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We discuss the second-order differential uniformity of vectorial Boolean functions. The closely related notion of second-order zero differential uniformity has recently been studied in connection to resistance to the boomerang attack. We prove that monomial functions with univariate form $x^d$ where $d=2^{2k}+2^k+1$ and $\gcd(k,n)=1$ have optimal second-order differential uniformity. Computational results suggest that, up to affine equivalence, these might be the only optimal cubic power functions. We begin work towards generalising such conditions to all monomial functions of algebraic degree 3. We also discuss further questions arising from computational results.

Clustering is an unsupervised learning task that aims to partition data into a set of clusters. In many applications, these clusters correspond to real-world constructs (e.g., electoral districts, playlists, TV channels) whose benefit can only be attained by groups when they reach a minimum level of representation (e.g., 50\% to elect their desired candidate). In this paper, we study the k-means and k-medians clustering problems with the additional constraint that each group (e.g., demographic group) must have a minimum level of representation in at least a given number of clusters. We formulate the problem through a mixed-integer optimization framework and present an alternating minimization algorithm, called MiniReL, that directly incorporates the fairness constraints. While incorporating the fairness criteria leads to an NP-Hard assignment problem within the algorithm, we provide computational approaches that make the algorithm practical even for large datasets. Numerical results show that the approach is able to create fairer clusters with practically no increase in the clustering cost across standard benchmark datasets., Comment: arXiv admin note: text overlap with arXiv:2302.03151

We introduce a version of Koszul duality for categories, which extends the Koszul duality of operads and right modules. We demonstrate that the derivatives which appear in Weiss calculus (with values in spectra) form a right module over the Koszul dual of the category of vector spaces and orthogonal surjections, resolving conjectures of Arone--Ching and Espic. Using categorical Fourier transforms, we then classify Weiss towers. In particular, we describe the $n$-th polynomial approximation as a pullback of the $(n-1)$-st polynomial approximation along a ``generalized norm map''.

AI Infrastructure plays a key role in the speed and cost-competitiveness of developing and deploying advanced AI models. The current demand for powerful AI infrastructure for model training is driven by the emergence of generative AI and foundational models, where on occasion thousands of GPUs must cooperate on a single training job for the model to be trained in a reasonable time. Delivering efficient and high-performing AI training requires an end-to-end solution that combines hardware, software and holistic telemetry to cater for multiple types of AI workloads. In this report, we describe IBM's hybrid cloud infrastructure that powers our generative AI model development. This infrastructure includes (1) Vela: an AI-optimized supercomputing capability directly integrated into the IBM Cloud, delivering scalable, dynamic, multi-tenant and geographically distributed infrastructure for large-scale model training and other AI workflow steps and (2) Blue Vela: a large-scale, purpose-built, on-premises hosting environment that is optimized to support our largest and most ambitious AI model training tasks. Vela provides IBM with the dual benefit of high performance for internal use along with the flexibility to adapt to an evolving commercial landscape. Blue Vela provides us with the benefits of rapid development of our largest and most ambitious models, as well as future-proofing against the evolving model landscape in the industry. Taken together, they provide IBM with the ability to rapidly innovate in the development of both AI models and commercial offerings., Comment: Corresponding Authors: Talia Gershon, Seetharami Seelam,Brian Belgodere, Milton Bonilla

There are holographic superconformal theories in all dimensions between two and six which allow arbitrary tree-level four-point functions to be fixed by basic consistency conditions. Although Mellin space is usually the most efficient setting for imposing these contraints, four-point functions in two dimensions have thus far been an exception due to their more intricate dependence on the conformal cross-ratios. In this paper, we introduce a simple fix which exploits the relation between a parity-odd conformal block in two dimensions and a parity-even conformal block in four dimensions. We then apply the resulting toolkit to a study of the paradigmatic holographic theory in two dimensions which is the D1-D5 CFT. For correlators involving Kaluza-Klein modes of the tensor multiplet, this analysis reproduces results which were previously obtained using hidden conformal symmetry. With four Kaluza-Klein modes of the graviton multiplet, it yields new results including a compact formula for the correlators of all pairwise identical operators, Comment: 30 + 19 pages, 3 figures. Fixed typos and improved explanations

