Numerical Analysis
Residual Minimisation for Transport-Based Optimal Control
Tristan Pryer and Nikolaos Rekatsinas
We consider an optimal control problem governed by a stationary linear transport equation in two or three spatial dimensions, motivated by
photon transport in radiotherapy treatment planning. The control is an inflow boundary source, and the observation operator may track either the angular flux or its angular integral, the latter serving as a simplified dose surrogate. The associated optimality system consists of a transport–adjoint pair with angular dependence, coupled through a boundary optimality condition. We formulate a residual least-squares functional whose minimisers coincide with solutions of the Karush–Kuhn–Tucker system and show that the functional controls the $L^2$ errors in the state and adjoint and the flux-weighted $L^2$ error in the control. This yields a continuum-level a posteriori estimate without recourse to discretisation. An additional unweighted optimality residual certifies the control in the norm of the objective. The estimate holds for every admissible approximation and accounts for the different boundary measures in the control penalty and transport traces, without a positive lower bound on $|\omega\cdot n|$. We then parameterise the state, adjoint and control using neural networks and minimise over a neural network space using appropriate quadrature. The Monte Carlo formulation replaces each residual integral by a weighted sample mean, whose quadrature error enters the a posteriori estimate. We prove convergence under explicit assumptions on approximation, quadrature and optimisation and derive bounds on the total error in terms of approximation, quadrature and optimisation error. Numerical examples in two and three dimensions illustrate the residual–error relation and the flexibility of the residual framework for field- and dose-tracking control problems, including regular manufactured solutions.
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Distributed Computing
Real-time Optimization of Simulation and Data Processing Pipelines for Experiments on Exascale Computing Platforms
Thomas Wester, Harikrishna Tummalapalli and Christine M. Simpson
Current and next-generation large-scale experiments, especially in high-energy physics and cosmology, involve increasing volumes of data that require exascale computing power to analyze and model. Exascale machines present challenges for workflow scaling and efficient resource usage. We propose a multi-stage task scheduling approach for optimizing resource usage for these workflows. We demonstrate task scheduling for an example Monte Carlo simulation pipeline from the Short-Baseline Near Detector (SBND), and present theoretical and numerical tools for modeling task scheduling in these workflows that can be used to identify optimal scheduling strategies and choose resources for a given problem size.
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Machine Learning
LiteEMG-FM: An Efficient and Deployable Foundation Model for Robust EMG Sensing
Tianhao Wu, Xu Wu, Amirmohammad Radmehr et al. (+4 more)
Electromyography (EMG) signals vary substantially across individuals, body regions, recording sessions, and sensing hardware, limiting the generalization of models for assistive devices and human-computer interaction. Existing time-series foundation models are also computationally expensive for real-time wearable deployment and often fail to capture EMG-specific time-frequency characteristics. We present LiteEMG-FM, an efficient hybrid CNN-
Transformer foundation model for practical EMG sensing. Pretrained on 16 diverse upper- and lower-limb EMG
datasets, LiteEMG-FM learns representations that generalize across users and
datasets. For resource-constrained deployment, we implement a hierarchical wake-up architecture in which a lightweight, always-on 1D-CNN filters rest and non-target activity and activates LiteEMG-FM only for valid gestures. We evaluate full inference offloading, split inference, and full on-device processing, characterizing their trade-offs in latency, power consumption, and
memory footprint. Across diverse evaluation settings, LiteEMG-FM outperforms state-of-the-art time-series foundation models and supervised baselines, particularly under zero-calibration cross-participant and data-scarce conditions. These results demonstrate that LiteEMG-FM is an effective, efficient, and deployable foundation model for EMG applications.
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All authors Tianhao Wu, Xu Wu, Amirmohammad Radmehr, Jiawei Yu, Yi Wu, Phuc Nguyen, Jian Liu
Artificial Intelligence
"I just assumed that it would translate": examining MT risk awareness among healthcare staff with abbreviations as a use case
Eleanor Taylor-Stilgoe, Félix do Carmo and Constantin Orăsan
In the UK, public healthcare staff report turning to machine translation (MT) - predominantly Google Translate (GT) - to communicate with patients across
language barriers. Though intended to support their duty of care, potentially uninformed reliance on MT in such contexts could have serious consequences for patient safety. Research nonetheless remains limited on staff awareness of the possible risks posed by higher-stakes MT use in general and with patient medical records in particular, most existing literature instead examining its use in interpersonal situations or with patient-oriented documentation. Moreover, medical abbreviations are well-documented as increasing patient risk even monolingually, with outcomes from their misuse and/or misinterpretation ranging from temporary harm to the death of the patient. Abbreviations were therefore selected as a use case for identifying the potential risks posed by their translation with MT. Contextualised French and Spanish data examples drawn from authoritative clinical corpora and translated via GT were presented during semi-structured interviews to 21 healthcare staff participants in diverse roles and specialties. The results were then subject to qualitative analysis and cross-analysis.
