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We investigate how stellar feedback from the first stars (Population III) distributes metals through the interstellar and intergalactic medium using the star-by-star cosmological hydrodynamics simulation, Aeos. We find that energy injected from the supernovae of the first stars is enough to expel a majority of gas and injected metals beyond the virial radius of halos with mass $M_* \lesssim 10^7$ M$_\odot$, regardless of the number of supernovae. This prevents self-enrichment and results in a non-monotonic increase in metallicity at early times. Most minihalos ($M \gtrsim 10^5 \, \rm M_\odot$) do not retain significant fractions of the yields produced within their virial radii until they have grown to halo masses of $M \gtrsim 10^7 \, \rm M_\odot$. The loss of metals to regions well beyond the virial radius delays the onset of enriched star formation and extends the period that Population III star formation can persist. We also explore the contributions of different nucleosynthetic channels to 10 individual elements. On the timescale of the simulation (lowest redshift $z=14.3$), enrichment is dominated by core-collapse supernovae for all elements, but with a significant contribution from asymptotic giant branch winds to the s-process elements, which are normally thought to only be important at late times. In this work, we establish important mechanisms for early chemical enrichment which allows us to apply Aeos in later epochs to trace the evolution of enrichment during the complete transition from Population III to Population II stars., Comment: 16 pages, 12 figures, 1 animated figure (see source files), submitted to ApJ

We are interested in the nonlinear damped Klein-Gordon equation \[ \partial_t^2 u+2\alpha \partial_t u-\Delta u+u-|u|^{p-1}u=0 \] on $\mathbb{R}^d$ for $2\le d\le 5$ and energy sub-critical exponents $2 < p < \frac{d+2}{d-2}$. We construct multi-solitons, that is, solutions which behave for large times as a sum of decoupled solitons, in various configurations with symmetry: this includes multi-solitons whose soliton centers lie at the vertices of an expanding regular polygon (with or without a center), of a regular polyhedron (with a center), or of a higher dimensional regular polytope. We give a precise description of these multi-solitons: in particular the interaction between nearest neighbour solitons is asymptotic to $\ln (t)$ as $t \to +\infty$. We also prove that in any multi-soliton, the solitons can not all share the same sign. Both statements generalize and precise results from \cite{F98}, \cite{Nak} and are based on the analysis developed in \cite{CMYZ,CMY}.

We present a benchmark for Planning And Reasoning Tasks in humaN-Robot collaboration (PARTNR) designed to study human-robot coordination in household activities. PARTNR tasks exhibit characteristics of everyday tasks, such as spatial, temporal, and heterogeneous agent capability constraints. We employ a semi-automated task generation pipeline using Large Language Models (LLMs), incorporating simulation in the loop for grounding and verification. PARTNR stands as the largest benchmark of its kind, comprising 100,000 natural language tasks, spanning 60 houses and 5,819 unique objects. We analyze state-of-the-art LLMs on PARTNR tasks, across the axes of planning, perception and skill execution. The analysis reveals significant limitations in SoTA models, such as poor coordination and failures in task tracking and recovery from errors. When LLMs are paired with real humans, they require 1.5x as many steps as two humans collaborating and 1.1x more steps than a single human, underscoring the potential for improvement in these models. We further show that fine-tuning smaller LLMs with planning data can achieve performance on par with models 9 times larger, while being 8.6x faster at inference. Overall, PARTNR highlights significant challenges facing collaborative embodied agents and aims to drive research in this direction., Comment: Alphabetical author order

We introduce a machine learning prediction workflow to study the impact of defects on the Raman response of 2D materials. By combining the use of machine-learned interatomic potentials, the Raman-active $\Gamma$-weighted density of states method and splitting configurations in independant patches, we are able to reach simulation sizes in the tens of thousands of atoms, with diagonalization now being the main bottleneck of the simulation. We apply the method to two systems, isotopic graphene and defective hexagonal boron nitride, and compare our predicted Raman response to experimental results, with good agreement. Our method opens up many possibilities for future studies of Raman response in solid-state physics., Comment: 9 pages, 6 figures

The topology of the tree underlying a tree-structured Markov random field (MRF) is central to the understanding of its stochastic dynamics: it is, after all, what synthesizes the rich dependence relations within the MRF. In this paper, we shed light on the influence of the tree's topology, through an extensive comparison-based analysis, on the aggregate distribution of the MRF. This is done within the framework of a recently introduced family of tree-structured MRFs with the uncommon property of having fixed Poisson marginal distributions unaffected by the dependence scheme. We establish convex orderings of sums of MRFs encrypted on trees having different topologies, leading to the devising of a new poset of trees. Hasse diagrams, cataloguing trees of dimension up to 9, and methods for the comparison of higher-dimension trees are provided to offer an exhaustive investigation of the new poset. We also briefly discuss its relation to other existing posets of trees and to invariants from spectral graph theory. Such an analysis requires, beforehand, to study the joint distribution of a MRF's component and its sum, a random vector we refer to as a synecdochic pair. To assess if a component is less or more contributing than another to the sum, we employ stochastic orders to compare synecdochic pairs within a MRF. The resulting orderings are reflected through allocation-related quantities, which thus act as centrality indices., Comment: 22 pages, 12 figures

Using density functional theory calculations with spin-orbit coupling (SOC), we report on the temperature-dependent thermodynamical properties of Pb: electrical resistivity, thermal expansion (TE), heat capacity, bulk modulus and its pressure derivative. For the former, we employed the state-of-the-art ab initio Boltzmann Transport Equation formalism, and we calculated the effect of TE. In accordance with previous work, we show that SOC improves the description of the phonon dispersion and the resistivity. We argue that this is caused by a joint mutual effect of an increase in the electronic nesting and an increase in the electron-phonon coupling. Interestingly, including TE incorporates non-linearity into the resistivity at high temperatures, whose magnitude depends on whether SOC is included or not. We suggest that mechanisms beyond the quasi-harmonic approximation should be considered to get a better description of Pb with SOC at high temperatures., Comment: 19 pages, 10 figures

Many common Markov chain Monte Carlo (MCMC) kernels can be formulated using a deterministic involutive proposal with a step size parameter. Selecting an appropriate step size is often a challenging task in practice; and for complex multiscale targets, there may not be one choice of step size that works well globally. In this work, we address this problem with a novel class of involutive MCMC methods -- AutoStep MCMC -- that selects an appropriate step size at each iteration adapted to the local geometry of the target distribution. We prove that AutoStep MCMC is $\pi$-invariant and has other desirable properties under mild assumptions on the target distribution $\pi$ and involutive proposal. Empirical results examine the effect of various step size selection design choices, and show that AutoStep MCMC is competitive with state-of-the-art methods in terms of effective sample size per unit cost on a range of challenging target distributions.