ARINC 429 is a ubiquitous data bus for civil avionics, enabling reliable communication between devices from disparate manufacturers. However, ARINC 429 lacks any form of encryption or authentication, making it an inherently insecure communication protocol and rendering any connected avionics vulnerable to a range of attacks. We constructed a hardware-in-the-loop simulator with ARINC 429 buses, explored these vulnerabilities, and identified their potential to deny, degrade, or disrupt aircraft capabilities. We performed a denial-of-service attack against a multi-function display via a compromised ARINC 429 bus using commercially available tools, which succeeded in disabling important navigational aids. This proven attack on physical avionics illustrates the risk inherent in ARINC 429 and the need for the ability to detect these attacks. One potential mitigation is an intrusion detection system (IDS) trained on data collected from the electrical properties of the physical bus. Although previous research has demonstrated the feasibility of an IDS on an ARINC 429 bus, no IDS has been trained on data generated by avionics hardware. To facilitate this, we recorded voltage traces and message history generated by avionics and adversarial devices on the ARINC 429 bus. To the best of our knowledge, this is the first publicly available collection of hardware-generated ARINC 429 signal data., Comment: 7 pages, 3 figures. Intended for publication in IEEE Transactions on Aerospace and Electronic Systems

Designing synthetically accessible molecules and recommending analogs to unsynthesizable molecules are important problems for accelerating molecular discovery. We reconceptualize both problems using ideas from program synthesis. Drawing inspiration from syntax-guided synthesis approaches, we decouple the syntactic skeleton from the semantics of a synthetic tree to create a bilevel framework for reasoning about the combinatorial space of synthesis pathways. Given a molecule we aim to generate analogs for, we iteratively refine its skeletal characteristics via Markov Chain Monte Carlo simulations over the space of syntactic skeletons. Given a black-box oracle to optimize, we formulate a joint design space over syntactic templates and molecular descriptors and introduce evolutionary algorithms that optimize both syntactic and semantic dimensions synergistically. Our key insight is that once the syntactic skeleton is set, we can amortize over the search complexity of deriving the program's semantics by training policies to fully utilize the fixed horizon Markov Decision Process imposed by the syntactic template. We demonstrate performance advantages of our bilevel framework for synthesizable analog generation and synthesizable molecule design. Notably, our approach offers the user explicit control over the resources required to perform synthesis and biases the design space towards simpler solutions, making it particularly promising for autonomous synthesis platforms.

In the dynamics of atoms and molecules at metal surfaces, electron-hole pair excitations can play a crucial role. In the case of hyperthermal hydrogen atom scattering, they lead to nonadiabatic energy loss and highly inelastic scattering. Molecular dynamics with electronic friction simulations where friction is computed under an isotropic homogeneous electron gas approximation have previously shown good agreement with measured kinetic energy loss distributions, suggesting that this level of theoretical description is sufficient to describe nonadiabatic effects of atomic scattering. In this work, we show that similar agreement with room temperature experiments can also be achieved with friction derived from density functional theory linear response calculations. The apparent agreement of the homogeneous electron gas approximation with experiment arises from a fortuitous cancellation of errors where friction is overestimated close to the surface and the spin transition is neglected. Only for scattering at low temperatures can both approximations be distinguished and differences rationalised in terms of the number of bounces of the atom on the surface. We identify the signatures of nonadiabatic energy loss of different levels of theory, which future low-temperature scattering experiments will be able to measure., Comment: 30 pages, 8 figures, includes supplemental material