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Commutative Algebra
The Delta Set of a Numerical Monoid Generated by a Generalized Arithmetic Sequence
Ashwin Narayan
Let \[ S_h=\langle a,ah+d,ah+2d,\ldots,ah+kd\rangle, \qquad \gcd(a,d)=1,\quad 1<k<a,\quad h> 1, \] be a numerical monoid generated by a generalized arithmetic sequence. In this paper, we determine the delta set \[\Delta(S_h),\] resolving an open problem posed by Christopher O'Neill and Roberto Pelayo in 2014 \cite{ONeill}. Writing $e=h-1$ and letting $E(e,d)$ denote the set of values arising from the subtractive Euclidean
algorithm applied to $e$ and $d$, we prove that \[ \Delta(S_h) = E(h-1,d)\cup \{M-r(h-1):M-r(h-1)>0,\ r\geq0\}, \] where \[ M=\left\lceil\frac{a}{k}\right\rceil(h-1)+d \] is the maximal element of $\Delta(S_h)$. In particular, $d$ and $h-1$ always belong to $\Delta(S_h)$. We further establish a reduction
theorem showing that $\Delta(S_h)$ is a multiple of the delta set of a primitive monoid satisfying $\gcd(d,h-1)=1$, and deduce that the minimum delta is $\gcd(d,h-1)$. We investigate the relationship between delta sets and catenary degrees for these monoids, obtaining an explicit connection between their maximal values and formulating several
conjectures concerning the catenary degree set. We also find an interesting way to generate metallic fibonacci sequences through Delta Sets. These results provide a structural description of factorization invariants for generalized arithmetic numerical monoids and suggest several directions for further study.
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Computer Vision
DeepStratNet: A Context-Aware Coordinate Regression Framework for Seismic Horizon Tracking under Sparse Labels
Aniq Ahmad, Musham Ahmad Malik, Ahmad Mustafa et al. (+1 more)
Automatic horizon tracking is a foundational task in 3D seismic interpretation. Most existing deep learning approaches formulate it as dense semantic
segmentation, typically using U-Net-based architectures. The model produces a probability map over all pixels that must be post-processed to extract precise horizon coordinates, while horizon picks in time/depth must be converted into dense masks for training. Unpicked seismic traces are consequently treated as background, which can hinder convergence, and both pre- and post-processing can introduce errors into the final interpretation. Moreover, 2D
segmentation models do not inherently capture inter-slice context, while 3D models are often computationally prohibitive. We instead formulate horizon tracking as a bounded coordinate regression problem, where the model directly predicts the time/depth coordinate of the target horizon at each lateral position. We propose a lightweight regression head compatible with any pretrained
vision backbone, coupled with an LSTM module to model inter-slice context and produce a continuous horizon surface across the volume. A combination of L1 and L2 losses supervises predictions at valid horizon picks, while a geology-informed regularization enforces lateral continuity between successive traces. Under controlled experimental conditions, we evaluate four pretrained
vision backbones under both
segmentation and regression configurations on a seismic volume from New Zealand. The proposed approach consistently outperforms its
segmentation counterparts quantitatively, using metrics including RMSE and PCC, and qualitatively, while also demonstrating greater robustness to increasing sparsity of training picks. Finally, we show that prediction variation across successive traces captures local variations in geological complexity, providing an automated quality control measure for downstream seismic interpretation.
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All authors Aniq Ahmad, Musham Ahmad Malik, Ahmad Mustafa, Heather Bedle
Mesoscale and Nanoscale Physics
Magnetic-field response of generalized Wigner crystals in twisted MoTe$_2$
F. K. Wolff, S. Jiao, H. Park et al. (+9 more)
We report a magnetotransport study of fractional hole-filling states in the layer-polarized regime of a twisted MoTe$_2$ homobilayer. A perpendicular
magnetic field suppresses the resistance peak at the two-thirds filling while enhancing the one-third peak by several orders of magnitude. Both remain near their commensurate densities. We argue that these commensurate states are generalized Wigner
crystals whose distinct charge configurations define different
magnetic lattices, leading to contrasting responses to
spin polarization. Near half filling, we observe a qualitatively different state whose resistance maximum shifts approximately quadratically with field and exhibits pronounced transport anisotropy consistent with a stripe phase. These results reveal a strong dependence of magnetotransport on fractional filling and open a route to
magnetic control of transport in moiré charge-ordered states.
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All authors F. K. Wolff, S. Jiao, H. Park, J. Cai, E. Anderson, X. Liu, C. Wang, T. Taniguchi, K. Watanabe, X. Xu, D. Xiao, S. Vaitiekėnas
Artificial Intelligence
Right Order, Wrong Scale: Auditing LLM Judges for Occupational AI Measurement
Harry Lyu and Neil Thompson
LLM judges are increasingly used to assess whether AI outputs meet workplace requirements, but agreement on response rankings does not establish agreement on acceptance rates or occupational aggregates. We introduce O*NET-BENCH, an audit suite derived from an existing survey of 45,796 worker ratings, and evaluate 33 pre-existing judge configurations across six model families on 4,501 test ratings. Twenty-five configurations achieve tie-aware pair accuracy of at least 0.60, although a train-fitted response-only TF-IDF baseline nearly matches the strongest judge. Despite this ordering agreement, judges estimate that 3.0%-97.9% of responses are acceptable, compared with 61.1% for occupation-matched workers. In one fine-tuned lineage, changing from pointwise scoring to a bundled few-shot/listwise protocol improves response ordering while reducing agreement with worker means at the task and occupation levels; this reversal replicates on a task- and worker-disjoint validation split under prespecified criteria. Cross-validated calibration largely removes mean bias, but calibrated scores explain at most 8.5% of individual worker-rating variance. Prediction-assisted estimation yields at most small precision gains at the studied label budgets. These results show that ranking agreement alone is insufficient for occupational measurement. Judges should be validated against the acceptance rates and aggregates their scores will be used to estimate.
