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All of arXiv

Friday 18 September

Adaptation and Self-Organizing Systems

Deviations from global coupling in adaptive oscillator networks: a mean-field theory for the variance of coupling weights

Richard Gast, Shotaro Takasu, Juergen Kurths et al. (+1 more)

A wide range of physical and biological systems are adaptive networks, in which the dynamics of the nodes and of the edges connecting them co-evolve. Mean-field reductions of such systems typically track only the average coupling strength, and therefore cannot determine when the coupling stays effectively homogeneous and when structured connectivity emerges. Here, we present a second-order moment closure that allows us to derive mean-field equations for the coupling-weight variance in networks of heterogeneous phase oscillators with adaptive coupling, starting from uniform coupling weights. In agreement with network simulations, we find a nonlinear, non-monotonic dependence of the relative weight variance on the oscillator heterogeneity that is mediated by the phase coherence. Moreover, we find that deviations from global coupling strongly depend on an interaction between the oscillator heterogeneity and the adaptation rule. Whereas symmetric adaptation causes a strongly coupled core of coherent oscillators to emerge and creates a bistable regime that is absent without adaptation, antisymmetric adaptation leads to antisymmetric coupling within the same core, thereby destabilizing it. Our equations therefore delineate the regimes in which adaptive networks behave like globally coupled systems from those in which more complex coupling patterns form.
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All authors Richard Gast, Shotaro Takasu, Juergen Kurths, Ann Kennedy

Earth and Planetary Astrophysics

Post-perihelion Photometric and Spectroscopic Monitoring of the Interstellar Comet 3I/ATLAS

Goldy Ahuja, Shashikiran Ganesh, K. Aravind et al. (+12 more)

The third interstellar object, comet 3I/ATLAS, was observed using various Indian telescopes during its post-perihelion evolution. We carried out imaging and spectroscopic observations of the comet at multiple epochs using the 0.5-m, 1.2-m, and 2.5-m telescopes of the Physical Research Laboratory and the 2-m Himalayan Chandra Telescope (HCT) operated by the Indian Institute of Astrophysics. Additionally, time-series photometry was obtained on 7 epochs using the 0.132-m refractor of Cepheid Observatory. The spectroscopic observations of 3I/ATLAS reveal signatures of molecular emission from CN, C$_2$, and C$_3$, as commonly observed in the emission spectra of solar system comets. The production rates and rate ratios indicate that the composition of the 3I/ATLAS transitioned from carbon-depleted (pre-perihelion) to carbon-typical (post-perihelion). The change in carbon composition could be due to exposure of fresh material from subsurface layers near perihelion. We also performed photometric observations to determine broadband colours and the spin period. The measured colours are $B-V=$ 1.03 $\pm$ 0.13 mag, $V-R=$ 0.59 $\pm$ 0.11 mag, $R-I=$ 0.08 $\pm$ 0.04 mag, $g-r=$ 0.52 $\pm$ 0.09 mag, and $r-i=$ 0.13 $\pm$ 0.08 mag. The colours are redder than the Long-Period Comets of the solar system and the Sun in $B-V$ and $V-R$, but near solar in $R-I$. The measured colours remain nearly constant throughout the observing period and are consistent with the reported pre-perihelion values. The colours and the reflectivity gradient match the photometric colours of the `ultrared-material rich' objects in the solar system. The nuclear radius derived from non-gravitational force lies between 0.45 and 0.65 km.
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All authors Goldy Ahuja, Shashikiran Ganesh, K. Aravind, Emmanuel Jehin, Bhavya Ailawadhi, Vikrant K. Agnihotri, B. Arvind, Pallavi Saraf, Alka Singh, Deekshya R. Sarkar, Sunil Chandra, Prithish Halder, Devendra Sahu, T. Sivarani, Anil Bhardwaj

Probability

Diffusion Approximations to Schrödinger Bridges and the Convergence of Entropic Potentials