We present millimeter observations of the host galaxy of the most distant blazar known, VLASSJ041009.05-013919.88 (hereafter J0410-0139) at z=7, using ALMA and NOEMA observations. The ALMA data reveal a 2e42 erg/s [CII] 158um emission line at z=6.9964 with a [CII]-inferred star-formation rate of 58 Msun/yr. We estimate a dynamical mass of 4.6e9 Msun, implying a black hole mass to host a dynamical mass ratio of 0.15. The 238 GHz continuum (rest-frame IR) decreased by ~33% from the NOEMA to the ALMA observations taken ~10 months apart. The VLA 3-10 GHz radio flux densities showed a ~37% decrease in a similar time frame, suggesting a causal connection. At face value, J0410-0139 would have the lowest [CII]-to-IR luminosity ratio of a z>5.7 quasar reported to date (~1e-4). However, if only <20% of the measured IR luminosity were due to thermal emission from dust, the [CII]-to-IR luminosity ratio would be typical of (U)LIRGS, and the star formation rates derived from [CII] and IR luminosities would be consistent. These results provide further evidence that synchrotron emission significantly contributes to the observed rest-frame IR emission of J0410-0139, similar to what has been reported in some radio-loud AGN at z<1., Comment: Version after addressing referee report. See also companion paper: arXiv:2407.07236

The Laser Interferometer Space Antenna (LISA) will observe gravitational-wave signals from a wide range of sources, including massive black hole binaries. Although numerous techniques have been developed to perform Bayesian inference for LISA, they are often computationally expensive; analyses often take at least $\sim 1$ month on a single CPU, even when using accelerated techniques. Not only does this make it difficult to concurrently analyse more than one gravitational-wave signal, it also makes it challenging to rapidly produce parameter estimates for possible electromagnetic follow-up campaigns. simple-pe was recently developed to produce rapid parameter estimates for gravitational-wave signals observed with ground-based gravitational-wave detectors. In this work, we extend simple-pe to produce rapid parameter estimates for LISA sources, including the effects of higher order multipole moments. We show that simple-pe infers the source properties of massive black hole binaries in zero-noise at least $\sim 100\times$ faster than existing techniques; $\sim 12$ hours on a single CPU. We further demonstrate that simple-pe can be applied before existing Bayesian techniques to mitigate biases in multi-modal parameter estimation analyses of MBHBs., Comment: 28 pages, 8 figures

Space debris and inactive satellites pose a threat to the safety and integrity of operational spacecraft and motivate the need for space situational awareness techniques. These uncooperative targets create a challenging tracking and detection problem due to a lack of prior knowledge of their features, trajectories, or even existence. Recent advancements in computer vision models can be used to improve upon existing methods for tracking such uncooperative targets to make them more robust and reliable to the wide-ranging nature of the target. This paper introduces an autonomous detection model designed to identify and monitor these objects using learning and computer vision. The autonomous detection method aims to identify and accurately track the uncooperative targets in varied circumstances, including different camera spectral sensitivities, lighting, and backgrounds. Our method adapts to the relative distance between the observing spacecraft and the target, and different detection strategies are adjusted based on distance. At larger distances, we utilize You Only Look Once (YOLOv8), a multitask Convolutional Neural Network (CNN), for zero-shot and domain-specific single-shot real time detection of the target. At shorter distances, we use knowledge distillation to combine visual foundation models with a lightweight fast segmentation CNN (Fast-SCNN) to segment the spacecraft components with low storage requirements and fast inference times, and to enable weight updates from earth and possible onboard training. Lastly, we test our method on a custom dataset simulating the unique conditions encountered in space, as well as a publicly-available dataset., Comment: Small Satellite 2024 Conference, 13 pages, 8 figures, 6 tables