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Artificial Intelligence
What Does a Token Cost? A Mixture-of-Agents Measurement of Sufficient Per-Token Compute
Zhixu Du, Weijia Han, Hai Helen Li et al. (+1 more)
Large
language models spend the same amount of computation on every
token they generate, regardless of how difficult each
token is to produce. Methods such as speculative decoding and model routing are built on the premise that much of this computation is unnecessary, yet the computation an individual
token actually requires has not been measured. We measure it through a Mixture-of-
Agents (MoA) lens: a panel of fifteen
language models of increasing capacity, drawn from three families, in which every
agent attempts to reproduce a reference sequence
token by
token, conditioned on the correct preceding
tokens. We define the inference cost of the smallest
agent that succeeds as the
token's sufficient compute, which upper-bounds what the
token requires. On three core
benchmarks, a 0.5B
agent reproduces 92–95% of reference
tokens. Across Qwen, OLMo, and R1-distilled panels, the most expensive 10% account for 64–80% of estimated FLOPs. On all 500 MATH-500 problems, the MoA-derived map helps model routing reduce projected latency from 7.59 to 5.12 seconds while slightly improving accuracy, relative to the best confidence-routing baseline. The MoA-map helps drafting use 32.6% fewer draft
tokens and approximately 20% lower projected latency than fixed-window drafting at similar accuracy. These comparisons reveal remaining allocation headroom, motivating controllers that exploit sufficient-compute structure.
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All authors Zhixu Du, Weijia Han, Hai Helen Li, Yiran Chen
Soft Condensed Matter
How Does Hard Magnetic Soft Matter Deform?
Daniel Katusele, Carmel Majidi, Liping Liu et al. (+2 more)
Hard
Magnetic Soft Materials, i.e., elastomers seeded with hard
magnetic particles, convert
magnetic energy into complex motion and have become central to the design of untethered soft
robots, biomedical devices, and, in general, for enabling fast, wireless actuation. Their behavior depends critically on how the surrounding soft
matrix deforms and transmits torque to each magnetized inclusion, yet there is no consensus on the correct mapping between macroscopic strain and microscopic motion. Competing models predict conflicting particle rotations and
magnetic responses under identical loads. Here, we construct counterexamples that show the key shortcomings in these models, and then establish a first-principles framework that leads to an optimal deformation mapping. The resulting closed-form law unifies conflicting models and shows that they are, in fact, simply different limits of our general approach. Our work permits the rational design of magnetically actuated soft devices and a unified view of deformation in
magnetic soft matter, and broadly, in similar architectured materials.
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All authors Daniel Katusele, Carmel Majidi, Liping Liu, Pradeep Sharma, Kaushik Dayal
Combinatorics
Pattern restricted parking functions with limited preferences
Kassie Archer and Robert Laudone
A parking function is said to have $\ell$-limited preferences if there are at most $\ell$ copies of each element in the parking function. In this paper, we define a notion of pattern avoidance for parking functions and enumerate those $2$-limited parking functions that avoid certain patterns.
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Machine Learning
Harnessing LLMs as Agents: What Does It Cost?
Zelin Zhao, Xinyu Guo, Jingyuan Zhang et al. (+2 more)
Language-model
agents increasingly rely on harnesses that manage bounded context, persistent
memory, tools, verification, and repeated execution, yet existing notions of model capability do not quantify the computational resources these mechanisms consume. We introduce the
Language Model
Agent Machine (LAM), a resource-bounded abstraction that fixes the underlying semantic model while explicitly charging harness-level resources. We establish four classes of results. Communication: LAM execution is instancewise equivalent to red–blue pebbling under simultaneous call–transfer budgets, transferring classical I/O lower bounds to context–
memory traffic. Access:
memory interfaces induce asymptotic separations, including a $\Theta(n)$ gap between random and non-speculative sequential access on pointer chasing. Recomputation: bit-reversal DAGs require $\Theta(n^2/(C+S)+n)$ model calls with context capacity $C$ and persistent-
memory capacity $S$, quantifying when stored intermediate state avoids repeated semantic computation. Reliability: we derive tight stage-local sampling bounds, exact imperfect-verification costs, and a Young–Daly-type checkpoint law with a closed-form optimal verification interval. Controlled and held-out experiments on GPT-6 Astra test communication and reliability predictions, including checkpoint optima, policy selection under programmatic checking, and tradeoffs among call granularity, logical input traffic, and reliability on chained MATH tasks. Together, these results provide a resource theory for the computational cost of
language-model
agent harnesses.
