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Algorithms with (machine-learned) predictions is a powerful framework for combining traditional worst-case algorithms with modern machine learning. However, the vast majority of work in this space assumes that the prediction itself is non-probabilistic, even if it is generated by some stochastic process (such as a machine learning system). This is a poor fit for modern ML, particularly modern neural networks, which naturally generate a distribution. We initiate the study of algorithms with distributional predictions, where the prediction itself is a distribution. We focus on one of the simplest yet fundamental settings: binary search (or searching a sorted array). This setting has one of the simplest algorithms with a point prediction, but what happens if the prediction is a distribution? We show that this is a richer setting: there are simple distributions where using the classical prediction-based algorithm with any single prediction does poorly. Motivated by this, as our main result, we give an algorithm with query complexity $O(H(p) + \log \eta)$, where $H(p)$ is the entropy of the true distribution $p$ and $\eta$ is the earth mover's distance between $p$ and the predicted distribution $\hat p$. This also yields the first distributionally-robust algorithm for the classical problem of computing an optimal binary search tree given a distribution over target keys. We complement this with a lower bound showing that this query complexity is essentially optimal (up to constants), and experiments validating the practical usefulness of our algorithm.

Population balance equation (PBE) models have potential to automate many engineering processes with far-reaching implications. In the pharmaceutical sector, crystallization model-based design can contribute to shortening excessive drug development timelines. Even so, two major barriers, typical of most transport equations, not just PBEs, have limited this potential. Notably, the time taken to compute a solution to these models with representative accuracy is frequently limiting. Likewise, the model construction process is often tedious and wastes valuable time, owing to the reliance on human expertise to guess constituent models from empirical data. Hybrid models promise to overcome both barriers through tight integration of neural networks with physical PBE models. Towards eliminating experimental guesswork, hybrid models facilitate determining physical relationships from data, also known as 'discovering physics'. Here, we aim to prepare for planned Scientific Machine Learning (SciML) integration through a contemporary implementation of an existing PBE algorithm, one with computational efficiency and differentiability at the forefront. To accomplish this, we utilized JAX, a cutting-edge library for accelerated computing. We showcase the speed benefits of this modern take on PBE modelling by benchmarking our solver to others we prepared using older, more widespread software. Primarily among these software tools is the ubiquitous NumPy, where we show JAX achieves up to 300x relative acceleration in PBE simulations. Our solver is also fully differentiable, which we demonstrate is the only feasible option for integrating learnable data-driven models at scale. We show that differentiability can be 40x faster for optimizing larger models than conventional approaches, which represents the key to neural network integration for physics discovery in later work.

We propose a workflow based on physics-informed neural networks (PINNs) to model multiphase fluid flow in fractured porous media. After validating the workflow in forward and inverse modeling of a synthetic problem of flow in fractured porous media, we applied it to a real experimental dataset in which brine is injected at a constant pressure drop into a CO2 saturated naturally fractured shale core plug. The exact spatial positions of natural fractures and the dynamic in-situ distribution of fluids were imaged using a CT-scan setup. To model the targeted system, we followed a domain decomposition approach for matrix and fractures and a multi-network architecture for the separate calculation of water saturation and pressure. The flow equations in the matrix, fractures and interplay between them were solved during training. Prior to fully-coupled simulations, we proposed pre-training the model. This aided in a more efficient and successful training of the coupled system. Both for the synthetic and experimental inverse problems, we determined flow parameters within the matrix and the fractures. Multiple random initializations of network and system parameters were performed to assess the uncertainty and uniqueness of the results. The results confirmed the precision of the inverse calculated parameters in retrieving the main flow characteristics of the system. The consideration of multiscale matrix-fracture impacts is commonly overlooked in existing workflows. Accounting for them led to several orders of magnitude variations in the calculated flow properties compared to not accounting for them. To the best of our knowledge, the proposed PINNs-based workflow is the first to offer a reliable and computationally efficient solution for inverse modeling of multiphase flow in fractured porous media, achieved through history-matching noisy and multi-fidelity experimental measurements., Comment: 47 pages of paper, including 19 figures

