 figures. Submitted for publication in MNRAS

High energy x-ray diffraction microscopy was used to image the microstructure of $\alpha$-Fe before and after a 600 $^\circ$C anneal. These data were used to determine the areas, curvatures, energies, and velocities of approximately 40,000 grain boundaries. The measured grain boundary properties depend on the five macroscopic grain boundary parameters. The velocities are not correlated with the product of the mean boundary curvature and grain boundary energy, usually assumed to be the driving force. Boundary migration is made up of area changes (lateral motion) and translation (normal motion) and both contribute to the total migration. Through the lateral motion component of the migration, low energy boundaries tend to expand in area while high energy boundaries shrink, reducing the average energy through grain boundary replacement. The driving force for this process is not related to curvature and might disrupt the expected curvature-velocity relationship., Comment: 33 pages, double spaced, accepted for publication in Acta Materialia

Brown dwarfs serve as ideal laboratories for studying the atmospheres of giant exoplanets on wide orbits as the governing physical and chemical processes in them are nearly identical. Understanding the formation of gas giant planets is challenging, often involving the endeavour to link atmospheric abundance ratios, such as the carbon-to-oxygen (C/O) ratio, to formation scenarios. However, the complexity of planet formation requires additional tracers, as the unambiguous interpretation of the measured C/O ratio is fraught with complexity. Isotope ratios, such as deuterium-to-hydrogen and 14N/15N, offer a promising avenue to gain further insight into this formation process, mirroring their utility within the solar system. For exoplanets only a handful of constraints on 12C/13C exist, pointing to the accretion of 13C-rich ice from beyond the disks' CO iceline. Here we report on the mid-infrared detection of the 14NH3 and 15NH3 isotopologues in the atmosphere of a cool brown dwarf with an effective temperature of 380 K in a spectrum taken with the Mid-InfraRed Instrument of the James Webb Space Telescope. As expected, our results reveal a 14N/15N value consistent with star-like formation by gravitational collapse, demonstrating that this ratio can be accurately constrained. Since young stars and their planets should be more strongly enriched in the 15N isotope, we expect that 15NH3 will be detectable in a number of cold, wide-separation exoplanets., Comment: Accepted by Nature. 28 pages, 7 figures, uses nature3.cls

We constrain cosmology and baryonic feedback scenarios with a joint analysis of weak lensing, galaxy clustering, cosmic microwave background (CMB) lensing, and their cross-correlations (so-called 6$\times$2) using data from the Dark Energy Survey (DES) Y1 and the Planck satellite mission. Noteworthy features of our 6$\times$2 pipeline are: We extend CMB lensing cross-correlation measurements to a band surrounding the DES Y1 footprint (a $\sim 25\%$ gain in pairs), and we develop analytic covariance capabilities that account for different footprints and all cross-terms in the 6$\times$2 analysis. We also measure the DES Y1 cosmic shear two-point correlation function (2PCF) down to $0.^\prime 25$, but find that going below $2.^\prime 5$ does not increase cosmological information due to shape noise. We model baryonic physics uncertainties via the amplitude of Principal Components (PCs) derived from a set of hydro-simulations. Given our statistical uncertainties, varying the first PC amplitude $Q_1$ is sufficient to model small-scale cosmic shear 2PCF. For DES Y1+Planck 6$\times$2 we find $S_8=0.799\pm0.016$, comparable to the 5$\times$2 result of DES Y3+SPT/Planck $S_8=0.773\pm0.016$. Combined with our most informative cosmology priors -- baryon acoustic oscillation (BAO), big bang nucleosynthesis (BBN), type Ia supernovae (SNe Ia), and Planck 2018 EE+lowE, we measure $S_8=0.817\pm 0.011$. Regarding baryonic physics constraints, our 6$\times$2 analysis finds $Q_1=2.8\pm1.8$. Combined with the aforementioned priors, it improves the constraint to $Q_1=3.5\pm1.3$. For comparison, the strongest feedback scenario considered in this paper, the cosmo-OWLS AGN ($\Delta T_\mathrm{heat}=10^{8.7}$ K), corresponds to $Q_1=5.84$., Comment: 24 pages, 13 figures, comments are welcome!