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All authors Zelin Zhao, Xinyu Guo, Jingyuan Zhang, Yuxuan Zhang, Yongxin Chen
Machine Learning
Threshold-Aware Conformal Routing
Shiwei Tan, Huzefa Rangwala and Danielle C. Maddix
High-fidelity simulations are essential to scientific and engineering design, but can be expensive to run repeatedly. Learned surrogates offer a faster alternative, yet their higher errors may alter downstream decisions. This accuracy-speed tradeoff creates a need to determine whether a surrogate can be used or the full simulator remains necessary. We study decisions determined by whether a scalar quantity of interest lies above or below a fixed threshold. For each input, we use the surrogate when its conformal interval lies entirely on one side of the threshold and route the input to simulation when the interval intersects it. Standard conformal prediction constructs intervals without reference to the downstream decision threshold: even a narrow interval near the threshold can cross it and trigger simulation, whereas a wider interval farther away can remain entirely on one side and require no simulation. We introduce Threshold-Aware Conformal Routing (TACR), which learns an input-dependent scale using a threshold-aware objective that concentrates interval tightness near the decision boundary. Exact split-conformal calibration on held-out data preserves distribution-free marginal coverage, which also upper-bounds the probability of an incorrect threshold decision that is not routed. Across various scientific and engineering
datasets, TACR reduces simulator deferrals by 14-75% relative to standard conformal prediction at the same coverage target. Against a variant without threshold-local weighting but with similar predictor accuracy, TACR further reduces deferrals by 10-24% on four
datasets. These results show that optimizing interval allocation for routing can reduce simulator calls without weakening the standard conformal guarantee.
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Computation and Language
From Retrieval to Typed Decisions: Calibrated System One Models from Biomedical Sentence Encoders
Pritam Deka
Typed decision models answer schema-constrained questions about a text in one forward pass and return probabilities meant to be thresholded. We ask whether biomedical sentence encoders trained for
retrieval are good starting points for such models. We present SBERT2S1, which converts Sentence-
Transformers encoders into bi-encoder, cross-head (C) and prior-fused residual (PFR) decision models, together with BIODECIDE, a biomedical typed-decision suite, and MEDLINE-S1, 243k training decisions derived from NLM indexing. Across six parent-retriever pairs,
retrieval training improves zero-shot matching of content-bearing options. After fine-tuning, its effect depends on the head: across five pairs and three training-set sizes,
retrieval training significantly helps PFR, which keeps the
retrieval prior, in 10 of 15 comparisons, but helps C in one and hurts it in five. A matched grid of two heads and five training objectives shows that C outperforms PFR under every objective, and that the released RLCD recipe of open System One models trails cross-
entropy by 2.5-3.0 points. The deficit stems mainly from its reward normalisation, which inflates the noisy score-function term 3.6-15-fold; an unbiased leave-one-out
estimator recovers most of the gap. After temperature scaling, no objective is clearly better calibrated than cross-
entropy. We release the code, the MEDLINE-S1 labels and a model.
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Optimization and Control
Mean-variance portfolio selection: connections between mean-field systems and forward-backward stochastic systems under initial-terminal cost coupling
Xun Li, Hongyu Shi and Zhen Wu
This paper investigates the connection between mean-field systems and forward-backward
stochastic systems arising from the mean-variance portfolio selection problem. By introducing the conditional expectation process of terminal wealth, the mean-field term is represented by a backward state, leading to a class of control problems for forward-backward
stochastic systems with coupled initial-terminal values. The coupling between the terminal value of the forward state and the initial value of the backward state in the cost functional prevents classical methods for forward-backward
stochastic optimal control from being directly applicable. To overcome this difficulty, we establish a
stochastic maximum principle for control problems with running costs and coupled initial-terminal values, and provide sufficient conditions for optimality. Furthermore, we investigate a class of generalized
stochastic linear-quadratic control problems with initial-terminal coupling, allowing the control weight in the running cost to be indefinite, and derive the optimal feedback representation via a Riccati equation. The classical mean-variance portfolio selection model is shown to be a special case, for which the corresponding efficient investment strategy and efficient frontier are obtained explicitly, and numerical simulations are presented to illustrate the results and examine parameter sensitivity and its financial implications.
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Functional Analysis
Orthogonality, Spectral Filling, and Uncertainty
Travis Alvarez, Trevor Camper and Mishko Mitkovski
Let a normalized continuous Parseval frame describe the phase space of a reproducing kernel
Hilbert space. The frame coefficients of an orthonormal family have total mass equal to the number of states and pointwise mass at most one. This elementary exclusion principle gives explicit lower bounds for the total cost of a family in terms of the volume of low-cost regions. For radial costs, it yields collective mean-dispersion, umbrella, and transport inequalities. The same argument applies to normalized Bessel families, with the Bessel bound measuring the permitted overlap. We also consider semiclassical families for which the frame measures vary. Weak convergence of the normalized measures, together with averaged localization of the normalized kernels, yields continuous-symbol Szegő limits and sharp asymptotics for the lowest Toeplitz energies. The results apply to Bargmann–Fock and weighted Bergman spaces, Gabor and Paley–Wiener spaces, and orthogonal-
polynomial and determinantal ensembles, including the GUE.