We study an online generalization of the classic Joint Replenishment Problem (JRP) that models the trade-off between ordering costs, holding costs, and backlog costs in supply chain planning systems. A retailer places orders to a supplier for multiple items over time: each request is for some item that the retailer needs in the future, and has an arrival time and a soft deadline. If a request is served before its deadline, the retailer pays a holding cost per unit of the item until the deadline. However, if a request is served after its deadline, the retailer pays a backlog cost per unit. Each service incurs a fixed joint service cost and a fixed item-dependent cost for every item included in a service. These fixed costs are the same irrespective of the units of each item ordered. The goal is to schedule services to satisfy all the online requests while minimizing the sum of the service costs, the holding costs, and the backlog costs. Constant competitive online algorithms have been developed for two special cases: the make-to-order version when the deadlines are equal to arrival times (Buchbinder et al., 2013), and the make-to-stock version with hard deadlines with zero holding costs (Bienkowski et al., 2014). Our general model with holding and backlog costs has not been investigated earlier, and no online algorithms are known even in the make-to-stock version with hard deadlines and non-zero holding costs. We develop a new online algorithm for the general version of online JRP with both holding and backlog costs and establish that it is 30-competitive. Along the way, we develop a 3-competitive algorithm for the single-item case that we build on to get our final result. Our algorithm uses a greedy strategy and its competitiveness is shown using a dual fitting analysis.

The EXperiment for Cryogenic Large-Aperture Intensity Mapping (EXCLAIM) is a balloon-borne telescope designed to survey star formation over cosmological time scales using intensity mapping in the 420 - 540 GHz frequency range. EXCLAIM uses a fully cryogenic telescope coupled to six on-chip spectrometers featuring kinetic inductance detectors (KIDs) to achieve high sensitivity, allowing for fast integration in dark atmospheric windows. The telescope receiver is cooled to $\approx$ 1.7 K by immersion in a superfluid helium bath and enclosed in a superfluid-tight shell with a meta-material anti-reflection coated silicon window. In addition to the optics and the spectrometer package, the receiver contains the magnetic shielding, the cryogenic segment of the spectrometer readout, and the sub-Kelvin cooling system. A three-stage continuous adiabatic demagnetization refrigerator (CADR) keeps the detectors at 100 mK while a $^4$He sorption cooler provides a 900 mK thermal intercept for mechanical suspensions and coaxial cables. We present the design of the EXCLAIM receiver and report on the flight-like testing of major receiver components, including the superfluid-tight receiver window and the sub-Kelvin coolers., Comment: 13 pages, 7 figures, 1 table

Physics Informed Neural Networks (PINNs) offer several advantages when compared to traditional numerical methods for solving PDEs, such as being a mesh-free approach and being easily extendable to solving inverse problems. One promising approach for allowing PINNs to scale to multi-scale problems is to combine them with domain decomposition; for example, finite basis physics-informed neural networks (FBPINNs) replace the global PINN network with many localised networks which are summed together to approximate the solution. In this work, we significantly accelerate the training of FBPINNs by linearising their underlying optimisation problem. We achieve this by employing extreme learning machines (ELMs) as their subdomain networks and showing that this turns the FBPINN optimisation problem into one of solving a linear system or least-squares problem. We test our workflow in a preliminary fashion by using it to solve an illustrative 1D problem.

We study nonlocal bright solitons subject to external spatially nonuniform potentials. If the potential is slowly varying on the soliton scale, we derive analytical soliton solutions behaving like Newtonian particles. If the potential has the form of an attractive delta-like point defect, we identify different dynamical regimes, defined by the relative strength of the nonlocality and the point defect. In these regimes, the soliton can be trapped at the defect's location, via a nonlinear resonance with a defect mode -- which is found analytically -- reflected by or transmitted through the defect, featuring a wave behavior. Our analytical predictions are corroborated by results of direct numerical simulations., Comment: To appear in Phys. Lett. A

While Rotary Position Embeddings (RoPE) for large language models have become widely adopted, their application for other modalities has been slower. Here, we introduce Lie group Relative position Encodings (LieRE) that goes beyond RoPE in supporting n-dimensional inputs. We evaluate the performance of LieRE on 2D and 3D image classification tasks and observe that LieRE leads to marked relative improvements in performance (up to 9.7% for 2D and up to 25.5% for 3D), training efficiency (3.5x reduction), data efficiency (30%) compared to the baselines of DeiT III, RoPE-Mixed and Vision-Llama. https://github.com/Stanford-AIMI/LieRE