We introduce PACOH-RL, a novel model-based Meta-Reinforcement Learning (Meta-RL) algorithm designed to efficiently adapt control policies to changing dynamics. PACOH-RL meta-learns priors for the dynamics model, allowing swift adaptation to new dynamics with minimal interaction data. Existing Meta-RL methods require abundant meta-learning data, limiting their applicability in settings such as robotics, where data is costly to obtain. To address this, PACOH-RL incorporates regularization and epistemic uncertainty quantification in both the meta-learning and task adaptation stages. When facing new dynamics, we use these uncertainty estimates to effectively guide exploration and data collection. Overall, this enables positive transfer, even when access to data from prior tasks or dynamic settings is severely limited. Our experiment results demonstrate that PACOH-RL outperforms model-based RL and model-based Meta-RL baselines in adapting to new dynamic conditions. Finally, on a real robotic car, we showcase the potential for efficient RL policy adaptation in diverse, data-scarce conditions.

Certifiable, adaptive uncertainty estimates for unknown quantities are an essential ingredient of sequential decision-making algorithms. Standard approaches rely on problem-dependent concentration results and are limited to a specific combination of parameterization, noise family, and estimator. In this paper, we revisit the likelihood-based inference principle and propose to use likelihood ratios to construct any-time valid confidence sequences without requiring specialized treatment in each application scenario. Our method is especially suitable for problems with well-specified likelihoods, and the resulting sets always maintain the prescribed coverage in a model-agnostic manner. The size of the sets depends on a choice of estimator sequence in the likelihood ratio. We discuss how to provably choose the best sequence of estimators and shed light on connections to online convex optimization with algorithms such as Follow-the-Regularized-Leader. To counteract the initially large bias of the estimators, we propose a reweighting scheme that also opens up deployment in non-parametric settings such as RKHS function classes. We provide a non-asymptotic analysis of the likelihood ratio confidence sets size for generalized linear models, using insights from convex duality and online learning. We showcase the practical strength of our method on generalized linear bandit problems, survival analysis, and bandits with various additive noise distributions.

Many modern machine learning applications - from online principal component analysis to covariance matrix identification and dictionary learning - can be formulated as minimization problems on Riemannian manifolds, and are typically solved with a Riemannian stochastic gradient method (or some variant thereof). However, in many cases of interest, the resulting minimization problem is not geodesically convex, so the convergence of the chosen solver to a desirable solution - i.e., a local minimizer - is by no means guaranteed. In this paper, we study precisely this question, that is, whether stochastic Riemannian optimization algorithms are guaranteed to avoid saddle points with probability 1. For generality, we study a family of retraction-based methods which, in addition to having a potentially much lower per-iteration cost relative to Riemannian gradient descent, include other widely used algorithms, such as natural policy gradient methods and mirror descent in ordinary convex spaces. In this general setting, we show that, under mild assumptions for the ambient manifold and the oracle providing gradient information, the policies under study avoid strict saddle points / submanifolds with probability 1, from any initial condition. This result provides an important sanity check for the use of gradient methods on manifolds as it shows that, almost always, the limit state of a stochastic Riemannian algorithm can only be a local minimizer., Comment: 27 pages, 3 figures

The GERmanium Detector Array (GERDA) experiment operated enriched high-purity germanium detectors in a liquid argon cryostat, which contains 0.33% of $^{36}$Ar, a candidate isotope for the two-neutrino double-electron capture (2$\nu$ECEC) and therefore for the neutrinoless double-electron capture (0$\nu$ECEC). If detected, this process would give evidence of lepton number violation and the Majorana nature of neutrinos. In the radiative 0$\nu$ECEC of $^{36}$Ar, a monochromatic photon is emitted with an energy of 429.88 keV, which may be detected by the GERDA germanium detectors. We searched for the $^{36}$Ar 0$\nu$ECEC with GERDA data, with a total live time of 4.34 yr (3.08 yr accumulated during GERDA Phase II and 1.26 yr during GERDA Phase I). No signal was found and a 90% C.L. lower limit on the half-life of this process was established T$_{1/2}$ > 1.5x10$^{22}$ yr, Comment: 10 pages, 5 figures, 1 table

Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this technique to higher dimensions is to leverage the implicit low-dimensional manifold upon which the data actually lies, as postulated by the manifold hypothesis. Prior work ordinarily requires the manifold structure to be explicitly provided though, i.e. given by a mesh or be known to be one of the well-known manifolds like the sphere. In contrast, in this paper we propose a Gaussian process regression technique capable of inferring implicit structure directly from data (labeled and unlabeled) in a fully differentiable way. For the resulting model, we discuss its convergence to the Mat\'ern Gaussian process on the assumed manifold. Our technique scales up to hundreds of thousands of data points, and may improve the predictive performance and calibration of the standard Gaussian process regression in high-dimensional settings.