Anonymity is an important principle online. However, malicious actors have long used misleading identities to conduct fraud, spread disinformation, and carry out other deceptive schemes. With the advent of increasingly capable AI, bad actors can amplify the potential scale and effectiveness of their operations, intensifying the challenge of balancing anonymity and trustworthiness online. In this paper, we analyze the value of a new tool to address this challenge: "personhood credentials" (PHCs), digital credentials that empower users to demonstrate that they are real people -- not AIs -- to online services, without disclosing any personal information. Such credentials can be issued by a range of trusted institutions -- governments or otherwise. A PHC system, according to our definition, could be local or global, and does not need to be biometrics-based. Two trends in AI contribute to the urgency of the challenge: AI's increasing indistinguishability from people online (i.e., lifelike content and avatars, agentic activity), and AI's increasing scalability (i.e., cost-effectiveness, accessibility). Drawing on a long history of research into anonymous credentials and "proof-of-personhood" systems, personhood credentials give people a way to signal their trustworthiness on online platforms, and offer service providers new tools for reducing misuse by bad actors. In contrast, existing countermeasures to automated deception -- such as CAPTCHAs -- are inadequate against sophisticated AI, while stringent identity verification solutions are insufficiently private for many use-cases. After surveying the benefits of personhood credentials, we also examine deployment risks and design challenges. We conclude with actionable next steps for policymakers, technologists, and standards bodies to consider in consultation with the public., Comment: 63 pages, 7 figures, 5 tables; minor additions to acknowledgments and wording changes for clarity; corrected typo

A cryptographic compiler introduced by Kalai et al. (STOC'23) converts any nonlocal game into an interactive protocol with a single computationally bounded prover. Although the compiler is known to be sound in the case of classical provers and complete in the quantum case, quantum soundness has so far only been established for special classes of games. In this work, we establish a quantum soundness result for all compiled two-player nonlocal games. In particular, we prove that the quantum commuting operator value of the underlying nonlocal game is an upper bound on the quantum value of the compiled game. Our result employs techniques from operator algebras in a computational and cryptographic setting to establish information-theoretic objects in the asymptotic limit of the security parameter. It further relies on a sequential characterization of quantum commuting operator correlations which may be of independent interest., Comment: v2: 30 pages, 1 figure, added an asymptotic self-testing result and citations to related works

We study the problem of cross-embodiment inverse reinforcement learning, where we wish to learn a reward function from video demonstrations in one or more embodiments and then transfer the learned reward to a different embodiment (e.g., different action space, dynamics, size, shape, etc.). Learning reward functions that transfer across embodiments is important in settings such as teaching a robot a policy via human video demonstrations or teaching a robot to imitate a policy from another robot with a different embodiment. However, prior work has only focused on cases where near-optimal demonstrations are available, which is often difficult to ensure. By contrast, we study the setting of cross-embodiment reward learning from mixed-quality demonstrations. We demonstrate that prior work struggles to learn generalizable reward representations when learning from mixed-quality data. We then analyze several techniques that leverage human feedback for representation learning and alignment to enable effective cross-embodiment learning. Our results give insight into how different representation learning techniques lead to qualitatively different reward shaping behaviors and the importance of human feedback when learning from mixed-quality, mixed-embodiment data., Comment: First Two Authors Share Equal Contribution. 19 Pages, 4 Figures

Classical T Tauri Stars (CTTSs) are highly variable stars that possess gas- and dust-rich disks from which planets form. Much of their variability is driven by mass accretion from the surrounding disk, a process that is still not entirely understood. A multi-epoch optical spectral monitoring campaign of four CTTSs (TW Hya, RU Lup, BP Tau, and GM Aur) was conducted along with contemporaneous HST UV spectra and ground-based photometry in an effort to determine accretion characteristics and gauge variability in this sample. Using an accretion flow model, we find that the magnetospheric truncation radius varies between 2.5-5 R* across all of our observations. There is also significant variability in all emission lines studied, particularly Halpha, Hbeta, and Hgamma. Using previously established relationships between line luminosity and accretion, we find that, on average, most lines reproduce accretion rates consistent with accretion shock modeling of HST spectra to within 0.5 dex. Looking at individual contemporaneous observations, however, these relationships are less accurate, suggesting that variability trends differ from the trends of the population and that these empirical relationships should be used with caution in studies of variability., Comment: 39 pages, 10 figures, 12 tables