We study the sensitivity of presupernova evolution and supernova nucleosynthesis yields of massive stars to variations of the initial composition. We use the solar abundances from Lodders (2009), and compute two different initial stellar compositions: i) scaled solar abundances, and ii) the isotopic galactic chemical history model (GCH) developed by West and Heger (2013b). We run a grid of models using the KEPLER stellar evolution code, with 7 initial stellar masses, 12 initial metallicities, and two for each scaling method to explore the effects on nucleosynthesis over a metallicity range of $-4.0\leq[Z]\leq+0.3$. We find that the compositions from the GCH model better reproduce the weak \emph{s}-process peak than the scaled solar models. The model yields are then used in the OMEGA Galactic Chemical Evolution (GCE) code to assess this result further. We find that initial abundances used in computing stellar structure have more of an impact on GCE results than initial abundances used in the burn network, with the GCH model again being favored when compared to observations. Lastly, a machine learning algorithm was used to verify the free parameter values of the GCH model, which were previously found by West and Heger (2013b) using a stochastic fitting process. The updated model is provided as an accessible tool for further nucleosynthesis studies.

The AEOS project introduces a series of high-resolution cosmological simulations that model star-by-star chemical enrichment and galaxy formation in the early Universe, achieving 1 pc resolution. These simulations capture the complexities of galaxy evolution within the first ~300 Myr by modeling individual stars and their feedback processes. By incorporating chemical yields from individual stars, AEOS generates galaxies with diverse stellar chemical abundances, linking them to hierarchical galaxy formation and early nucleosynthetic events. These simulations underscore the importance of chemical abundance patterns in ancient stars as vital probes of early nucleosynthesis, star formation histories, and galaxy formation. We examine the metallicity floors of various elements resulting from Pop III enrichment, providing best-fit values for eight different metals (e.g., [O/H] = -4.0) to guide simulations without Pop III models. Additionally, we identify galaxies that begin star formation with Pop II after external enrichment and investigate the frequency of CEMP stars at varying metallicities. The AEOS simulations offer detailed insights into the relationship between star formation, feedback, and chemical enrichment. Future work will extend these simulations to later epochs to interpret the diverse stellar populations of the Milky Way and its satellites., Comment: 16 pages, 10 figures, submitted to ApJ

The Hamiltonian Monte Carlo (HMC) algorithm is often lauded for its ability to effectively sample from high-dimensional distributions. In this paper we challenge the presumed domination of HMC for the Bayesian analysis of GLMs. By utilizing the structure of the compute graph rather than the graphical model, we reduce the time per sweep of a full-scan Gibbs sampler from $O(d^2)$ to $O(d)$, where $d$ is the number of GLM parameters. Our simple changes to the implementation of the Gibbs sampler allow us to perform Bayesian inference on high-dimensional GLMs that are practically infeasible with traditional Gibbs sampler implementations. We empirically demonstrate a substantial increase in effective sample size per time when comparing our Gibbs algorithms to state-of-the-art HMC algorithms. While Gibbs is superior in terms of dimension scaling, neither Gibbs nor HMC dominate the other: we provide numerical and theoretical evidence that HMC retains an edge in certain circumstances thanks to its advantageous condition number scaling. Interestingly, for GLMs of fixed data size, we observe that increasing dimensionality can stabilize or even decrease condition number, shedding light on the empirical advantage of our efficient Gibbs sampler.

As small radiation fields play an ever-increasing role in radiation therapy, accurate dosimetry of these fields becomes critical to ensure high quality dose calculation and treatment optimization. The PRB-0002, a new plastic scintillation detector (PSD) part of the Hyperscint RP-200 dosimetric platform from Medscint, can potentially facilitate small field measurements. In this work our objective is twofold: first we perform a detailed characterization of the field output correction factors of the PRB-0002 over a wide range of field sizes; second we demonstrate how this PSD can be used to determine the field output correction factors for other small field detectors. Uncertainties were carefully considered and a detailed uncertainty budget is provided. EGSnrc Monte Carlo simulations were conducted to determine the impact of detector composition, surrounding materials, dose averaging within the sensitive volume as well as ionization quenching. From these simulations, the field output correction factors of this PSD were determined. Then, by experimental comparisons, field output correction factors for 2 solid state detectors and 3 small volume ion chambers were. With PRB-0002, the material composition was found to be balanced with the ionization quenching making the field output correction factor near unity. For fields between 0.6 $\times$ 0.6 and 30 $\times$ 30~cm$^2$, the field output correction factors of the PRB-0002 were between 1.002 and 0.999 with a total uncertainty of 0.5 %. Analysis of the uncertainty budget showed that an overall uncertainty of 0.59% can be achieved for a 1 $\times$ 1~cm$^2$ using PRB-0002. We conclude that PRB-0002 is a near-ideal detector for small field dosimetry. Furthermore, it can be used to experimentally determine the field output correction factors of other dosimeters with great accuracy.

The assembly of galaxy clusters is understood to be a hierarchical process with a continuous accretion of galaxies over time, which increases the cluster size and mass. Late-type galaxies that fall into clusters can undergo ram-pressure stripping, forming extended gas tails within which star formation can happen. The number, location, and tail orientations of such galaxies provide clues about the galaxy infall process, the assembly of the cluster over time, and the consequences of infall for galaxy evolution. Here, we utilise the $\sim$ 0.5 degree diameter circular field of the Ultraviolet Imaging Telescope to image six galaxy clusters at z < 0.06 that are known to contain jellyfish galaxies. We searched for stripping candidates in the ultraviolet images of these clusters, which revealed 54 candidates showing signs of unilateral extra-planar emission, due to ram-pressure stripping. Seven candidates had already been identified as likely stripping based on optical B-band imaging. We identified 47 new candidates through UV imaging. Spectroscopic redshift information is available for 39 of these candidate galaxies, of which 19 are associated with six clusters. The galaxies with spectroscopic redshifts that are not part of the clusters appear to be within structures at different redshifts identified as additional peaks in the redshift distribution of galaxies, indicating that they might be ram-pressure stripped or disturbed galaxies in other structures along the line of sight. We examine the orbital history of these galaxies based on their location in the position-velocity phase-space diagram and explore a possible connection to the orientation of the tail direction among cluster member candidates. The tails of confirmed cluster member galaxies are found to be oriented away from the cluster centre., Comment: Accepted for publication in A&A