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Classical Analysis and ODEs
Maximal directional singular integrals
Francesco Di Plinio and Ioannis Parissis
We survey maximal directional averages and directional singular integrals, and their connections with Kakeya–Nikodym phenomena, differentiation theory and the Carleson operator. The exposition is organized by the structure of the set of directions: lacunary and arbitrary finite sets, vector fields as in the
conjectures of Zygmund and Stein, and, in higher dimensions, algebraic sets of directions and subspaces. The unifying tool is almost orthogonality, which rests on the ordering of the circle in the plane and on
polynomial partitioning in higher dimensions. We explain where it yields sharp or nearly sharp bounds and where new ideas are needed, notably for multiscale averages along algebraic curves and for vector-valued single-annulus estimates, and we collect open problems.
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Space Physics
A Student Sounding Rocket Experiment to Probe Electron Density in the Lower Ionosphere
Joshua Goodwill, Timothy Tomaszewski, Jarrod Bieber et al. (+17 more)
Earth's ionosphere is primarily generated by the Sun's ionization of atoms in the upper atmosphere. This
plasma environment is highly dynamic, exhibits strong spatial and temporal, variations and significantly impacts power systems,
navigation, and satellite and ground communications. The University of Delaware Ionospheric Probe (UDIP) was developed as a hands-on learning experience for University of Delaware students on the ionosphere itself and on the development of space technology. Students (mostly undergraduates) have led all aspects of the experiment including mission planning, electronics development, mechanical development, software development, and scientific data analysis. The present study is intended as a guide to readers on how the development of space and near-space flight missions can be successfully incorporated into an undergraduate physics curriculum. The fourth version of the experiment (UDIP-4) flew along with student experiments from across the USA on the 2024 RockSat-C sounding rocket, which was launched from NASA Wallops Flight Facility. During the flight, UDIP-4's Langmuir probe successfully measured the ionosphere's density profile – electron density as a function of altitude – up to an apogee of 114 km. Though the measured density profile agrees well overall with the predictions of theoretical models, UDIP-4 identified a thin layer of enhanced electron density at an altitude of approximately 110 km that is consistent with a sporadic E layer.
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All authors Joshua Goodwill, Timothy Tomaszewski, Jarrod Bieber, Carson P. Brown, Ashton Southwick, Samuel Auerbach, Sreenidhi Banda, Alex Bruce, Marisol Catalan Olais, Markos Duey, Ranyah Khan, Connor McCleery, Jonathan Rosado, Amanda Swenson, Matthew Ward, Jarod Dagney, David Sundkvist, John W. Bonnell, William H. Matthaeus, Bennett A. Maruca
Algebraic Geometry
The Mumford–Tate group of a very general Lagrangian fiber
Edward Varvak
For a primitive
symplectic variety $X$ admitting a holomorphic Lagrangian fibration $f: X \to B$, we classify the possible Mumford–Tate groups of the very general fiber. We extract as a consequence that the discriminant of $f$ has codimension one in $B$. In the special case when $X$ is a hyper-Kähler
manifold which is general among those admitting a Lagrangian fibration, and $b_2(X) \geq 7$, we further show that the very general fiber of $f$ is Hodge-generic. Finally, as an application of our classification, we confirm an expectation of Li–Tosatti that when $f$ is not isotrivial, the special Kähler metric on $B$ has positive holomorphic sectional
curvature on the regular values of $f$.
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Artificial Intelligence
MEA: A Reward-Driven Multi-Agent System for Faithful Model Explanations
Yuyang Cheng, Raghav Kaushik Ravi, Srivarshinee Sridhar et al. (+3 more)
Recent years have seen the employment of a plethora of machine learning (ML) models in high-stakes domains, but they remain largely opaque to the practitioners who act on their predictions. While post-hoc explanation methods offer a lens into this model behavior, wielding them effectively demands expertise most domain experts lack: navigating high-dimensional outputs, selecting the best explanations, and synthesizing evidence across disparate tools. To this end, we present MEA, a multi-
agent framework that removes the explanation knowledge barrier entirely: a Proposer
agent selects and configures explanation tools based on the question and modality, while an Actor
agent is optimized end-to-end against faithfulness, transforming the outputs into natural
language explanations grounded in model behavior across tabular, text, and
vision modalities. Further, we introduce diverse question types spanning feature attribution, counterfactual
reasoning, and spurious feature detection, each paired with a perturbation-based faithfulness metric. We find that frontier LLMs systematically produce unfaithful explanations. By optimizing against faithfulness rewards augmented with a modality-adaptive penalty, MEA consistently outperforms post hoc explainers, agentic, and closed-source baselines across six
datasets, with reward-driven optimization yielding faithfulness gains of +28% (tabular), +21% (text), and +34% (
vision) over the untrained backbone. More broadly, our findings suggest that AI
agents themselves can serve as a scalable, adaptable interface to ML explainability, opening a path toward natural-
language explainability that generalizes beyond the fixed, single-purpose tools that have long defined the field.