Reinforcement learning algorithms typically consider discrete-time dynamics, even though the underlying systems are often continuous in time. In this paper, we introduce a model-based reinforcement learning algorithm that represents continuous-time dynamics using nonlinear ordinary differential equations (ODEs). We capture epistemic uncertainty using well-calibrated probabilistic models, and use the optimistic principle for exploration. Our regret bounds surface the importance of the measurement selection strategy(MSS), since in continuous time we not only must decide how to explore, but also when to observe the underlying system. Our analysis demonstrates that the regret is sublinear when modeling ODEs with Gaussian Processes (GP) for common choices of MSS, such as equidistant sampling. Additionally, we propose an adaptive, data-dependent, practical MSS that, when combined with GP dynamics, also achieves sublinear regret with significantly fewer samples. We showcase the benefits of continuous-time modeling over its discrete-time counterpart, as well as our proposed adaptive MSS over standard baselines, on several applications.

Various applications ranging from robotics to climate science require modeling signals on non-Euclidean domains, such as the sphere. Gaussian process models on manifolds have recently been proposed for such tasks, in particular when uncertainty quantification is needed. In the manifold setting, vector-valued signals can behave very differently from scalar-valued ones, with much of the progress so far focused on modeling the latter. The former, however, are crucial for many applications, such as modeling wind speeds or force fields of unknown dynamical systems. In this paper, we propose novel Gaussian process models for vector-valued signals on manifolds that are intrinsically defined and account for the geometry of the space in consideration. We provide computational primitives needed to deploy the resulting Hodge-Mat\'ern Gaussian vector fields on the two-dimensional sphere and the hypertori. Further, we highlight two generalization directions: discrete two-dimensional meshes and "ideal" manifolds like hyperspheres, Lie groups, and homogeneous spaces. Finally, we show that our Gaussian vector fields constitute considerably more refined inductive biases than the extrinsic fields proposed before., Comment: Version accepted at AISTATS 2024

We introduce contextual stochastic bilevel optimization (CSBO) -- a stochastic bilevel optimization framework with the lower-level problem minimizing an expectation conditioned on some contextual information and the upper-level decision variable. This framework extends classical stochastic bilevel optimization when the lower-level decision maker responds optimally not only to the decision of the upper-level decision maker but also to some side information and when there are multiple or even infinite many followers. It captures important applications such as meta-learning, personalized federated learning, end-to-end learning, and Wasserstein distributionally robust optimization with side information (WDRO-SI). Due to the presence of contextual information, existing single-loop methods for classical stochastic bilevel optimization are unable to converge. To overcome this challenge, we introduce an efficient double-loop gradient method based on the Multilevel Monte-Carlo (MLMC) technique and establish its sample and computational complexities. When specialized to stochastic nonconvex optimization, our method matches existing lower bounds. For meta-learning, the complexity of our method does not depend on the number of tasks. Numerical experiments further validate our theoretical results., Comment: The paper is accepted by NeurIPS 2023

We develop a novel approach towards causal inference. Rather than structural equations over a causal graph, we learn stochastic differential equations (SDEs) whose stationary densities model a system's behavior under interventions. These stationary diffusion models do not require the formalism of causal graphs, let alone the common assumption of acyclicity. We show that in several cases, they generalize to unseen interventions on their variables, often better than classical approaches. Our inference method is based on a new theoretical result that expresses a stationarity condition on the diffusion's generator in a reproducing kernel Hilbert space. The resulting kernel deviation from stationarity (KDS) is an objective function of independent interest., Comment: AISTATS 2024