In recent years, deep neural networks (DNNs) have demonstrated remarkable performance in pathology applications, potentially even outperforming expert pathologists due to their ability to learn subtle features from large datasets. One complication in preparing digital pathology datasets for DNN tasks is variation in tinctorial qualities. A common way to address this is to perform stain normalization on the images. In this study, we show that a well-trained DNN model trained on one batch of histological slides failed to generalize to another batch prepared at a different time from the same tissue blocks, even when stain normalization methods were applied. This study used sample data from a previously reported DNN that was able to identify patients with early stage non-small cell lung cancer (NSCLC) whose tumors did and did not metastasize, with high accuracy, based on training and then testing of digital images from H&E stained primary tumor tissue sections processed at the same time. In this study we obtained a new series of histologic slides from the adjacent recuts of same tissue blocks processed in the same lab but at a different time. We found that the DNN trained on the either batch of slides/images was unable to generalize and failed to predict progression in the other batch of slides/images (AUC_cross-batch = 0.52 - 0.53 compared to AUC_same-batch = 0.74 - 0.81). The failure to generalize did not improve even when the tinctorial difference correction were made through either traditional color-tuning or stain normalization with the help of a Cycle Generative Adversarial Network (CycleGAN) process. This highlights the need to develop an entirely new way to process and collect consistent microscopy images from histologic slides that can be used to both train and allow for the general application of predictive DNN algorithms.

We examine the prevalence of truncated star-forming disks in the Virgo cluster down to $M_* \simeq 10^7 ~\text{M}_{\odot}$. This work makes use of deep, high-resolution imaging in the H$\alpha$+[NII] narrow-band from the Virgo Environmental Survey Tracing Ionised Gas Emission (VESTIGE) and optical imaging from the Next Generation Virgo Survey (NGVS). To aid in understanding the effects of the cluster environment on star formation in Virgo galaxies, we take a physically-motivated approach to define the edge of the star-forming disk via a drop-off in the radial specific star formation rate profile. Comparing with the expected sizes of normal galactic disks provides a measure of how truncated star-forming disks are in the cluster. We find that truncated star-forming disks are nearly ubiquitous across all regions of the Virgo cluster, including beyond the virial radius (0.974 Mpc). The majority of truncated disks at large clustercentric radii are of galaxies likely on first infall. As the intra-cluster medium density is low in this region, it is difficult to explain this population with solely ram-pressure stripping. A plausible explanation is that these galaxies are undergoing starvation of their gas supply before ram-pressure stripping becomes the dominant quenching mechanism. A simple model of starvation shows that this mechanism can produce moderate disk truncations within 1-2 Gyr. This model is consistent with `slow-then-rapid' or `delayed-then-rapid' quenching, where the early starvation mode drives disk truncations without significant change to the integrated star formation rate, and the later ram-pressure stripping mode rapidly quenches the galaxy. The origin of starvation may be in the group structures that exist around the main Virgo cluster, which indicates the importance of understanding pre-processing of galaxies beyond the cluster virial radius., Comment: 22 pages, 12 figures, accepted in Astronomy&Astrophysics

The first achievement of highly radiating plasmas in negative triangularity is shown with an operational space featuring high core radiation at high Greenwald fraction obtained with the injection of reactor-relevant seeded gases. These negative triangularity (NT) shape diverted discharges reach high values of normalized plasma pressure (BetaN > 2) at high radiation fraction with no ELMs. We demonstrate that as long as the impurity level in the core is kept low to avoid excessive fuel dilution and impurity accumulation, integration of NT configuration with high radiation fraction not only is achievable but it can lead to confinement improvement with stabilization effects originating from collisionality, ExB shear and profiles changes due to impurity radiation cooling. The underlying physics mechanism is robust and holds for a variety of impurity species. The absence of the requirement to stay in H-mode translates in a higher core radiation fraction potentially allowed in NT shape effectively mitigating the power exhaust issue. The results presented here demonstrate a path to high performance, ELM free and highly radiative regime with rector-relevant seeding gases making this regime a potential new scenario for reactor operation.

The Fusion Synthesis Engine (FUSE) is a state-of-the-art software suite designed to revolutionize fusion power plant design. FUSE integrates first-principle models, machine learning, and reduced models into a unified framework, enabling comprehensive simulations that go beyond traditional 0D systems studies. FUSE's modular structure supports a hierarchy of model fidelities, from steady-state to time-dependent simulations, allowing for both pre-conceptual design and operational scenario development. This framework accelerates the design process by enabling self-consistent solutions across physics, engineering, and control systems, minimizing the need for iterative expert evaluations. Leveraging modern software practices and parallel computing, FUSE also provides multi-objective optimization, balancing cost, efficiency, and operational constraints. Developed in Julia, FUSE is fully open-source under the Apache 2.0 license, promoting transparency and collaboration within the fusion research community.

A new family of tree-structured Markov random fields for a vector of discrete counting random variables is introduced. According to the characteristics of the family, the marginal distributions of the Markov random fields are all Poisson with the same mean, and are untied from the strength or structure of their built-in dependence. This key feature is uncommon for Markov random fields and most convenient for applications purposes. The specific properties of this new family confer a straightforward sampling procedure and analytic expressions for the joint probability mass function and the joint probability generating function of the vector of counting random variables, thus granting computational methods that scale well to vectors of high dimension. We study the distribution of the sum of random variables constituting a Markov random field from the proposed family, analyze a random variable's individual contribution to that sum through expected allocations, and establish stochastic orderings to assess a wide understanding of their behavior., Comment: 26 pages, 8 figures

Annealed Sequential Monte Carlo (SMC) samplers are special cases of SMC samplers where the sequence of distributions can be embedded in a smooth path of distributions. Using this underlying path of distributions and a performance model based on the variance of the normalisation constant estimator, we systematically study dense schedule and large particle limits. From our theory and adaptive methods emerges a notion of global barrier capturing the inherent complexity of normalisation constant approximation under our performance model. We then turn the resulting approximations into surrogate objective functions of algorithm performance, and use them for methodology development. We obtain novel adaptive methodologies, Sequential SMC (SSMC) and Sequential AIS (SAIS) samplers, which address practical difficulties inherent in previous adaptive SMC methods. First, our SSMC algorithms are predictable: they produce a sequence of increasingly precise estimates at deterministic and known times. Second, SAIS, a special case of SSMC, enables schedule adaptation at a memory cost constant in the number of particles and require much less communication. Finally, these characteristics make SAIS highly efficient on GPUs. We develop an open-source, high-performance GPU implementation based on our methodology and demonstrate up to a hundred-fold speed improvement compared to state-of-the-art adaptive AIS methods., Comment: 65 pages, 7 figures