The ability of Large Language Models (LLMs) to generate structured outputs, such as JSON, is crucial for their use in Compound AI Systems. However, evaluating and improving this capability remains challenging. In this work, we introduce StructuredRAG, a benchmark of six tasks designed to assess LLMs' proficiency in following response format instructions. We evaluate two state-of-the-art LLMs, Gemini 1.5 Pro and Llama 3 8B-instruct with 4-bit quantization using two distinct prompting strategies. We introduce these prompting strategies as f-String and Follow the Format (FF) prompting. Across 24 experiments, we find an average success rate of 82.55%. We further find a high variance in performance across tasks, models, and prompting strategies with success rates ranging from 0 to 100%. We find that Llama 3 8B-instruct often performs competitively with Gemini 1.5 Pro. We observe that task complexity significantly influences performance, with tasks involving lists or composite object outputs proving more challenging. Our findings highlight the need for further research into improving the reliability and consistency of structured output generation in LLMs. We have open-sourced our experimental code and results at github.com/weaviate/structured-rag., Comment: Preprint. 10 pages, 6 figures

The search for earth-like exoplanets with the Doppler radial velocity technique is an extremely challenging and multifaceted precision spectroscopy problem. Currently, one of the limiting instrumental factors in reaching the required long-term $10^{-10}$ level of radial velocity precision is the defect-driven sub-pixel quantum efficiency variations in the large-format detector arrays used by precision echelle spectrographs. Tunable frequency comb calibration sources that can fully map the point spread function across a spectrograph's entire bandwidth are necessary for quantifying and correcting these detector artifacts. In this work, we demonstrate a combination of laser frequency and mode spacing control that allows full and deterministic tunability of a 30 GHz electro-optic comb together with its filter cavity. After supercontinuum generation, this gives access to any optical frequency across 700 - 1300 nm. Our specific implementation is intended for the comb deployed at the Habitable Zone Planet Finder spectrograph and its near-infrared Hawaii-2RG array, but the techniques apply to all laser frequency combs used for precision astronomical spectrograph calibration and other applications that require broadband tuning., Comment: 6 pages, 5 figures

Climate change not only threatens agricultural producers but also strains financial institutions. These important food system actors include government entities tasked with both insuring grower livelihoods and supporting response to continued global warming. We use an artificial neural network to predict future maize yields in the U.S. Corn Belt, finding alarming changes to institutional risk exposure within the Federal Crop Insurance Program. Specifically, our machine learning method anticipates more frequent and more severe yield losses that would result in the annual probability of Yield Protection (YP) claims to more than double at mid-century relative to simulations without continued climate change. Furthermore, our dual finding of relatively unchanged average yields paired with decreasing yield stability reveals targeted opportunities to adjust coverage formulas to include variability. This important structural shift may help regulators support grower adaptation to continued climate change by recognizing the value of risk-reducing strategies such as regenerative agriculture. Altogether, paired with open source interactive tools for deeper investigation, our risk profile simulations fill an actionable gap in current understanding, bridging granular historic yield estimation and climate-informed prediction of future insurer-relevant loss., Comment: 24 pages, 6 figures

The Type D asymmetric simple exclusion process (ASEP) is a particle system involving two classes of particles that can be viewed from both a probabilistic and an algebraic perspective (arXiv:2011.13473). From a probabilistic perspective, we perform stochastic fusion on the Type D ASEP and analyze the outcome on generator matrices, limits of drift speed, stationary distributions, and Markov self-duality. From an algebraic perspective, we construct a fused Type D ASEP system from a Casimir element of $U_q(so_6)$, using crystal bases to analyze and manipulate various representations of $U_q(so_6)$. We conclude that both approaches produce different processes and therefore the previous method of arXiv:1908.02359, which analyzed the usual ASEP, does not generalize to all finite-dimensional simple Lie algebras., Comment: 79 pages, 7 figures. This research was conducted during a mathematics REU at Texas A&M University: an accessible version will be available at https://www.math.tamu.edu/reu/