In this series of studies, we establish homogenized lattice Boltzmann methods (HLBM) for simulating fluid flow through porous media. Our contributions in part I are twofold. First, we assemble the targeted partial differential equation system by formally unifying the governing equations for nonstationary fluid flow in porous media. A matrix of regularly arranged, equally sized obstacles is placed into the domain to model fluid flow through porous structures governed by the incompressible nonstationary Navier--Stokes equations (NSE). Depending on the ratio of geometric parameters in the matrix arrangement, several homogenized equations are obtained. We review existing methods for homogenizing the nonstationary NSE for specific porosities and discuss the applicability of the resulting model equations. Consequently, the homogenized NSE are expressed as targeted partial differential equations that jointly incorporate the derived aspects. Second, we propose a kinetic model, the homogenized Bhatnagar--Gross--Krook Boltzmann equation, which approximates the homogenized nonstationary NSE. We formally prove that the zeroth and first order moments of the kinetic model provide solutions to the mass and momentum balance variables of the macrocopic model up to specific orders in the scaling parameter. Based on the present contributions, in the sequel (part II), the homogenized NSE are consistently approximated by deriving a limit consistent HLBM discretization of the homogenized Bhatnagar--Gross--Krook Boltzmann equation.

The multi planet system HR8799 is the first target observed with MIRI's coronagraphs as part of the MIRI-EC Guaranteed Time Observations exoplanets programme in Nov. 2022. We obtained deep observations in three coronagraphic filters from 10 to 15mic (F1065C, F1140C, F1550C), and one standard imaging filter at 20 mic (F2100W), with the goal to extract the photometry of the four planets, as well as to detect and investigate the distribution of circumstellar dust. Using dedicated observations of a reference star, we tested several algorithms to subtract the stellar diffraction pattern while preserving the fluxes of planets, which can be significantly affected by over-subtraction. Measuring correctly the planet's flux values requires accounting for the attenuation by the coronagraphs as a function of their position, and to estimate the normalisation with respect to the central star. We tested several procedures to derive averaged photometric values and error bars. These observations have enabled us to obtain two main results. First of all, the four planets in the system are well recovered, and their mid-IR fluxes, combined with near-IR flux values from the literature, are compared to two exoplanet atmosphere models, ATMO and Exo-REM. As a main outcome, the MIRI photometric data points imply larger radii (0.86 or 1.07 RJ for planet b) and cooler temperatures (950 or 1100 K for planet b), especially for planet b, in better agreement with evolutionary models. Second of all, these JWST/MIRI coronagraphic data also deliver the first spatially resolved detection of the inner warm debris disk, the radius of which is constrained to about 15 au, with flux densities comparable, but lower than former unresolved spectroscopic measurements with Spitzer. abridged..., Comment: submitted on Sep; 8th, 2023

Task-specific deep learning models in histopathology offer promising opportunities for improving diagnosis, clinical research, and precision medicine. However, development of such models is often limited by availability of high-quality data. Foundation models in histopathology that learn general representations across a wide range of tissue types, diagnoses, and magnifications offer the potential to reduce the data, compute, and technical expertise necessary to develop task-specific deep learning models with the required level of model performance. In this work, we describe the development and evaluation of foundation models for histopathology via self-supervised learning (SSL). We first establish a diverse set of benchmark tasks involving 17 unique tissue types and 12 unique cancer types and spanning different optimal magnifications and task types. Next, we use this benchmark to explore and evaluate histopathology-specific SSL methods followed by further evaluation on held out patch-level and weakly supervised tasks. We found that standard SSL methods thoughtfully applied to histopathology images are performant across our benchmark tasks and that domain-specific methodological improvements can further increase performance. Our findings reinforce the value of using domain-specific SSL methods in pathology, and establish a set of high quality foundation models to enable further research across diverse applications., Comment: 4 main tables, 3 main figures, additional supplemental tables and figures

We develop prismatic and syntomic cohomology relative to a $\delta$-ring. This simultaneously generalizes Bhatt and Scholze's absolute and relative prismatic cohomology and shows that the latter, which was defined relative to a prism, is in fact independent of the prism structure and only depends on the underlying $\delta$-ring. We give several possible definitions of our new version of prismatic cohomology: a site theoretic definition, one using prismatic crystals, and a stack theoretic definition. These are equivalent under mild syntomicity hypotheses. As an application, we note how the theory of prismatic cohomology of filtered rings arises naturally in this context.