Second-order Raman scattering has been extensively studied in carbon-based nanomaterials, \emph{e.g.} nanotube and graphene, because it activates normally forbidden Raman modes that are sensitive to crystal disorder, such as defects, dopants, strain, etc. The sp$^2$-hybridized carbon systems are, however, the exception among most nanomaterials, where first-order Raman processes usually dominate. Here we report the identification of four second-order Raman modes, named $D_1$, $D_1'$, $D_2$ and $D_2'$, in exfoliated black phosphorus (P(black)), an elemental direct-gap semiconductor exhibiting strong mechanical and electronic anisotropies. Located in close proximity to the $A^1_g$ and $A^2_g$ modes, these new modes dominate at an excitation wavelength of 633 nm. Their evolutions as a function of sample thickness, excitation wavelength, and defect density indicate that they are defect-activated and involve high-momentum phonons in a doubly-resonant Raman process. \emph{Ab initio} simulations of a monolayer reveal that the $D'$ and $D$ modes occur through intravalley scatterings with split contributions in the armchair and zigzag directions, respectively. The high sensitivity of these $D$ modes to disorder helps explaining several discrepancies found in the literature., Comment: 18 pages, 5 figures, with supplementary file

Context. The explosive burning that drives nova eruptions results in unique nucleosynthesis that heavily over-produces certain isotopes relative to the solar abundance. However, novae are often ignored when considering the chemical evolution of our Galaxy due to their low ejecta masses. Aims. In this work, we use previously computed synthetic nova populations and the galactic chemical evolution code OMEGA+ to assess the impact that novae have on the evolution of stable elemental and isotopic abundances. Methods. We combine populations of novae computed using the binary population synthesis code binary_c with the galactic chemical evolution code OMEGA+ and detailed, white dwarf mass-dependent nova yields to model the nucleosynthetic contributions of novae to the evolution of the Milky Way. We consider three different nova yield profiles, each corresponding to a different set of nova yield calculations. Results. Despite novae from low-mass white dwarfs (WDs) dominating nova ejecta contributions, we find that novae occurring on massive WDs are still able to contribute significantly to many isotopes, particularly those with high mass numbers. We find that novae can produce up to 35% of the Galactic 13C and 15N mass by the time the model Galaxy reaches [Fe/H] = 0, and earlier in the evolution of the Galaxy (between [Fe/H] = -2 and -1) novae may have been the dominant source of 15N. Predictions for [13C/Fe], [15N/Fe], 12C/13C, and 14N/15N abundances ratios vary by up to 0.2 dex at [Fe/H] = 0 and by up to 0.7 dex in [15N/Fe] and 14N/15N between [Fe/H] = -2 and -1 (corresponding approximately to Galactic ages of 170 Myr and 1 Gyr in our model). The Galactic evolution of other stable isotopes (excluding Li) is not noticeably affected by including novae.

Large language models (LLMs) have been increasingly applied to tasks in language understanding and interactive decision-making, with their impressive performance largely attributed to the extensive domain knowledge embedded within them. However, the depth and breadth of this knowledge can vary across domains. Many existing approaches assume that LLMs possess a comprehensive understanding of their environment, often overlooking potential gaps in their grasp of actual world dynamics. To address this, we introduce Discover, Verify, and Evolve (DiVE), a framework that discovers world dynamics from a small number of demonstrations, verifies the accuracy of these dynamics, and evolves new, advanced dynamics tailored to the current situation. Through extensive evaluations, we assess the impact of each component on performance and compare the dynamics generated by DiVE to human-annotated dynamics. Our results show that LLMs guided by DiVE make more informed decisions, achieving rewards comparable to human players in the Crafter environment and surpassing methods that require prior task-specific training in the MiniHack environment.

Seamless interaction between AI agents and humans using natural language remains a key goal in AI research. This paper addresses the challenges of developing interactive agents capable of understanding and executing grounded natural language instructions through the IGLU competition at NeurIPS. Despite advancements, challenges such as a scarcity of appropriate datasets and the need for effective evaluation platforms persist. We introduce a scalable data collection tool for gathering interactive grounded language instructions within a Minecraft-like environment, resulting in a Multi-Modal dataset with around 9,000 utterances and over 1,000 clarification questions. Additionally, we present a Human-in-the-Loop interactive evaluation platform for qualitative analysis and comparison of agent performance through multi-turn communication with human annotators. We offer to the community these assets referred to as IDAT (IGLU Dataset And Toolkit) which aim to advance the development of intelligent, interactive AI agents and provide essential resources for further research.

As experts in voice modification, trans-feminine gender-affirming voice teachers have unique perspectives on voice that confound current understandings of speaker identity. To demonstrate this, we present the Versatile Voice Dataset (VVD), a collection of three speakers modifying their voices along gendered axes. The VVD illustrates that current approaches in speaker modeling, based on categorical notions of gender and a static understanding of vocal texture, fail to account for the flexibility of the vocal tract. Utilizing publicly-available speaker embeddings, we demonstrate that gender classification systems are highly sensitive to voice modification, and speaker verification systems fail to identify voices as coming from the same speaker as voice modification becomes more drastic. As one path towards moving beyond categorical and static notions of speaker identity, we propose modeling individual qualities of vocal texture such as pitch, resonance, and weight.