Garrett Mulcahy and Soumik Pal

Consider the Monge-Kantorovich optimal transport problem between two Euclidean densities $\mu$ and $\nu$ and quadratic cost. The $\varepsilon$-Schrödinger bridge is the solution to the entropic regularized problem with regularization parameter $\varepsilon$. By taking the conditional expectation of the second coordinate given the first under this coupling, we obtain the $\varepsilon$-entropic Brenier map. As $\varepsilon$ goes down to zero, it is known that the entropic Brenier map converges to the quadratic cost optimal transport map between the two measures, i.e., the Brenier map. We show that, under some smoothness and log-concavity constraints on the marginals, the difference between the entropic Brenier map and the Brenier map is equal to $\varepsilon$ times one-half of the score function of the first marginal plus an error that is $o(\varepsilon)$ in $\mathbf{L}^2(\mu)$. This expansion holds irrespective of the second marginal $\nu$. The proof relies on an approximation of the Schrödinger bridge by a noisy version of the McCann interpolation. Under additional assumptions we show a second approximation to the Schrödinger bridge via so-called Mirror Langevin diffusions, which are Langevin diffusions on the Hessian manifold generated by the Brenier map. These two approximations, that appear quite different at first glance, are nonetheless shown to be closely connected. Our proofs utilize a random surface and a novel stochastic operation called the tangent Markov projection.
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Robotics

Characterizing Wildlife Response to Biomimetic and Conventional Underwater Vehicles

Huy Pham, Levi Cai, Yogesh Girdhar et al. (+2 more)

Autonomous underwater vehicles (AUVs) are a promising alternative to divers for scalable collection of natural ocean ecology data. However, these robots may disturb local fauna and cause drastic behavioral differences compared to other monitoring techniques, decreasing their value as scientific tools. A promising prospect is to make AUVs that are more biomimetic, with the hope that taking on the form and behavior of a non-predatory animal may reduce adverse responses. We present the first dataset comparing fish disturbance in response to a conventional thruster-driven AUV, a sea turtle inspired flipper-driven AUV, and a diver. Experiments were conducted at a biodiversity hotspot in a Caribbean reef, and images of the scene were analyzed using computer vision to localize and study fish behavior change. Both AUVs cause measurable changes in fish behavior. Although no between-robot differences remain significant after correction for multiple comparisons, point estimates generally favor the biomimetic AUV, motivating larger studies capable of resolving modest effects and further design changes to optimize for disturbance. We also observe larger responses during diver transects than during AUV transects, although this exploratory comparison is based on a small diver sample with several confounds. While conclusions must be taken as preliminary due to operational and experimental limitations, this study provides the community with a first known dataset and benchmarks to quantify the behavioral impacts of biomimetic robots for ecological monitoring in the wild.
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All authors Huy Pham, Levi Cai, Yogesh Girdhar, Daniela Rus, Zach J. Patterson

Machine Learning

User-Level Handover Decision Making Based on Machine Learning Approaches

João Lima, Alvaro Medeiros, Eduardo Aguiar et al. (+2 more)

This letter covers a broad comparison of methods for classification and regression applications for a user-level handover decision making in scenarios with adverse propagation conditions involving buildings, coverage holes, and shadowing effects. The simulation campaigns are based on network simulator ns-3. The comparison encompasses classical machine learning approaches, such as KNN, SVM, and neural networks, but also state-of-the-art fuzzy logic systems and latter boosting machines. The results indicate that SVM and MLP are the most suitable for the classification of the best handover target, although fuzzy system SOFL can perform similarly with lower processing time. Additionally, for the download time estimation, LightGBM provides the smallest error with short processing time, even in hard propagation scenarios.
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All authors João Lima, Alvaro Medeiros, Eduardo Aguiar, Vicente Angelo de Sousa Junior, Tarciana Guerra