The field of spintronics has seen a surge of interest in altermagnetism due to novel predictions and many possible applications. MnTe is a leading altermagnetic candidate that is of significant interest across spintronics due to its layered antiferromagnetic structure, high Neel temperature (TN ~ 310 K) and semiconducting properties. We present results on molecular beam epitaxy (MBE) grown MnTe/InP(111) films. Here, it is found that the electronic and magnetic properties are driven by the natural stoichiometry of MnTe. Electronic transport and in situ angle-resolved photoemission spectroscopy show the films are natively metallic with the Fermi level in the valence band and the band structure is in good agreement with first principles calculations for altermagnetic spin-splitting. Neutron diffraction confirms that the film is antiferromagnetic with planar anisotropy and polarized neutron reflectometry indicates weak ferromagnetism, which is linked to a slight Mn-richness that is intrinsic to the MBE grown samples. When combined with the anomalous Hall effect, this work shows that the electronic response is strongly affected by the ferromagnetic moment. Altogether, this highlights potential mechanisms for controlling altermagnetic ordering for diverse spintronic applications., Comment: Accepted in Advanced Functional Materials

We investigate the gas-grain relative drift velocity distributions of charged astrophysical dust grains in MHD turbulence. We do this using a range of MHD-PIC simulations spanning different plasma-$\beta$, sonic/Alfv\'en Mach number, and with grains of varying size and charge-to-mass ratio. We find that the root-mean-square drift velocity is a strong function of the grain size, following a power law with a 1/2 slope. The r.m.s. value has only a very weak dependence on the charge-to-mass ratio. On the other hand, the shape of the distribution is a strong function of the grain charge-to-mass ratio, and in compressible turbulence, also the grain size. We then compare these results to simple analytic models based upon time-domain quasi-linear theory and solutions to the Fokker-Planck equation. These models explain qualitatively the r.m.s. drift velocity's lack of charge-to-mass ratio dependence, as well as why the shape of the distribution changes as the charge-to-mass ratio increases. Finally we scale our results to astrophysical conditions. As an example, at a length scale of one parsec in the cold neutral medium, 0.1 $\mu$m grains should be drifting at roughly 40% of the turbulent velocity dispersion. These findings may serve as a basis for a model for grain velocities in the context of grain-grain collisions, non-thermal sputtering, and accretion of metals. These findings also have implications for the transport of grains through the galaxy, suggesting that grains may have non-negligible random motions at length-scales that many modern galaxy simulations approach., Comment: 21 pages, 12 figures, submitted to MNRAS

Evaluating radiology reports is a challenging problem as factual correctness is extremely important due to the need for accurate medical communication about medical images. Existing automatic evaluation metrics either suffer from failing to consider factual correctness (e.g., BLEU and ROUGE) or are limited in their interpretability (e.g., F1CheXpert and F1RadGraph). In this paper, we introduce GREEN (Generative Radiology Report Evaluation and Error Notation), a radiology report generation metric that leverages the natural language understanding of language models to identify and explain clinically significant errors in candidate reports, both quantitatively and qualitatively. Compared to current metrics, GREEN offers: 1) a score aligned with expert preferences, 2) human interpretable explanations of clinically significant errors, enabling feedback loops with end-users, and 3) a lightweight open-source method that reaches the performance of commercial counterparts. We validate our GREEN metric by comparing it to GPT-4, as well as to error counts of 6 experts and preferences of 2 experts. Our method demonstrates not only higher correlation with expert error counts, but simultaneously higher alignment with expert preferences when compared to previous approaches."

Determining the maximum usage of random-access memory (RAM) on both the motherboard and on a graphical processing unit (GPU) over the lifetime of a computing task can be extremely useful for troubleshooting points of failure as well as optimizing memory utilization, especially within a high-performance computing (HPC) setting. While there are tools for tracking compute time and RAM, including by job management tools themselves, tracking of GPU usage, to our knowledge, does not currently have sufficient solutions. We present gpu_tracker, a Python package that tracks the computational resource usage of a task while running in the background, including the real compute time that the task takes to complete, its maximum RAM usage, and the maximum GPU RAM usage, specifically for Nvidia GPUs. We demonstrate that gpu_tracker can seamlessly track computational resource usage with minimal overhead, both within desktop and HPC execution environments.