We present $\sim300$ stellar metallicity measurements in two faint M31 dwarf galaxies, Andromeda XVI ($M_V = -7.5$) and Andromeda XXVIII ($M_V = -8.8$) derived using metallicity-sensitive Calcium H & K narrow-band Hubble Space Telescope imaging. These are the first individual stellar metallicities in And~XVI (95 stars). Our And~XXVIII sample (191 stars) is a factor of $\sim15$ increase over literature metallicities. For And~XVI, we measure $\langle \mbox{[Fe/H]}\rangle = -2.17^{+0.05}_{-0.05}$, $\sigma_{\mbox{[Fe/H]}}=0.33^{+0.07}_{-0.07}$, and $\nabla_{\mbox{[Fe/H]}} = -0.23\pm0.15$ dex $R_e^{-1}$. We find that And XVI is more metal-rich than MW UFDs of similar luminosity, which may be a result of its unusually extended star formation history. For And XXVIII, we measure $\langle \mbox{[Fe/H]}\rangle = -1.95^{+0.04}_{-0.04}$, $\sigma_{\mbox{[Fe/H]}}=0.34^{+0.07}_{-0.07}$, and $\nabla_{\mbox{[Fe/H]}} = -0.46 \pm 0.10$~dex~$R_e^{-1}$, placing it on the dwarf galaxy mass-metallicity relation. Neither galaxy has a metallicity distribution function with an abrupt metal-rich truncation, suggesting that star formation fell off gradually. The stellar metallicity gradient measurements are among the first for faint ($L \lesssim 10^6~L_{\odot}$) galaxies outside the Milky Way halo. Both galaxies' gradients are consistent with predictions from the FIRE simulations, where an age-gradient strength relationship is the observational consequence of stellar feedback that produces dark matter cores. We include a catalog for community spectroscopic follow-up, including 19 extremely metal poor ($\mbox{[Fe/H]} < -3.0$) star candidates, which make up 7% of And~XVI's MDF and 6% of And~XXVIII's., Comment: 17 pages, 5 figures, 4 tables, ApJ submitted; comments welcome!

The simplest Weyl semimetal with broken time-reversal symmetry consists of a pair of Weyl nodes located at wave vectors $\mathbf{K}_{\tau }=\tau \mathbf{b}$ in momentum space with $\tau =\pm 1$ the node index and chirality. The electronic dispersion near each node is linear. In a magnetic field $\mathbf{B}$ along $\mathbf{b}$, this dispersion is modified into a series of positive and negative energy Landau levels $n=\pm 1,\pm 2,\ldots ,$which disperse along the direction of the magnetic field, and a chiral Landau level, $n=0$, with a linear dispersion given by $e_{\tau ,n=0}\left( k_{z}\right) =-\tau \hslash v_{F}k_{z},$ where $k_{z}$ is the component of the wave vector $\mathbf{k}$ along the magnetic field and $v_{F}$ is the Fermi velocity. In the extreme quantum limit, the Fermi level is in the chiral levels near the Dirac point. When Coulomb interaction is considered, a Weyl semimetal may be unstable towards the formation of a condensate of internodal electron-hole pairs. In this article we use the full long-range Coulomb interaction and the self-consistent Hartree-Fock approximation to generate the condensed state. We study its stability with respect to a change in the Fermi velocity, doping and strength of the Coulomb interaction and also consider Weyl nodes with higher Chern number $C=2,3$. We derive the response functions of the excitonic state in the generalized random-phase approximation (GRPA). We show that, in the mean-field gap induced by the internodal coherence, there is, in the GRPA excitonic response, a series of bound electron-hole states with a binding energy that decreases until the Hartree-Fock energy gap is reached. In addition, there is a collective mode gapped at exactly the plasmon frequency: the gapless mode present in the proper excitonic response function is pushed to the plasmon frequency by the long-range Coulomb interaction., Comment: 23 pages, 11 figures

Kashiwara showed in 1996 that the categories of microlocalized D-modules can be canonically glued to give a sheaf of categories over a complex contact manifold. Much more recently, and by rather different considerations, we constructed a canonical notion of perverse microsheaves on the same class of spaces. Here we provide a Riemann-Hilbert correspondence., Comment: 47 pages

Non radiative solutions of the energy critical non linear wave equation are global solutions $u$ that furthermore have vanishing asymptotic energy outside the lightcone at both $t \to \pm \infty$: \[ \lim_{t \to \pm \infty} \| \nabla_{t,x} u(t) \|_{L^2(|x| \ge |t|+R)} = 0, \] for some $R \gt 0$. They were shown to play an important role in the analysis of long time dynamics of solutions, in particular regarding the soliton resolution: we refer to the seminal works of Duyckaerts, Kenig and Merle, see \cite{DKM:23} and the references therein. We show that the set of non radiative solutions which are small in the energy space is a manifold whose tangent space at $0$ is given by non radiative solutions to the linear equation (described in \cite{CL24}). We also construct nonlinear solutions with an arbitrary prescribed radiation field.

Automated scientific discovery promises to accelerate progress across scientific domains. However, developing and evaluating an AI agent's capacity for end-to-end scientific reasoning is challenging as running real-world experiments is often prohibitively expensive or infeasible. In this work we introduce DISCOVERYWORLD, the first virtual environment for developing and benchmarking an agent's ability to perform complete cycles of novel scientific discovery. DISCOVERYWORLD contains a variety of different challenges, covering topics as diverse as radioisotope dating, rocket science, and proteomics, to encourage development of general discovery skills rather than task-specific solutions. DISCOVERYWORLD itself is an inexpensive, simulated, text-based environment (with optional 2D visual overlay). It includes 120 different challenge tasks, spanning eight topics each with three levels of difficulty and several parametric variations. Each task requires an agent to form hypotheses, design and run experiments, analyze results, and act on conclusions. DISCOVERYWORLD further provides three automatic metrics for evaluating performance, based on (a) task completion, (b) task-relevant actions taken, and (c) the discovered explanatory knowledge. We find that strong baseline agents, that perform well in prior published environments, struggle on most DISCOVERYWORLD tasks, suggesting that DISCOVERYWORLD captures some of the novel challenges of discovery, and thus that DISCOVERYWORLD may help accelerate near-term development and assessment of scientific discovery competency in agents. Code available at: www.github.com/allenai/discoveryworld, Comment: Accepted to NeurIPS 2024 (Benchmark Track, Spotlight)

Virtual environments play a key role in benchmarking advances in complex planning and decision-making tasks but are expensive and complicated to build by hand. Can current language models themselves serve as world simulators, correctly predicting how actions change different world states, thus bypassing the need for extensive manual coding? Our goal is to answer this question in the context of text-based simulators. Our approach is to build and use a new benchmark, called ByteSized32-State-Prediction, containing a dataset of text game state transitions and accompanying game tasks. We use this to directly quantify, for the first time, how well LLMs can serve as text-based world simulators. We test GPT-4 on this dataset and find that, despite its impressive performance, it is still an unreliable world simulator without further innovations. This work thus contributes both new insights into current LLM's capabilities and weaknesses, as well as a novel benchmark to track future progress as new models appear., Comment: ACL 2024