Artificial Intelligence

AutoGym: Blueprint-First Generation of Verifiable Agent Gyms

Aarati Andrea Noronha, Kavya Ravikumar and Carly Xiaoyu Lin

Training agents with reinforcement learning requires a gym, comprising a task, an executable environment in which the task can be attempted, and a verifier that reliably distinguishes success from failure. Constructing such gyms remains manual, expensive, and static. Task sets saturate as models improve and are increasingly exposed to contamination. Synthetic generation offers scale, but single-pass synthesis produces tasks whose difficulty is largely cosmetic. Models comparable in capability solve them despite convoluted phrasing, and correctness must be adjudicated post-hoc by unreliable LLM judges. We present AutoGym, a framework that generates complete gyms (tasks, executable environments, and verifiers) from a minimal domain seed or prior model trajectories. AutoGym introduces three mechanisms. (1) Blueprint-first generation specifies the valid solution space, environment requirements, and verification criteria before the environment is materialized, making solvability a construction prerequisite rather than a property verified after the fact. (2) Explicit generation parameters control task topology, interaction depth, capability axes, question obfuscation, and distractor composition, enabling fine-grained difficulty steering. (3) Active curriculum synthesis uses performance-informed calibration to adjust the distribution over these parameters as model capabilities evolve. Across productivity and temporal-reasoning settings, AutoGym generates gyms spanning the capability spectrum, including instances that challenge frontier models.
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Robotics

REBOOT: From Failure to Recovery - A Dataset and Benchmark for Precision Assembly

Nana Yaw Owusu Ofori-Ampofo, Samira Ebrahimi Kahou and Joseph Thekinen

Robot learning policies fail in characteristic ways: they stall in uncertain states, drift during contact-rich alignment, and miss targets by millimetres in precision tasks. Yet training datasets consist largely of successful demonstrations, while real-world benchmarks often reduce performance to binary success. This limits both supervision for recovery and analysis of where failures occur. We introduce REBOOT (Recovery Episode Benchmark for Off-nominal Trajectories), the first robot manipulation benchmark designed around failure as a first-class signal. REBOOT contains 2,160 demonstrations across 18 precision assembly tasks, each decomposed into five shared phases: Align(pick), Engage(pick), Transport, Align(place), and Engage(place), enabling phase-level evaluation beyond terminal success. Failures are introduced across phases and paired with expert recovery trajectories that return the system to a valid continuation state. Tasks are annotated with rotational symmetry, engagement-clearance precision tier, and assembly direction through matched install-remove pairs. Failure episodes are labeled by phase and categorical failure mode, enabling attribution to kinematic stage and tolerance violation. Data includes synchronized RGB-D observations from four viewpoints and grounded natural-language descriptions of phase-level success and failure conditions. Half the dataset contains expert demonstrations; the other half contains recovery demonstrations sampled to reflect failures observed in imitation-learned policy rollouts. We benchmark action-chunked transformer, diffusion, and $\pi_0$-FAST policies using phase-level completion rates, revealing model-specific failure points hidden by binary evaluation. Dataset and code: https://nanayawoa.github.io/REBOOT
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Hardware Architecture

UniCASE: A Unified 16-bit Floating-Point Format with Criticality-Aware Selective ECC for Efficient DNN Protection

Amna Hassan and Semeen Rehman

Soft errors are an increasing reliability concern for Deep Neural Network execution because they can corrupt parameters, leading to accuracy degradation. While conventional ECC offers strong fault protection, it incurs additional parity storage and computational overhead. Embedded-parity formats reduce storage cost by reusing the least-significant bits, but they do not optimize protection while reducing computational overhead. We propose UniCASE, a unified 16-bit floating-point (FP) format that jointly optimizes data representation and error protection for reliable DNN execution. It identifies stable blocks across FP64, FP32, FP16, and BFloat16 that can be mapped into a unified representation. Based on bit-level criticality analysis, UniCASE uses selective ECC that assigns distinct levels of protection to different data bits according to their resilience against soft errors. Experimental results show that UniCASE reduces encoder/decoder cost by up to 30%, preserves model accuracy within 1% of the FP32 baseline, and provides significantly stronger soft error resilience than existing embedded-parity methods.
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Strongly Correlated Electrons

Structural and magnetic properties of TbCuAs$_2$ studied by X-ray and neutron scattering