We perform a thorough analysis of the projected shapes of nearby galaxies in both observations and cosmological simulations. We implement a forward-modeling approach to overcome the limitations in previous studies, which hinder accurate comparisons between observations and simulations. We measure axis ratios of $z=0$ (snapshot 99) TNG50 galaxies from their synthetic Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) images and compare them with those obtained from real HSC-SSP images of a matched galaxy sample. Remarkably, the comparison shows excellent agreement between the observations and the TNG50 simulation, challenging previous claims that $\Lambda$CDM models underproduced the abundance of thin galaxies. Specifically, for galaxies with stellar masses $10\leq \log (M_{\star}/M_{\odot}) \leq 11.5$, we find $\lesssim 0.1\sigma$ tensions between the observations and the simulation, a stark contrast to the previously reported $\gtrsim 10\sigma$ tensions. We reveal that low-mass galaxies ($M_{\star}\lesssim 10^{9.5}\,M_{\odot}$) in TNG50 are thicker than their observed counterparts in HSC-SSP and attribute this to the spurious dynamical heating effects that artificially puff up galaxies. We also find that, despite the overall broad agreement, TNG50 galaxies are more concentrated than the HSC-SSP ones at the low- and high-mass end of the stellar mass range of $9.0\leq \log (M_{\star}/M_{\odot}) \leq 11.2$ and are less concentrated at intermediate stellar masses. But we argue that the higher concentrations of the low-mass TNG50 galaxies are not likely the cause of their thicker/rounder appearances. Our study underscores the critical importance of conducting mock observations of simulations and applying consistent measurement methodologies to facilitate proper comparison with observations., Comment: 14 pages, 7 figures, published in ApJ

In this work, the novel, open-source humanoid robot, PANDORA, is presented where a majority of the structural elements are manufactured using 3D-printed compliant materials. As opposed to contemporary approaches that incorporate the elastic element into the actuator mechanisms, PANDORA is designed to be compliant under load, or in other words, structurally elastic. This design approach lowers manufacturing cost and time, design complexity, and assembly time while introducing controls challenges in state estimation, joint and whole-body control. This work features an in-depth description on the mechanical and electrical subsystems including details regarding additive manufacturing benefits and drawbacks, usage and placement of sensors, and networking between devices. In addition, the design of structural elastic components and their effects on overall performance from an estimation and control perspective are discussed. Finally, results are presented which demonstrate the robot completing a robust balancing objective in the presence of disturbances and stepping behaviors., Comment: This work has been submitted to the IEEE for possible publication

Merging and interactions can radically transform galaxies. However, identifying these events based solely on structure is challenging as the status of observed mergers is not easily accessible. Fortunately, cosmological simulations are now able to produce more realistic galaxy morphologies, allowing us to directly trace galaxy transformation throughout the merger sequence. To advance the potential of observational analysis closer to what is possible in simulations, we introduce a supervised deep learning Convolutional Neural Network (CNN) and Vision Transformer (ViT) hybrid framework, Mummi (MUlti Model Merger Identifier). Mummi is trained on realism-added synthetic data from IllustrisTNG100-1, and is comprised of a multi-step ensemble of models to identify mergers and non-mergers, and to subsequently classify the mergers as interacting pairs or post-mergers. To train this ensemble of models, we generate a large imaging dataset of 6.4 million images targeting UNIONS with RealSimCFIS. We show that Mummi offers a significant improvement over many previous machine learning classifiers, achieving 95% pure classifications even at Gyr long timescales when using a jury-based decision making process, mitigating class imbalance issues that arise when identifying real galaxy mergers from $z=0$ to $0.3$. Additionally, we can divide the identified mergers into pairs and post-mergers at 96% success rate. We drastically decrease the false positive rate in galaxy merger samples by 75%. By applying Mummi to the UNIONS DR5-SDSS DR7 overlap, we report a catalog of 13,448 high confidence galaxy merger candidates. Finally, we demonstrate that Mummi produces powerful representations solely using supervised learning, which can be used to bridge galaxy morphologies in simulations and observations., Comment: 23 pages, 16 figures. Accepted for publication in MNRAS