To a conical symplectic resolution with Hamiltonian torus action, Braden--Proudfoot--Licata--Webster associate a category O, defined using deformation quantization (DQ) modules. It has long been expected, though not stated precisely in the literature, that category O also admits a "Betti-type" realization as the Fukaya--Seidel category of a Lefschetz fibration. In this paper, we confirm that the category O associated to a toric hyperk\"ahler manifold is equivalent to the partially wrapped Fukaya category of a Liouville manifold stopped by the fiber of a J-holomorphic moment map. The proof involves relating earlier DQ-module computations to a new computation of microlocal perverse sheaves. Leveraging known results on (de Rham) hypertoric category O, we deduce several Floer-theoretic consequences, including formality of simple objects and Koszul duality for the (fully) wrapped Fukaya category; conversely, by applying results about microlocal sheaves, we produce a relative Calabi-Yau structure on category O., Comment: 41 pages, 3 figures. v2: Added applications of Koszul duality

Deep learning assisted digital pathology has the potential to impact clinical practice in significant ways. In recent studies, deep neural network (DNN) enabled analysis outperforms human pathologists. Increasing sizes and complexity of the DNN architecture generally improves performance at the cost of DNN's explainability. For pathology, this lack of DNN explainability is particularly problematic as it hinders the broader clinical interpretation of the pathology features that may provide physiological disease insights. To better assess the features that DNN uses in developing predictive algorithms to interpret digital microscopic images, we sought to understand the role of resolution and tissue scale and here describe a novel method for studying the predictive feature length-scale that underpins a DNN's predictive power. We applied the method to study a DNN's predictive capability in the case example of brain metastasis prediction from early-stage non-small-cell lung cancer biopsy slides. The study highlights the DNN attention in the brain metastasis prediction targeting both cellular scale (resolution) and tissue scale features on H&E-stained histological whole slide images. At the cellular scale, we see that DNN's predictive power is progressively increased at higher resolution (i.e., lower resolvable feature length) and is largely lost when the resolvable feature length is longer than 5 microns. In addition, DNN uses more macro-scale features (maximal feature length) associated with tissue organization/architecture and is optimized when assessing visual fields larger than 41 microns. This study for the first time demonstrates the length-scale requirements necessary for optimal DNN learning on digital whole slide images.

We present an analysis of Euclid observations of a 0.5 deg$^2$ field in the central region of the Fornax galaxy cluster that were acquired during the performance verification phase. With these data, we investigate the potential of Euclid for identifying GCs at 20 Mpc, and validate the search methods using artificial GCs and known GCs within the field from the literature. Our analysis of artificial GCs injected into the data shows that Euclid's data in $I_{\rm E}$ band is 80% complete at about $I_{\rm E} \sim 26.0$ mag ($M_{V\rm } \sim -5.0$ mag), and resolves GCs as small as $r_{\rm h} = 2.5$ pc. In the $I_{\rm E}$ band, we detect more than 95% of the known GCs from previous spectroscopic surveys and GC candidates of the ACS Fornax Cluster Survey, of which more than 80% are resolved. We identify more than 5000 new GC candidates within the field of view down to $I_{\rm E}$ mag, about 1.5 mag fainter than the typical GC luminosity function turn-over magnitude, and investigate their spatial distribution within the intracluster field. We then focus on the GC candidates around dwarf galaxies and investigate their numbers, stacked luminosity distribution and stacked radial distribution. While the overall GC properties are consistent with those in the literature, an interesting over-representation of relatively bright candidates is found within a small number of relatively GC-rich dwarf galaxies. Our work confirms the capabilities of Euclid data in detecting GCs and separating them from foreground and background contaminants at a distance of 20 Mpc, particularly for low-GC count systems such as dwarf galaxies., Comment: Paper submitted as part of the A&A special issue `Euclid on Sky', which contains Euclid key reference papers and first results from the Euclid Early Release Observations

Non-reversible parallel tempering (NRPT) is an effective algorithm for sampling from target distributions with complex geometry, such as those arising from posterior distributions of weakly identifiable and high-dimensional Bayesian models. In this work we establish the uniform (geometric) ergodicity of NRPT under a model of efficient local exploration. The uniform ergodicity log rates are inversely proportional to an easily-estimable divergence, the global communication barrier (GCB), which was recently introduced in the literature. We obtain analogous ergodicity results for classical reversible parallel tempering, providing new evidence that NRPT dominates its reversible counterpart. Our results are based on an analysis of the hitting time of a continuous-time persistent random walk, which is also of independent interest. The rates that we obtain reflect real experiments well for distributions where global exploration is not possible without parallel tempering.

Tokamak plasmas with strong negative triangularity (NT) shaping typically exhibit fundamentally different edge behavior than conventional L-mode or H-mode plasmas. Over the entire DIII-D database, plasmas with sufficiently negative triangularity are found to be inherently free of edge localized modes (ELMs), even at injected powers well above the predicted L-H power threshold. A critical triangularly ($\delta_\mathrm{crit}\simeq-0.15$), consistent with inherently ELM-free operation is identified, beyond which access to the second stability region for infinite-$n$ ballooning modes closes on DIII-D. It is also possible to close access to this region, and thereby prevent an H-mode transition, at weaker average triangularities ($\delta\lesssim\delta_\mathrm{crit}$) provided that at least one of the two x-points is still sufficiently negative. Enhanced low field side magnetic fluctuations during ELM-free operation are consistent with additional turbulence limiting the NT edge gradient. Despite the reduced upper limit on the pressure gradient imposed by ballooning stability, NT plasmas are able to support small pedestals and are typically characterized by an enhancement of edge pressure gradients beyond those found in traditional L-mode plasmas. Further, the pressure gradient inside of this small pedestal is unusually steep, allowing access to high core performance that is competitive with other ELM-free regimes previously achieved on DIII-D. Since ELM-free operation in NT is linked directly to the magnetic geometry, NT fusion pilot plants are predicted to maintain advantageous edge conditions even in burning plasma regimes, potentially eliminating reactor core-integration issues caused by ELMs.