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All authors Yuyang Cheng, Raghav Kaushik Ravi, Srivarshinee Sridhar, Sriparna Saha, Akash Ghosh, Chirag Agarwal
Data Structures and Algorithms
The Power of Flexible Budgets in Adwords
Suho Kang and Rajan Udwani
Search advertising platforms routinely spend beyond an advertiser's average daily budget on high-traffic days, so long as total spending over the month stays within the monthly budget. Motivated by this practice, we study a $D$-day generalization of the Adwords problem (Mehta et al. 2007), where each advertiser $i$ has a nominal (average) daily budget $B_i$ and a total horizon (monthly) budget $DB_i$. Given a flexibility parameter $\delta$, the platform may spend at most $\delta B_i$ on advertiser $i$ on any single day, subject to the horizon spending limit of $DB_i$. We quantify the power of $\delta$-flexible budgets by benchmarking against the inflexible offline optimum, which may spend at most $B_i$ on advertiser $i$ on each day. We show that no amount of flexibility helps direct generalizations of the classical
algorithm of Mehta et al. (2007). By contrast, for every fixed $\delta$, we design an
algorithm whose competitive ratio converges to $1-e^{-\delta}$ as $D\to\infty$, and we show that this is asymptotically optimal. Perhaps surprisingly, this matches the optimal competitive ratio in a more permissive setting where the
algorithm receives a fresh spending limit of $\delta B_i$ each day and may spend up to $\delta D B_i$ over the horizon. Along the way, we characterize the exact optimal competitive ratio for every pair $(D,\delta)$ on high-traffic instances, where the offline
benchmark exhausts every advertiser's budget on every day.
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Artificial Intelligence
Tropical Reinforcement Learning
Arip Asadulaev, Aladin Djuhera, Karim Salta et al. (+3 more)
Reinforcement learning for large
language models typically maximizes expected return, adding up the probabilities of all successful trajectories. However, the classical sum formulation can only report how often the model policy succeeds, not which solution actually worked, and because probabilities sum to one, reinforcing one solution can make the model forget another that was never shown to be wrong. This makes expected return a poor fit for compositional
reasoning, where a solution must be assembled from
reasoning steps that the model produces in separate, often failed, attempts but rarely produces together. To address this, we propose Tropical Reinforcement Learning, which rests on a simple change of
algebra: instead of adding the probabilities of alternative solutions, we take their maximum, which yields the tropical semiring. The value of a state then becomes the log-probability of its most likely verified solution, together with an explicit path that can be replayed and reused. This enables true composition, since the best prefix and the best suffix meeting at a shared state can be joined even when they come from different rollouts. To put this into practice, we introduce TROPIC, a training
algorithm for deterministic, resettable environments with verifiable outcomes. On four agentic tasks (Sokoban, Countdown, FrozenLake, WebShop), TROPIC outperforms the strongest on-policy baselines by up to 16 percentage points. Changing the
algebra of reinforcement learning, not just its
estimators, can thus substantially improve compositional
reasoning in
language models
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All authors Arip Asadulaev, Aladin Djuhera, Karim Salta, Holger Boche, Fakhri Karray, Martin Takac
Systems and Control
Modular Model Order Reduction for Inverter-Based Power Systems with Stability and Accuracy Guarantees
Hanqing Zhang, Pudong Ge, Mohammad Fahim Shakib et al. (+5 more)
This paper proposes a modular model order reduction framework for large-scale power grids integrated with renewable energy sources. The proposed framework has the advantage of reducing individual sub-areas independently while retaining the power grid interconnection structure. Moreover, given a user-defined accuracy specification on the overall reduced-order interconnected power grid, corresponding target specifications for the individual reduced sub-areas are determined: satisfaction of such individual specifications guarantees the overall user-defined accuracy specification, while also preserving the stability of the overall reduced-order interconnected power grid. The proposed framework is validated on a modified IEEE 118-bus system (where synchronous generators have been replaced by inverter-based resources) by assessing the accuracy specification satisfaction of the overall reduced-order interconnected power grid, in terms of frequency response, stability, active power, and sub-synchronous behaviour when injected with disturbances.
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All authors Hanqing Zhang, Pudong Ge, Mohammad Fahim Shakib, Adrià Junyent-Ferré, Balarko Chaudhuri, Luuk Poort, Lars A. L. Janssen, Giordano Scarciotti
Complex Variables
Real rational Herglotz-Nevanlinna functions in two variables and a class of extremals
Ludvig Fagrell and Annemarie Luger
We first revisit the Nevanlinna condition for representing measures of Herglotz-Nevanlinna functions in two variables and give a general operator-theoretic criterion for extremality. We then derive an explicit formula for the representing measure of a real rational Herglotz-Nevanlinna function in two variables, and combine it with the extremality criterion to obtain a family of extreme elements in the full cone of Nevanlinna measures. The family includes examples with reducible denominators, and these yield counterexamples to the irreducibility assertion in a
conjecture of Knese. We then characterize reducibility within this family both algebraically and geometrically.