The conditional displacement (CD) gate between an oscillator and a discrete-variable ancilla plays a key role in quantum information processing tasks, such as enabling universal control of the oscillator and longitudinal readout of the qubit. However, the gate is unprotected against the propagation of ancilla decay errors and hence not fault-tolerant. Here, we propose a CD gate scheme with fluxonium as the ancilla, which has been experimentally demonstrated to have a large noise bias and millisecond-level lifetimes. The proposed gate is applied cross-resonantly by modulating the external flux of the fluxonium at the frequency of the target oscillator, which requires minimal hardware overhead and does not increase sensitivity to decoherence mechanisms like dephasing. We further provide a perturbative description of the gate mechanism and identify the error budget. Additionally, we develop an approximate procedure for choosing device and gate parameters that optimizes gate performance. Following the procedure for multiple sets of fluxonium parameters from the literature, we numerically demonstrate CD gates with unitary fidelity exceeding 99.9% and gate times of hundreds of nanoseconds.

Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of machine learning, the use of data-driven population-level distributions (encoded, e.g., in a trained deep neural network) as priors is emerging as an appealing alternative to simple parametric priors in a variety of inverse problems. However, in many astrophysical applications, it is often difficult or even impossible to acquire independent and identically distributed samples from the underlying data-generating process of interest to train these models. In these cases, corrupted data or a surrogate, e.g. a simulator, is often used to produce training samples, meaning that there is a risk of obtaining misspecified priors. This, in turn, can bias the inferred posteriors in ways that are difficult to quantify, which limits the potential applicability of these models in real-world scenarios. In this work, we propose addressing this issue by iteratively updating the population-level distributions by retraining the model with posterior samples from different sets of observations and showcase the potential of this method on the problem of background image reconstruction in strong gravitational lensing when score-based models are used as data-driven priors. We show that starting from a misspecified prior distribution, the updated distribution becomes progressively closer to the underlying population-level distribution, and the resulting posterior samples exhibit reduced bias after several updates., Comment: 17 pages, 15 figures, Submitted to The Astrophysical Journal

The nonlinear curvature wavefront sensor (nlCWFS) uses multiple (typically four) out-of-focus images to reconstruct the phase and amplitude of a propagating light beam. Because these images are located between the pupil and focal planes, they contain tip/tilt information. Rather than using a separate sensor to measure image locations, it would be beneficial to extract tip/tilt information directly and routinely as part of the reconstruction process. In the presence of atmospheric turbulence, recovering precise centroid offsets for each out-of-focus image becomes a dynamic process as image structure is altered by changing aberrations. We examine several tip/tilt extraction methods and compare their precision and accuracy using numerical simulations. We find that the nlCWFS outer measurement planes confer more accurate and reliable tip/tilt information than the inner measurement planes, due to their larger geometric lever arm. However, in practice, finite field of view (detector region of interest) effects bias tip/tilt retrieval when using the outer planes due to diffraction. Using knowledge of the $z$-distance to each plane, we find that applying a best-fit linear model to multiple image centroid locations can offer fast and accurate tip/tilt mode retrieval. For the most demanding applications, a non-linear tip/tilt extraction method that self-consistently uses the speckle field may need to be developed.

In this expository article we revisit the Bernstein problem for several geometric PDEs including the minimal surface, Monge-Amp\`{e}re, and special Lagrangian equations. We also discuss the minimal surface system where appropriate. The article is based on a lecture series given by the author for the inaugural European Doctorate School of Differential Geometry, held in Granada in June 2024., Comment: typos corrected