We introduce a tensor network algorithm for the solution of $p$-spin models. We show that bond compression through rank-revealing decompositions performed during the tensor network contraction resolves logical redundancies in the system exactly and is thus lossless, yet leads to qualitative changes in runtime scaling in different regimes of the model. First, we find that bond compression emulates the so-called leaf-removal algorithm, solving the problem efficiently in the "easy" phase. Past a dynamical phase transition, we observe superpolynomial runtimes, reflecting the appearance of a core component. We then develop a graphical method to study the scaling of contraction for a minimal ensemble of core-only instances. We find subexponential scaling, improving on the exponential scaling that occurs without compression. Our results suggest that our tensor network algorithm subsumes the classical leaf removal algorithm and simplifies redundancies in the $p$-spin model through lossless compression, all without explicit knowledge of the problem's structure., Comment: 12 pages, 12 figures; Updated results; Corrected typos; Updated to the published version

Despite significant technological advancements, the process of programming robots for adaptive assembly remains labor-intensive, demanding expertise in multiple domains and often resulting in task-specific, inflexible code. This work explores the potential of Large Language Models (LLMs), like ChatGPT, to automate this process, leveraging their ability to understand natural language instructions, generalize examples to new tasks, and write code. In this paper, we suggest how these abilities can be harnessed and applied to real-world challenges in the manufacturing industry. We present a novel system that uses ChatGPT to automate the process of programming robots for adaptive assembly by decomposing complex tasks into simpler subtasks, generating robot control code, executing the code in a simulated workcell, and debugging syntax and control errors, such as collisions. We outline the architecture of this system and strategies for task decomposition and code generation. Finally, we demonstrate how our system can autonomously program robots for various assembly tasks in a real-world project.

While Large Language Models (LLMs) have demonstrated significant promise as agents in interactive tasks, their substantial computational requirements and restricted number of calls constrain their practical utility, especially in long-horizon interactive tasks such as decision-making or in scenarios involving continuous ongoing tasks. To address these constraints, we propose a method for transferring the performance of an LLM with billions of parameters to a much smaller language model (770M parameters). Our approach involves constructing a hierarchical agent comprising a planning module, which learns through Knowledge Distillation from an LLM to generate sub-goals, and an execution module, which learns to accomplish these sub-goals using elementary actions. In detail, we leverage an LLM to annotate an oracle path with a sequence of sub-goals towards completing a goal. Subsequently, we utilize this annotated data to fine-tune both the planning and execution modules. Importantly, neither module relies on real-time access to an LLM during inference, significantly reducing the overall cost associated with LLM interactions to a fixed cost. In ScienceWorld, a challenging and multi-task interactive text environment, our method surpasses standard imitation learning based solely on elementary actions by 16.7% (absolute). Our analysis highlights the efficiency of our approach compared to other LLM-based methods. Our code and annotated data for distillation can be found on GitHub.

We associate an invariant called the completed Tate cohomology to a filtered circle equivariant spectrum and a complex oriented cohomology theory. We show that when the filtered spectrum is the spectral symplectic cohomology of a Liouville manifold, this invariant depends only on the stable homotopy type of the underlying manifold. We make explicit computations for several complex oriented cohomology theories, including Eilenberg-Maclane spectra, Morava K-theories, their integral counterparts, and complex K-theory. We show that the result for Eilenberg-Maclane spectra depends only on the rational homology, and we use the computations for Morava K-theory to recover the integral homology (as an ungraded group). In a different direction, we use the completed Tate cohomology computations for the complex K-theory to recover the complex K-theory of the underlying manifold from its equivariant filtered Floer homotopy type. A key Floer theoretic input is the computation of local equivariant Floer theory near the orbit of an autonomous Hamiltonian, which may be of independent interest from the perspective of dynamics., Comment: 25 pages, 1 Figure. Minor changes. Comments are welcome

We present a Large Neighbourhood Search (LNS) based approach for solving complex long-term open-pit mine planning problems. An initial feasible solution, generated by a sliding windows heuristic, is improved through repeated solves of a restricted mixed integer program. Each iteration leaves only a subset of the variables in the planning model free to take on new values. We form these subsets through the use of a path-based neighbourhood structure, and neighbourhood formation strategies that exploit the structure of the planning model. We show that our method is able to find near-optimal solutions to problems that cannot be solved, or improved upon, by an off-the-shelf solver in a reasonable time, or with reasonable computational resources. Our method substantially reduces the solve times required for large models, allowing mine planners to explore multiple scenarios in a timely fashion. Our approach is being used by Rio Tinto for solving large life-of-mine planning problems, and has been responsible for generating millions of dollars in value insights.

The surface brightness fluctuation (SBF) method is a robust and efficient way of measuring distances to galaxies containing evolved stellar populations. Although many recent applications of the method have used space-based imaging, SBF remains a powerful technique for ground-based telescopes. Deep, wide-field imaging surveys with subarsecond seeing enable SBF measurements for numerous nearby galaxies. Using a preliminary calibration, Cantiello et al. (2018) presented SBF distances for 89 bright, mainly early-type galaxies observed in the Next Generation Virgo Cluster Survey (NGVS). Here, we present a refined calibration and SBF distances for 278 galaxies extending several magnitudes fainter than in previous work. The derived distances have uncertainties of 5-12\% depending on the properties of the individual galaxies, and our sample is more than three times larger than any previous SBF study of this region. Virgo has a famously complex structure with numerous subclusters, clouds and groups; we associate individual galaxies with the various substructures and map their three-dimensional spatial distribution. Curiously, subcluster A, centered around M87, appears to have two peaks in distance: the main peak at $\sim$16.5 Mpc and a smaller one at $\sim$19.4 Mpc. Subclusters B and C have distances of $\sim$15.8 Mpc. The W and W' groups form a filament-like structure, extending more than 15~Mpc behind the cluster with a commensurate velocity increase of $\sim$1000 \kms\ along its length. These measurements are a valuable resource for future studies of the relationship between galaxy properties and local environment within a dynamic and evolving region., Comment: 30 pages, 15 figures, Acccepted for publication on the ApJ

We study the size and structure of globular clusters (GC) systems of 118 early-type galaxies from the NGVS, MATLAS, and ACSVCS surveys. Fitting S\'ersic profiles, we investigate the relationship between effective radii of GC systems ($R_{e, \rm gc}$) and galaxy properties. GC systems are 2--4 times more extended than host galaxies across the entire stellar mass range of our sample ($10^{8.3} < M_* < 10^{11.6}~M_{\odot}$). The relationship between $R_{e, \rm gc}$ and galaxy stellar mass exhibits a characteristic "knee" at a stellar mass of $M_p \simeq 10^{10.8}$, similar to galaxy $R_e$--stellar mass relationship. We present a new characterization of the traditional blue and red GC color sub-populations, describing them with respect to host galaxy $(g'-i')$ color ($\Delta_{gi}$): GCs with similar colors to their hosts have a "red" $\Delta_{gi}$, and those significantly bluer GCs have a "blue" $\Delta_{gi}$. The GC populations with red $\Delta_{gi}$, even in dwarf galaxies, are twice as extended as the stars, suggesting that formation or survival mechanisms favor the outer regions. We find a tight correlation between $R_{e, \rm gc}$ and the total number of GCs, with intrinsic scatter $\lesssim 0.1$ dex spanning two and three orders of magnitude in size and number, respectively. This holds for both red and blue subpopulations, albeit with different slopes. Assuming that $N_{GC, Total}$ correlates with $M_{200}$, we find that the red GC systems have effective radii of roughly 1-5\% $R_{\rm 200}$, while the blue GC systems in massive galaxies can have sizes as large as $\sim$10\% $R_{\rm 200}$. Environmental dependence on $R_{e, \rm gc}$ is also found, with lower density environments exhibiting more extended GC systems at fixed mass., Comment: 28 pages, 18 Figures, 3 tables, accepted for publication in ApJ