M. G. Kim, T. Heitmann, S. Boney et al. (+8 more)

We investigated antiferromagnetic metal TbCuAs$_2$, which exhibits an anomalous resistivity upturn at low temperatures. This resistivity upturn has been proposed to originate from the material's magnetic ground state; however, the precise nature of the antiferromagnetic ordering in this compound has not been previously established. Here, we present a combined single crystal neutron diffraction, X-ray resonant magnetic scattering, and single crystal X-ray diffraction study of TbCuAs$_2$. These measurements unambiguously determine the Tb magnetic moment direction, the antiferromagnetic arrangement along high symmetry directions, the interplay between structure and magnetism, and their temperature dependence. Our observations are compared with previous studies on sister compounds in the rare-earth copper arsenide family ($R$CuAs$_2$, $R$ = Sm and Gd), which also displays resistivity anomalies. We suggest a common underlying physics governing the structural and magentic properties of rare-earth copper arsenides that exhibit low-temperature resistivity anomalies.
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All authors M. G. Kim, T. Heitmann, S. Boney, C. Neupane, R. Acevedo-Esteves, A. Sapkota, D. Evans, P. C. Canfield, C. Nelson, E. D. Mun, J.-W. Kim

Computer Vision

Seeing is not Enough: Vision-Language Models Perceive Evidence but Fail to Act

Yuyang Dai, Bofei Huang, Hongbo Zhang et al. (+1 more)

Vision-language models (VLMs) perform strongly on visual question answering benchmarks, yet often make decisions that contradict visual evidence they have already identified correctly. We distinguish perceptual failure, where relevant evidence is not recognized, from process failure, where recognized evidence fails to constrain the final decision. We introduce VPAC-Bench, a benchmark spanning nine real-image process families, with each image annotated by its current activity stage and nearby stage transition. We also propose State-Relevance-Target (SRT), a family of structured process-prior interventions that requires models to connect visible evidence to the relevant process state before answering. Across multiple VLMs, process failure is widespread: models that correctly enumerate visual candidates still over-commit to a single answer in more than 95% of ambiguous cases. An explicit process-structured intervention reduces this rate to below 13% without degrading performance on unambiguous cases. However, the transfer of process priors is model-dependent, and generic SRT does not consistently outperform strong chain-of-thought baselines. When the relevant stage transition is known, boundary-aligned SRT substantially outperforms generic process prompting and all tested chain-of-thought baselines across assembly, physical state transition, navigation and traffic, and object-use affordance tasks. These results show that process priors are most useful when aligned with the scene's specific decision boundary, motivating boundary-aware prior selection for process-grounded visual reasoning.
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All authors Yuyang Dai, Bofei Huang, Hongbo Zhang, Haoran Xie

Robotics

React When You Need To: Event-Triggered Asynchronous Inference for VLA Policies

Yansong Wu, Huaqing Li, Tianding Hou et al. (+2 more)

Vision-Language-Action (VLA) models commonly predict action chunks, limiting their ability to react to environmental changes during execution. Existing asynchronous inference methods improve reactivity but typically rely on a fixed inference gap. In this paper, we propose an event-guided dynamic inference strategy that adapts the inference gap according to scene changes observed since the previous inference. Thereby, it simultaneously preserves motion consistency and prompt reactivity. Across static and dynamic real-world settings, our method consistently performs best, averaging 95% success and exceeding the strongest baseline by 55 percentage points. The code will be made publicly available upon acceptance. The project page is available at https://react-when-you-need-to.github.io/.
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All authors Yansong Wu, Huaqing Li, Tianding Hou, Lingyun Chen, Alois Knoll

Sound

SEABED: SouthEast Asian Benchmark for Evaluating Audio Reasoning

Harshit Rajgarhia, Asif Shaik, Rachuri Lokesh et al. (+2 more)

Modern audio-language models are no longer judged only on what words they can transcribe, but on whether they can reason over what they hear: recovering meaning that lives in tone and prosody, telling dialects and regional languages apart, and resolving ambiguity that the written form leaves open. This capability is now measured by a growing family of audio-reasoning benchmarks, but almost entirely in English and on general-domain audio. Southeast Asia (SEA) is served instead by benchmarks that inherit an English task taxonomy of recognition, translation, and paralinguistic classification, and therefore test whether a model hears SEA speech rather than whether it can reason from it. We introduce SEABED, an audio-first question answering dataset designed to benchmark language and audio reasoning models on SEA speech. SEABED comprises a suite of six audio-reasoning tasks built entirely from real, openly available SEA speech corpora, yielding 5,404 question-answer pairs. We evaluate six frontier and region-specific audio LLMs: even the state-of-the-art model Gemini 3.5 Flash achieves only 50.3% weighted average accuracy. SEABED evaluates not only answer accuracy, but also whether models' stated reasoning is grounded in the audio evidence. A sample of the benchmark data is available here: https://huggingface.co/datasets/CentificAIResearch/SEABED.
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All authors Harshit Rajgarhia, Asif Shaik, Rachuri Lokesh, Sushanta Kumar Pani, Abhishek Mukherji