Many modern computing workloads are composed of parallelizable jobs. A single parallelizable job can be completed more quickly if it is run on additional servers, however each job is typically limited in the number of servers it can run on (its parallelizability level). A job's parallelizability level is determined by the type of computation the job performs and how it was implemented. As a result, a single workload of parallelizable jobs generally consists of multiple $\textit{job classes}$, where jobs from different classes may have different parallelizability levels. The inherent sizes of jobs from different classes may also be vastly different. This paper considers the important, practical problem of how to schedule an arbitrary number of classes of parallelizable jobs. Here, each class of jobs has an associated job size distribution and parallelizability level. Given a limited number of servers, $k$, we ask how to allocate the $k$ servers across a stream of arriving jobs in order to minimize the $\textit{mean response time}$ -- the average time from when a job arrives to the system until it is completed. The problem of optimal scheduling in multiserver systems is known to be difficult, even when jobs are not parallelizable. To solve the harder problem of scheduling multiple classes of parallelizable jobs, we turn to asymptotic scaling regimes. We find that in lighter-load regimes (i.e., Sub-Halfin-Whitt), the optimal allocation algorithm is Least-Parallelizable-First (LPF), a policy that prioritizes jobs from the least parallelizable job classes. By contrast, we also find that in the heavier-load regimes (i.e., Super-NDS), the optimal allocation algorithm prioritizes the jobs with the Shortest Expected Remaining Processing Time (SERPT). We also develop scheduling policies that perform optimally when the scaling regime is not known to the system a priori.

Online decision-makers often obtain predictions on future variables, such as arrivals, demands, inventories, and so on. These predictions can be generated from simple forecasting algorithms for univariate time-series, all the way to state-of-the-art machine learning models that leverage multiple time-series and additional feature information. However, the prediction accuracy is unknown to decision-makers a priori, hence blindly following the predictions can be harmful. In this paper, we address this problem by developing algorithms that utilize predictions in a manner that is robust to the unknown prediction accuracy. We consider the Online Resource Allocation Problem, a generic model for online decision-making, in which a limited amount of resources may be used to satisfy a sequence of arriving requests. Prior work has characterized the best achievable performances when the arrivals are either generated stochastically (i.i.d.) or completely adversarially, and shown that algorithms exist which match these bounds under both arrival models, without ``knowing'' the underlying model. To this backdrop, we introduce predictions in the form of shadow prices on each type of resource. Prediction accuracy is naturally defined to be the distance between the predictions and the actual shadow prices. We tightly characterize, via a formal lower bound, the extent to which any algorithm can optimally leverage predictions (that is, to ``follow'' the predictions when accurate, and ``ignore'' them when inaccurate) without knowing the prediction accuracy or the underlying arrival model. Our main contribution is then an algorithm which achieves this lower bound. Finally, we empirically validate our algorithm with a large-scale experiment on real data from the retailer H&M.

This paper leverages the framework of algorithms-with-predictions to design data structures for two fundamental dynamic graph problems: incremental topological ordering and cycle detection. In these problems, the input is a directed graph on $n$ nodes, and the $m$ edges arrive one by one. The data structure must maintain a topological ordering of the vertices at all times and detect if the newly inserted edge creates a cycle. The theoretically best worst-case algorithms for these problems have high update cost (polynomial in $n$ and $m$). In practice, greedy heuristics (that recompute the solution from scratch each time) perform well but can have high update cost in the worst case. In this paper, we bridge this gap by leveraging predictions to design a learned new data structure for the problems. Our data structure guarantees consistency, robustness, and smoothness with respect to predictions -- that is, it has the best possible running time under perfect predictions, never performs worse than the best-known worst-case methods, and its running time degrades smoothly with the prediction error. Moreover, we demonstrate empirically that predictions, learned from a very small training dataset, are sufficient to provide significant speed-ups on real datasets.