Embodied Instruction Following (EIF) is a crucial task in embodied learning, requiring agents to interact with their environment through egocentric observations to fulfill natural language instructions. Recent advancements have seen a surge in employing large language models (LLMs) within a framework-centric approach to enhance performance in embodied learning tasks, including EIF. Despite these efforts, there exists a lack of a unified understanding regarding the impact of various components-ranging from visual perception to action execution-on task performance. To address this gap, we introduce OPEx, a comprehensive framework that delineates the core components essential for solving embodied learning tasks: Observer, Planner, and Executor. Through extensive evaluations, we provide a deep analysis of how each component influences EIF task performance. Furthermore, we innovate within this space by deploying a multi-agent dialogue strategy on a TextWorld counterpart, further enhancing task performance. Our findings reveal that LLM-centric design markedly improves EIF outcomes, identify visual perception and low-level action execution as critical bottlenecks, and demonstrate that augmenting LLMs with a multi-agent framework further elevates performance.

We consider the modified Korteweg-de Vries equation. Given a self-similar solution, and a subcritical perturbation of any size, we prove that there exists a unique solution to the equation which behaves at blow-up time as the self-similar solution plus the perturbation. To this end, we develop the first robust analysis in spaces of functions with bounded Fourier transforms. To begin, we prove the local well-posedness in subcritical spaces through an appropriate restriction norm method. As this method is not sufficient to capture the critical self-similar dynamics, we develop an infinite normal form reduction (INFR) to derive time-dependent a priori $L^\infty$ bounds in frequency variables. Both approaches rely on frequency-restricted estimates, which are specific positive multiplier estimates capable of capturing the oscillatory nature of the equation. As a consequence of our analysis, we also prove local well-posedness for small subcritical perturbations of self-similar solutions at positive time.

We present an algorithm for skill discovery from expert demonstrations. The algorithm first utilizes Large Language Models (LLMs) to propose an initial segmentation of the trajectories. Following that, a hierarchical variational inference framework incorporates the LLM-generated segmentation information to discover reusable skills by merging trajectory segments. To further control the trade-off between compression and reusability, we introduce a novel auxiliary objective based on the Minimum Description Length principle that helps guide this skill discovery process. Our results demonstrate that agents equipped with our method are able to discover skills that help accelerate learning and outperform baseline skill learning approaches on new long-horizon tasks in BabyAI, a grid world navigation environment, as well as ALFRED, a household simulation environment., Comment: ICML 2024

The Cosmological Advanced Survey Telescope for Optical and UV Research (CASTOR) is a planned flagship space telescope, covering the blue-optical and UV part of the spectrum. Here we introduce the CASTOR image simulator, a Python GalSim package-based script capable of generating mock CASTOR images from an input catalogue. We generate example images from the CASTOR Wide, Deep, and Ultra-Deep surveys using simulated light-cones from the Santa Cruz Semi-Analytic Model. We make predictions for the performance of these surveys by comparing galaxies that are extracted from each image using Source Extractor to the input catalogue. We find that the Wide, Deep, and Ultra-Deep surveys will be complete to ~27, 29 and 30 mag, respectively, in the UV, u, and g filters, with the UV-split and u-split filters reaching a shallower depth. With a large area of ~2200 deg$^2$, the Wide survey will detect hundreds of millions of galaxies out to z~4, mostly with $M_\ast \gtrsim 10^9 M_\odot$. The Ultra-Deep survey will probe to z~5, detecting a large fraction of $M_\ast \simeq 10^8 M_\odot$ galaxies. These powerful samples will enable precision measurements of the distribution of star formation in the cosmic web, connecting the growth of stellar mass to the assembly of dark matter halos over two thirds of the history of the Universe, and other core goals of CASTOR's legacy surveys. These image simulations and the tools developed to generate them will be a vital planning tool to estimate CASTOR's performance and iterate the telescope and survey designs prior to launch., Comment: Submitted to AJ

This paper is intended to appear as a chapter for the Handbook of Markov Chain Monte Carlo. The goal of this chapter is to unify various problems at the intersection of Markov chain Monte Carlo (MCMC) and machine learning$\unicode{x2014}$which includes black-box variational inference, adaptive MCMC, normalizing flow construction and transport-assisted MCMC, surrogate-likelihood MCMC, coreset construction for MCMC with big data, Markov chain gradient descent, Markovian score climbing, and more$\unicode{x2014}$within one common framework. By doing so, the theory and methods developed for each may be translated and generalized.

The Cosmological Advanced Survey Telescope for Optical and ultraviolet Research (CASTOR) is a proposed Canadian-led 1m-class space telescope that will carry out ultraviolet and blue-optical wide-field imaging, spectroscopy, and photometry. CASTOR will provide an essential bridge in the post-Hubble era, preventing a protracted UV-optical gap in space astronomy and enabling an enormous range of discovery opportunities from the solar system to the nature of the Cosmos, in conjunction with the other great wide-field observatories of the next decade (e.g., Euclid, Roman, Vera Rubin). FORECASTOR (Finding Optics Requirements and Exposure times for CASTOR) will supply a coordinated suite of mission-planning tools that will serve as the one-stop shop for proposal preparation, data reduction, and analysis for the CASTOR mission. We present the first of these tools: a pixel-based, user-friendly, extensible, multi-mission exposure time calculator (ETC) built in Python, including a modern browser-based graphical user interface that updates in real time. We then provide several illustrative examples of FORECASTOR's use that advance the design of planned legacy surveys for the CASTOR mission: a search for the most massive white dwarfs in the Magellanic Clouds; a study of the frequency of flaring activity in M stars, their distribution and impacts on habitability of exoplanets; mapping the proper motions of faint stars in the Milky Way; wide and deep galaxy surveys; and time-domain studies of active galactic nuclei., Comment: Updated references and acknowledgements to match published version. 24 pages, 16 figures, 3 tables, published in AJ