The increasing statistical precision of photometric redshift surveys requires improved accuracy of theoretical predictions for large-scale structure observables to obtain unbiased cosmological constraints. In $\Lambda$CDM cosmologies, massive neutrinos stream freely at small cosmological scales, suppressing the small-scale power spectrum. In massive neutrino cosmologies, galaxy bias modeling needs to accurately relate the scale-dependent growth of the underlying matter field to observed galaxy clustering statistics. In this work, we implement a computationally efficient approximation of the neutrino-induced scale-dependent bias (NISDB). Through simulated likelihood analyses of Dark Energy Survey Year 3 (DESY3) and Legacy Survey of Space and Time Year 1 (LSSTY1) synthetic data that contain an appreciable NISDB, we examine the impact of linear galaxy bias and neutrino mass modeling choices on cosmological parameter inference. We find model misspecification of the NISDB approximation and neutrino mass models to decrease the constraining power of photometric galaxy surveys and cause parameter biases in the cosmological interpretation of future surveys. We quantify these biases and devise mitigation strategies., Comment: 23 pages, 5 figures

Protein interactions and assembly formation are fundamental to most biological processes. Predicting the assembly structure from constituent proteins -- referred to as the protein docking task -- is thus a crucial step in protein design applications. Most traditional and deep learning methods for docking have focused mainly on binary docking, following either a search-based, regression-based, or generative modeling paradigm. In this paper, we focus on the less-studied multimeric (i.e., two or more proteins) docking problem. We introduce DockGame, a novel game-theoretic framework for docking -- we view protein docking as a cooperative game between proteins, where the final assembly structure(s) constitute stable equilibria w.r.t. the underlying game potential. Since we do not have access to the true potential, we consider two approaches - i) learning a surrogate game potential guided by physics-based energy functions and computing equilibria by simultaneous gradient updates, and ii) sampling from the Gibbs distribution of the true potential by learning a diffusion generative model over the action spaces (rotations and translations) of all proteins. Empirically, on the Docking Benchmark 5.5 (DB5.5) dataset, DockGame has much faster runtimes than traditional docking methods, can generate multiple plausible assembly structures, and achieves comparable performance to existing binary docking baselines, despite solving the harder task of coordinating multiple protein chains., Comment: Under Review

The increasing global emphasis on sustainability and reducing carbon emissions is pushing governments and corporations to rethink their approach to data center design and operation. Given their high energy consumption and exponentially large computational workloads, data centers are prime candidates for optimizing power consumption, especially in areas such as cooling and IT energy usage. A significant challenge in this pursuit is the lack of a configurable and scalable thermal data center model that offers an end-to-end pipeline. Data centers consist of multiple IT components whose geometric configuration and heat dissipation make thermal modeling difficult. This paper presents PyDCM, a customizable Data Center Model implemented in Python, that allows users to create unique configurations of IT equipment with custom server specifications and geometric arrangements of IT cabinets. The use of vectorized thermal calculations makes PyDCM orders of magnitude faster (30 times) than current Energy Plus modeling implementations and scales sublinearly with the number of CPUs. Also, PyDCM enables the use of Deep Reinforcement Learning via the Gymnasium wrapper to optimize data center cooling and offers a user-friendly platform for testing various data center design prototypes., Comment: The 10th ACM International Conference on Systems for Energy-Efficient Buildings, Cities, and Transportation (BuildSys '23), November 15-16, 2023, Istanbul, Turkey

Approximated forms of the RII and RIII redistribution matrices are frequently applied to simplify the numerical solution of the radiative transfer problem for polarized radiation, taking partial frequency redistribution (PRD) effects into account. A widely used approximation for RIII is to consider its expression under the assumption of complete frequency redistribution (CRD) in the observer frame (RIII CRD). The adequacy of this approximation for modeling the intensity profiles has been firmly established. By contrast, its suitability for modeling scattering polarization signals has only been analyzed in a few studies, considering simplified settings. In this work, we aim at quantitatively assessing the impact and the range of validity of the RIII CRD approximation in the modeling of scattering polarization. Methods. We first present an analytic comparison between RIII and RIII CRD. We then compare the results of radiative transfer calculations, out of local thermodynamic equilibrium, performed with RIII and RIII CRD in realistic 1D atmospheric models. We focus on the chromospheric Ca i line at 4227 A and on the photospheric Sr i line at 4607 A.