Datalogo is an extension of Datalog that allows for aggregation and recursion over an arbitrary commutative semiring. Like Datalog, Datalogo programs can be evaluated via the natural iterative algorithm until a fixed point is reached. However unlike Datalog, the natural iterative evaluation of some Datalogo programs over some semirings may not converge. It is known that the commutative semirings for which the iterative evaluation of Datalogo programs is guaranteed to converge are exactly those semirings that are stable [7]. Previously, the best known upper bound on the number of iterations until convergence over $p$-stable semirings is $\sum_{i=1}^n (p+2)^i = \Theta(p^n)$ steps, where $n$ is (essentially) the output size. We establish that, in fact, the natural iterative evaluation of a Datalogoprogram over a $p$-stable semiring converges within a polynomial number of iterations. In particular our upper bound is $O( \sigma p n^2( n^2 \lg \lambda + \lg \sigma))$ where $\sigma$ is the number of elements in the semiring present in either the input databases or the Datalogo program, and $\lambda$ is the maximum number of terms in any product in the Datalogo program.

We describe a testbed to characterize the optical response of compact superconducting on-chip spectrometers in development for the Experiment for Cryogenic Large-Aperture Intensity Mapping (EXCLAIM) mission. EXCLAIM is a balloonborne far-infrared experiment to probe the CO and CII emission lines in galaxies from redshift 3.5 to the present. The spectrometer, called u-Spec, comprises a diffraction grating on a silicon chip coupled to kinetic inductance detectors (KIDs) read out via a single microwave feedline. We use a prototype spectrometer for EXCLAIM to demonstrate our ability to characterize the spectrometers spectral response using a photomixer source. We utilize an on-chip reference detector to normalize relative to spectral structure from the off-chip optics and a silicon etalon to calibrate the absolute frequency.

The classical ski-rental problem admits a textbook 2-competitive deterministic algorithm, and a simple randomized algorithm that is $\frac{e}{e-1}$-competitive in expectation. The randomized algorithm, while optimal in expectation, has a large variance in its performance: it has more than a 37% chance of competitive ratio exceeding 2, and a $\Theta(1/n)$ chance of the competitive ratio exceeding $n$! We ask what happens to the optimal solution if we insist that the tail risk, i.e., the chance of the competitive ratio exceeding a specific value, is bounded by some constant $\delta$. We find that this additional modification significantly changes the structure of the optimal solution. The probability of purchasing skis on a given day becomes non-monotone, discontinuous, and arbitrarily large (for sufficiently small tail risk $\delta$ and large purchase cost $n$)., Comment: 28 pages, 2 figures

This paper considers correlation clustering on unweighted complete graphs. We give a combinatorial algorithm that returns a single clustering solution that is simultaneously $O(1)$-approximate for all $\ell_p$-norms of the disagreement vector; in other words, a combinatorial $O(1)$-approximation of the all-norms objective for correlation clustering. This is the first proof that minimal sacrifice is needed in order to optimize different norms of the disagreement vector. In addition, our algorithm is the first combinatorial approximation algorithm for the $\ell_2$-norm objective, and more generally the first combinatorial algorithm for the $\ell_p$-norm objective when $1 < p < \infty$. It is also faster than all previous algorithms that minimize the $\ell_p$-norm of the disagreement vector, with run-time $O(n^\omega)$, where $O(n^\omega)$ is the time for matrix multiplication on $n \times n$ matrices. When the maximum positive degree in the graph is at most $\Delta$, this can be improved to a run-time of $O(n\Delta^2 \log n)$., Comment: 27 pages, 2 figures

A critical challenge in developing scalable error-corrected quantum systems is the accumulation of errors while performing operations and measurements. One promising approach is to design a system where errors can be detected and converted into erasures. Such a system utilizing erasure qubits are known to have relaxed requirements for quantum error correction. A recent proposal aims to do this using a dual-rail encoding with superconducting cavities. However, experimental characterization and demonstration of a dual-rail cavity qubit has not yet been realized. In this work, we implement such a dual-rail cavity qubit; we demonstrate a projective logical measurement with integrated erasure detection and use it to measure dual-rail qubit idling errors. We measure logical state preparation and measurement errors at the $0.01\%$-level and detect over $99\%$ of cavity decay events as erasures. We use the precision of this new measurement protocol to distinguish different types of errors in this system, finding that while decay errors occur with probability $\sim 0.2\%$ per microsecond, phase errors occur 6 times less frequently and bit flips occur at least 140 times less frequently. These findings represent the first confirmation of the expected error hierarchy necessary to concatenate dual-rail erasure qubits into a highly efficient erasure code.