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High Energy Astrophysical Phenomena
Suppression of spiral density waves in collisionless accretion flows
Stephen Majeski, Matthew W. Kunz and Jason Dexter
Spiral density waves are ubiquitous phenomena in differentially rotating flows. They are non-modal, non-axisymmetric perturbations that, due to shear in the background flow, possess time-evolving wavenumbers, frequencies, and amplitudes. In global simulations of optically thin, low-luminosity black-hole
accretion flows, the excitation of such waves leads to spiral patterns in the
plasma density that influence the morphology of the emission region. As such, the observed variabilities of such
accretion flows are expected to be affected by the behavior of spiral density waves. Thus far, investigations of spiral density waves in
accretion flows have exclusively used the assumption that the
accretion-flow
plasmas are in local thermodynamic
equilibrium (LTE) at all times. In reality, hot and diffuse
accretion-flow
plasmas are expected to deviate far from LTE, and should be modeled accordingly. Here, we employ a combination of kinetic and fluid models to describe spiral density wave propagation, damping, and excitation in a collisionless shearing sheet, which more accurately represents the
plasma conditions of low-luminosity
accretion flows than do models that assume LTE. We find that micro-physical
plasma instabilities are especially important in determining how spiral density waves behave, because the weak particle scattering that they induce leads to appreciable viscous damping. Observational implications of these results include reduced emission-region variability, which may improve agreement between Event Horizon
Telescope (EHT) observations and simulation/theory, as well as a reduction in emission-region pattern speeds compared to simulations employing LTE, which bears on the interpretation of eventual EHT movies.
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Fluid Dynamics
Linear stability of electroconvection in a viscoelastic electrolyte: polymeric-work pathways and eigenmode selection
Minyoung Kim
Electroconvective (EC) instability near ion-selective surfaces plays a key role in electro-chemical transport beyond the
diffusion-limited regime. While EC instability in Newtonian electrolytes has been extensively investigated, the influence of viscoelasticity on the instability mechanism remains less understood. In the present study, we investigate the viscoelastic modulation of EC instability using linear stability, eigenspectrum, and mechanical-work analyses, supported by asymptotic pathway ordering. The analysis reveals a non-monotonic dependence on the Weissenberg number Wi, with the maximum growth rate and minimum critical voltage occurring near Wi ~ O(1). The mechanical-work balance separates electric, solvent-viscous, and polymeric contributions, and further decomposes the polymeric work into normal-stress-difference and shear-stress pathways according to their constitutive origins. For Wi << 1, the
polymer stress recovers Newtonian viscous dissipation at leading order. As Wi approaches unity, the phase efficiencies of the Newtonian-like polymeric pathways decrease substantially, causing the negative polymeric work to collapse and the instability to intensify. At intermediate Wi, an additional minimum in the critical voltage appears at low wavenumbers. Eigenspectrum analysis attributes this feature to the selection of a slowly propagating mode that retains substantial negative polymeric work. At large Wi, this mode no longer determines the instability threshold, and the low-wavenumber minimum disappears. The normal-stress-difference and shear-stress work then nearly cancel, accompanied by stronger ESC-localized shear deformation and predominantly solvent-viscous dissipation. Thus, the non-monotonic response is governed by stress-deformation phase relations, solvent dissipation, and eigenmode selection rather than stress magnitude or a single polymeric contribution.
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Quantum Physics
Single-photon addition to multimode quantum fields at telecom wavelengths using lithium niobate and its doped variants
Naveen V, Nicolas Treps, Raghavan G et al. (+2 more)
Multimode spectro-temporal non-Gaussian
quantum states of light play a crucial role in continuous-variable
quantum information processing. In particular, the non-Gaussian
quantum states generated through a single-
photon addition (SPA) to multimode
quantum fields at telecommunication wavelengths constitute a useful resource for
quantum technologies. We present a detailed theoretical analysis and numerical simulations of single-
photon addition (SPA) and mode-selective single-
photon addition (MSSPA) to a multimode
quantum field at telecommunication wavelengths. The analysis is performed for congruently grown lithium niobate (LN), $5\%$ MgO-doped lithium niobate (MgO:LN) and various concentrations of ZnO-doped lithium niobate (ZnO:LN) bulk
crystals. We investigate MSSPA using type-II parametric down-conversion (PDC) and SPA using the type-I PDC processes. We further present spectro-temporal mode-selective SPA at the telecom wavelength using $5\%$ MgO:LN for temperatures ranging from $0^\circ C$ to $15^\circ C$. In addition, we perform simulations to investigate SPA based on the noncollinear type-I PDC configuration. These theoretical results identify optimal experimental conditions and phase-matching parameters to achieve SPA and mode-selective SPA for LN-based
crystals, providing a potential platform for non-Gaussian
quantum state engineering at telecommunication wavelengths, mainly at $1550$ nm.