We present relativistic magnetohydrodynamic modelling of jets running into hydrostatic, spherically symmetric cluster atmospheres. For the first time in a numerical simulation, we present model cluster atmospheres based upon the Universal Pressure Profile (UPP), incorporating a temperature profile for a typical self-similar atmosphere described by only one parameter - $M_{500}$. We explore a comprehensive range of realistic atmospheres and jet powers and derive dynamic, energetic and polarimetric data which provide insight into what we should expect of future high-resolution studies of AGN outflows. From the simulated synchrotron emission maps which include Doppler beaming we find sidedness distributions that agree well with observations. We replicated a number of findings from our previous work, such as higher power jets inflating larger aspect-ratio lobes and the cluster environment impacting the distribution of energy between the lobe and shocked regions. Comparing UPP and $\beta$-profiles we find that the cluster model chosen results in a different morphology for the resultant lobes with the UPP more able to clear lobe material from the core; and that these different atmospheres influence the ratio between the various forms of energy in the fully developed lobes. This work also highlights the key role played by Kelvin-Helmholtz (KH) instabilities in the formation of realistic lobe aspect-ratios. Our simulations point to the need for additional lobe-widening mechanisms at high jet powers, for example jet precession. Given that the UPP is our most representative general cluster atmosphere, these numerical simulations represent the most realistic models yet for spherically symmetric atmospheres., Comment: 20 pages, 18 figures, 2 tables, accepted for publication in MNRAS, minor correction to references in section 4.2

We prove versions of Goldbach conjectures for Gaussian primes in arbitrary sectors. Fix an interval $\omega \subset \mathbb{T}$. There is an integer $N_\omega $, so that every odd integer $n$ with $N(n)>N_\omega $ and $\text{dist}( \text{arg}(n) , \mathbb{T}\setminus \omega ) > (\log N(n)) ^{-B}$, is a sum of three Gaussian primes $n=p_1+p_2+p_3$, with $\text{arg}(p_j) \in \omega $, for $j=1,2,3$. A density version of the binary Goldbach conjecture in a sector is also proved., Comment: 36 pages. V2: For the 3 Prime Goldbach Conjecture, we require the odd integer to be not too close to the boundary of the sector

In many well-motivated models of the electroweak scale, cascade decays of new particles can result in highly boosted hadronic resonances (e.g. $Z/W/h$). This can make these models rich and promising targets for recently developed resonant anomaly detection methods powered by modern machine learning. We demonstrate this using the state-of-the-art CATHODE method applied to supersymmetry scenarios with gluino pair production. We show that CATHODE, despite being model-agnostic, is nevertheless competitive with dedicated cut-based searches, while simultaneously covering a much wider region of parameter space. The gluino events also populate the tails of the missing energy and $H_T$ distributions, making this a novel combination of resonant and tail-based anomaly detection., Comment: 13 pages, 15 figures

The innermost regions of most galaxies are characterised by the presence of extremely dense nuclear star clusters. Nevertheless, these clusters are not the only stellar component present in galactic nuclei, where larger stellar structures known as nuclear stellar discs, have also been found. Understanding the relation between nuclear star clusters and nuclear stellar discs is challenging due to the large distance towards other galaxies which limits their analysis to integrated light. The Milky Way's centre, at only 8 kpc, hosts a nuclear star cluster and a nuclear stellar disc, constituting a unique template to understand their relation and formation scenario. We aim to study the kinematics and stellar metallicity of stars from the Milky Way's nuclear star cluster and disc to shed light on the relation between these two Galactic centre components. We used publicly available photometric, proper motions, and spectroscopic catalogues to analyse a region of $\sim2.8'\times4.9'$ centred on the Milky Way's nuclear star cluster. We built colour magnitude diagrams, and applied colour cuts to analyse the kinematic and metallicity distributions of Milky Way's nuclear star cluster and disc stars with different extinction along the line of sight. We detect kinematics and metallicity gradients for the analysed stars along the line of sight towards the Milky Way's nuclear star cluster, suggesting a smooth transition between the nuclear stellar disc and cluster. We also find a bi-modal metallicity distribution for all the analysed colour bins, which is compatible with previous work on the bulk population of the nuclear stellar disc and cluster. Our results suggest that these two Galactic centre components might be part of the same structure with the Milky Way's nuclear stellar disc being the grown edge of the nuclear star cluster., Comment: Accepted for publication in A&A. 13 pages, 9 figures