Many social and environmental phenomena are associated with macroscopic changes in the built environment, captured by satellite imagery on a global scale and with daily temporal resolution. While widely used for prediction, these images and especially image sequences remain underutilized for causal inference, especially in the context of randomized controlled trials (RCTs), where causal identification is established by design. In this paper, we develop and compare a set of general tools for analyzing Conditional Average Treatment Effects (CATEs) from temporal satellite data that can be applied to any RCT where geographical identifiers are available. Through a simulation study, we analyze different modeling strategies for estimating CATE in sequences of satellite images. We find that image sequence representation models with more parameters generally yield a greater ability to detect heterogeneity. To explore the role of model and data choice in practice, we apply the approaches to two influential RCTs -- Banerjee et al. (2015), a poverty study in Cusco, Peru, and Bolsen et al. (2014), a water conservation experiment in Georgia, USA. We benchmark our image sequence models against image-only, tabular-only, and combined image-tabular data sources, summarizing practical implications for investigators in a multivariate analysis. Land cover classifications over satellite images facilitate interpretation of what image features drive heterogeneity. We also show robustness to data and model choice of satellite-based generalization of the RCT results to larger geographical areas outside the original. Overall, this paper shows how satellite sequence data can be incorporated into the analysis of RCTs, and provides evidence about the implications of data, model, and evaluation metric choice for causal analysis.

The field of Neural-Symbolic (NeSy) systems is growing rapidly. Proposed approaches show great promise in achieving symbiotic unions of neural and symbolic methods. However, each NeSy system differs in fundamental ways. There is a pressing need for a unifying theory to illuminate the commonalities and differences in approaches and enable further progress. In this paper, we introduce Neural-Symbolic Energy-Based Models (NeSy-EBMs), a unifying mathematical framework for discriminative and generative modeling with probabilistic and non-probabilistic NeSy approaches. We utilize NeSy-EBMs to develop a taxonomy of modeling paradigms focusing on a system's neural-symbolic interface and reasoning capabilities. Additionally, we introduce a suite of learning techniques for NeSy-EBMs. Importantly, NeSy-EBMs allow the derivation of general expressions for gradients of prominent learning losses, and we provide four learning approaches that leverage methods from multiple domains, including bilevel and stochastic policy optimization. Finally, we present Neural Probabilistic Soft Logic (NeuPSL), an open-source NeSy-EBM library designed for scalability and expressivity, facilitating real-world application of NeSy systems. Through extensive empirical analysis across multiple datasets, we demonstrate the practical advantages of NeSy-EBMs in various tasks, including image classification, graph node labeling, autonomous vehicle situation awareness, and question answering.

We present an enhanced version of the publicly-available Stripe 82X catalog (S82-XL), featuring a comprehensive set of 22,737 unique X-ray point sources identified with a significance $\gtrsim 4\sigma$. This catalog is four times larger than the original Stripe 82X catalog, by including additional archival data from the Chandra and XMM-Newton telescopes. Now covering $\sim54.8$ deg$^2$ of non-overlapping sky area, the S82-XL catalog roughly doubles the area and depth of the original catalog, with limiting fluxes (half-area fluxes) of 3.4$\times 10^{-16}$ (2.4$\times 10^{-15}$), 2.9$\times 10^{-15}$ (1.5$\times 10^{-14}$), and 1.4$\times 10^{-15}$ (9.5$\times 10^{-15}$) erg s$^{-1}$ cm$^{-2}$ across the soft (0.5-2 keV), hard (2-10 keV), and full (0.5-10 keV) bands, respectively. S82-XL occupies a unique region of flux-area parameter space compared to other X-ray surveys, identifying sources with rest-frame luminosities from $1.2\times 10^{38}$ to $1.6\times 10^{47}$ erg s$^{-1}$ in the 2-10 keV band (median X-ray luminosity, $7.2\times 10^{43}$ erg s$^{-1}$), and spectroscopic redshifts up to $z\sim6$. By using hardness ratios, we derived Active Galactic Nuclei (AGNs) obscuration obtaining a median value of $N_H=21.6_{-1.6}^{+1.0}$, and an overall, obscured fraction ($\log N_H/\mathrm{cm^{-2}}>22$) of $\sim 36.9\%$. S82-XL serves as a benchmark in X-ray surveys and, with its extensive multiwavelength data, is especially valuable for comprehensive studies of luminous AGNs., Comment: Accepted for publication in ApJ

We present a study of the molecular gas in five closely-spaced ($R_{\perp}<20$ kpc) dual quasars ($L_{\rm bol}\gtrsim10^{44}~\mathrm{erg~s}^{-1}$) at redshifts $0.4