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All authors Naveen V, Nicolas Treps, Raghavan G, Valentina Parigi, Srinivasan K
Computation and Language
APDMem: Agent-Controlled Progressive Disclosure for Query-Adaptive Long-Term Memory
Chin-Lun Fu, Anagha Kulkarni, Hong Ni et al. (+1 more)
Personalized LLM assistants must recover sparse evidence from long conversation histories across queries of varying complexity. We introduce APDMem (
Agent-controlled Progressive Disclosure
Memory), a hierarchical long-term
memory architecture that applies progressive disclosure to
memory retrieval. Rather than relying on a flat
memory store or fixed
retrieval granularity, APDMem represents conversation history as four progressively detailed layers: thematic summaries, personalized key facts, turn-level evidence notes, and raw messages. At inference time, a controller applies progressive disclosure to the
memory hierarchy: it first reads high-level summaries and drills into finer evidence only when needed. This creates an adaptive cost-fidelity trade-off: simple queries can terminate early, while complex temporal, multi-hop, or exact-evidence queries trigger deeper inspection. A note synthesizer converts retrieved evidence into a query-focused structure that consolidates facts, orders events, and flags contradictions before final answer generation. Experiments on LongMemEval show that APDMem achieves strong performance for long-context
memory reasoning while accessing only 8% of the total conversations.
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All authors Chin-Lun Fu, Anagha Kulkarni, Hong Ni, Behrouz Madahian
Quantum Physics
Passive-reflector bounds and robust bilateral nonequilibrium Casimir repulsion
Mohamed R. Khodja and Belkacem E. Khodja
Nonequilibrium electromagnetic fluctuations can generate repulsive Casimir–Lifshitz pressures, but optimizing a cavity at one operating point does not establish that the repulsion survives uncertainty or exceeds ordinary far-field radiation pressure. We formulate a two-sided biased-
semiconductor cavity as a constrained max–min problem that maximizes the smaller outward pressure on its two reflectors. In the optically thick-slab limit, identical reflectors admit a symmetric global optimizer, and a passive-reflector bound separates cavity enhancement from the driven far-field plateau. At $300~\mathrm{K}$, a biased-GaAs cavity with $\pm10~\mathrm{nm}$ gap uncertainty and $\pm0.005$ drive uncertainty sustains a worst-case pressure of $2.257~\mathrm{mPa}$ with ideal reflectors. Reoptimization with a causal gold response retains $2.164~\mathrm{mPa}$. The nominal and robust optima lie within $2~\mathrm{nm}$ of one another, so the main value of the max–min calculation here is a quantitative performance certificate rather than a large
geometric redesign. A full finite-slab calculation and an alternative published GaAs response change the reported pressures by at most $1.60\times10^{-3}\%$ and $4.44\times10^{-2}\%$, respectively. These results establish a reproducible design bound for bilateral nonequilibrium repulsion under dimensional, drive, reflector, and optical-model variations.
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Astrophysics of Galaxies
X-ray Characterization of Galaxy Groups and Hickson Groups in COSMOS-Web to z~3.8 I. X-ray Luminosity Function Evolution
Ghassem Gozaliasl, Günther Hasinger, Gavin Leroy et al. (+35 more)
Galaxy groups are the dominant
halo environment in the Universe and a sensitive laboratory for feedback and gas-cycling physics, yet a uniform, intermediate-
redshift X-ray characterization of the group population has been limited by the availability of deep, wide-area imaging. We present a uniform X-ray characterization of the COSMOS-Web
galaxy group population: 1,678 groups (CW-All) identified with the AMICO
algorithm applied to the JWST-selected COSMOS-Web photometric catalog ($0.08 \lesssim z \lesssim 3.7$), and a parallel sample of 993 Hickson compact groups (CW-HCG; $0.08 \lesssim z \lesssim 3.82$) over $0.45~\mathrm{deg}^2$. We apply a uniform aperture-photometry X-ray pipeline to the combined Chandra and XMM-Newton COSMOS mosaic, measuring fluxes, luminosities, temperatures, and
halo masses and radii for every group, together with detections, upper limits, and quality flags. We detect X-ray emission from 499 CW-All groups (29.7%) and 332 CW-HCG groups (33.4%) at SNR~$\geq 2.0$, and present the X-ray luminosity function in four
redshift bins. The characteristic luminosity $L^\star$ rises monotonically by $\sim$1.9–2.1~dex from the lowest to highest
redshift bin in both catalogs, a trend that persists under two independent cross-check binning schemes and is not explained by mass or richness selection of the detected population. A targeted search for diffuse X-ray emission from the AmicOne protocluster candidate at $2.50 \lesssim z < 3.09$ finds no statistically significant signal at the current depth. We publicly release the X-ray measurements and derived properties for both catalogs.
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All authors Ghassem Gozaliasl, Günther Hasinger, Gavin Leroy, Alexis Finoguenov, Fatemeh Abedini, Hollis B. Akins, Rafael C. Arango-Toro, Arif Babul, Caitlin M. Casey, Nicole E. Drakos, Andreas L. Faisst, Carter Flayhart, Maximilien Franco, Zohreh Ghaffari, Santosh Harish, Hossein Hatamnia, Olivier Ilbert, Jeyhan S. Kartaltepe, Ali Ahmad Khostovan, Maarit Korpi-Lagg, Ronaldo Laishram, Daizhong Liu, Matteo Maturi, Henry Joy McCracken, Jed McKinney, Nicolas McMahon, Lauro Moscardini, Mahdiyar Mousavi-Sadr, Jason Rhodes, Brant E. Robertson, Louise Paquereau, Rasha M. Samir, Mark Sargent, Diana Scognamiglio, Marko Shuntov, Greta Toni, Francesco Ubertosi, Eleni Vardoulaki