The conditions required for massive star formation are debated, particularly whether massive stars must form in conjunction with massive clusters. Some authors have advanced the view that stars of any mass (below the total cluster mass) can form in clusters of any mass with some probability (random sampling). Others pointed out that the scatter in the determinations of the most massive star mass for a given cluster mass was consistent with the measurement error, such that the mass of the most massive star was determined by the total cluster mass (optimal sampling). Here we investigate the relation between cluster mass (M\textsubscript{ecl}) and the maximum stellar mass (M\textsubscript{max}) using a suite of SPH simulations. Varying cloud mass and turbulence random seed results in a range of cluster masses which we compare with their respective maximum star masses. We find that more massive clusters will have, on average, higher mass stars with this trend being steeper at lower cluster masses ($M\textsubscript{max} \propto M\textsubscript{ecl}^{0.31}$ for $M\textsubscript{ecl}<500M\,_{\odot}$) and flattening at higher cluster masses ($M\textsubscript{max} \propto M\textsubscript{ecl}^{0.11}$ for $M\textsubscript{ecl}>500M\,_{\odot}$). This rules out purely stochastic star formation in our simulations. Significant scatter in the maximum masses with identical initial conditions also rules out the possibility that the relation is purely deterministic (that is that a given cluster mass will result in a specific maximum stellar mass). In conclusion our simulations disagree with both random and optimal sampling of the initial mass function., Comment: Accepted in MNRAS

Anisotropic diffusion processes with a diffusion tensor are important in image analysis, physics, and engineering. However, their numerical approximation has a strong impact on dissipative artefacts and deviations from rotation invariance. In this work, we study a large family of finite difference discretisations on a 3 x 3 stencil. We derive it by splitting 2-D anisotropic diffusion into four 1-D diffusions. The resulting stencil class involves one free parameter and covers a wide range of existing discretisations. It comprises the full stencil family of Weickert et al. (2013) and shows that their two parameters contain redundancy. Furthermore, we establish a bound on the spectral norm of the matrix corresponding to the stencil. This gives time step size limits that guarantee stability of an explicit scheme in the Euclidean norm. Our directional splitting also allows a very natural translation of the explicit scheme into ResNet blocks. Employing neural network libraries enables simple and highly efficient parallel implementations on GPUs., Comment: To appear

Large Language Models (LLMs) have become ubiquitous across various domains, transforming the way we interact with information and conduct research. However, most high-performing LLMs remain confined behind proprietary walls, hindering scientific progress. Most open-source LLMs, on the other hand, are limited in their ability to support longer sequence lengths, which is a key requirement for many tasks that require inference over an input context. To address this, we have trained XGen, a series of 7B parameter models on up to 8K sequence length for up to 1.5T tokens. We have also finetuned the XGen models on public-domain instructional data, creating their instruction-tuned counterparts (XGen-Inst). We open-source our models for both research advancements and commercial applications. Our evaluation on standard benchmarks shows that XGen models achieve comparable or better results when compared with state-of-the-art open-source LLMs. Our targeted evaluation on long sequence modeling tasks shows the benefits of our 8K-sequence models over 2K-sequence open-source LLMs.

Three major challenges in reinforcement learning are the complex dynamical systems with large state spaces, the costly data acquisition processes, and the deviation of real-world dynamics from the training environment deployment. To overcome these issues, we study distributionally robust Markov decision processes with continuous state spaces under the widely used Kullback-Leibler, chi-square, and total variation uncertainty sets. We propose a model-based approach that utilizes Gaussian Processes and the maximum variance reduction algorithm to efficiently learn multi-output nominal transition dynamics, leveraging access to a generative model (i.e., simulator). We further demonstrate the statistical sample complexity of the proposed method for different uncertainty sets. These complexity bounds are independent of the number of states and extend beyond linear dynamics, ensuring the effectiveness of our approach in identifying near-optimal distributionally-robust policies. The proposed method can be further combined with other model-free distributionally robust reinforcement learning methods to obtain a near-optimal robust policy. Experimental results demonstrate the robustness of our algorithm to distributional shifts and its superior performance in terms of the number of samples needed.