Machine Learning

TWIG: A Time-Causal Wavelet Operator for Autoregressive Forecasting on Irregular Graphs

Subashree Venkatasubramanian, David A. Barajas-Solano, Chuyang Liu et al. (+2 more)

We introduce TWIG (Time-Causal Wavelet Operator for Irregular Graphs), a graph-native neural operator for autoregressive surrogate modeling on static irregular graphs. TWIG transforms each node history into causal multiscale temporal features that separate recent variation from progressively slower memory components, then propagates these features through graph-wavelet operator blocks with gated pointwise channel mixing. The architecture is causal by construction and designed for closed-loop forecasting, where predictions are recursively reused as future inputs. We evaluate TWIG on three irregular-domain forecasting problems spanning regional diffusion, three-dimensional subsurface hydrology, and aerodynamic flow, with graphs ranging from 400 to 5,233 nodes and model capacities from approximately 70k to 10M parameters. TWIG achieves the lowest aggregate rollout errors on the subsurface-hydrology and regional-diffusion benchmarks and ranks second on the 10M-parameter aerodynamic-flow benchmark, behind the GPS Transformer. Across all three settings, TWIG consistently outperforms the corresponding non-time-causal Graph WNO baseline. These results demonstrate that TWIG provides an effective and scalable approach to stable autoregressive forecasting of dynamical fields on irregular graphs.
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All authors Subashree Venkatasubramanian, David A. Barajas-Solano, Chuyang Liu, Daniel M. Tartakovsky, Dipankar Dwivedi

Machine Learning

Augmenting PID Control with Deep Reinforcement Learning: A Hybrid Approach to the Industrial Benchmark

Zhengyang Gu, Joseph E. Hernandez, John Burtenshaw et al. (+3 more)

As industrial processes grow in complexity, traditional Proportional-Integral-Derivative (PID) controllers are often insufficient for handling their non-linear, multi-input dynamics. We propose using advanced Deep Reinforcement Learning (DRL) to prove its advantages in these complex environments. To do this, we rely on the Industrial Benchmark (IB). The IB is a realistic simulation that tests DRL algorithms against the key challenges of industrial applications: high-dimensional state spaces, delayed effects, and conflicting multi-criterial objectives. This testbed highlights DRL's core trade-off: while its final policies can often be unstable, its unique strength is the ability to autonomously discover optimal, non-obvious policies in multi-dimensional spaces where simple controllers fail. In this paper, we propose a novel hybrid PID-RL controller that leverages DRL's discovery capability while ensuring Reliability. After developing a multi-objective reward function to make DRL viable, we use a twin-delayed deep deterministic (TD3) agent as a discovery tool to find the optimal, non-obvious settings for the IB's 'Gain' and 'Shift' parameters. By feeding these discovered parameters to a simple, tuned PID controller, our hybrid model successfully combines all three characteristics: it achieves the optimal Performance and Efficiency of the best DRL agent with the Reliability of a classical controller. This work demonstrates a practical methodology for using DRL to augment, rather than replace, trusted industrial control systems.
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All authors Zhengyang Gu, Joseph E. Hernandez, John Burtenshaw, Sean Scott, Thomas Cook, Chris Couch

Machine Learning

Benchmarking Hybrid Deep Learning Architectures for Predictive Maintenance in Industry 4.0

Zhengyang Gu, Joseph E. Hernandez, Thomas Cook et al. (+3 more)

Predictive maintenance in Industry 4.0 refers to using data from sensors, machines, and production systems to estimate when equipment is likely to fail, so maintenance can be planned before a breakdown occurs [1]. However, a model that predicts maintenance may work perfectly in the lab but fail unexpectedly when applied to real factory data [2]. To solve this "reliability" gap, we evaluated six deep learning architectures across more than 700 experimental runs. We focused on the two dominant approaches in the field: Recurrent Neural Networks (RNNs), which process data step-by-step, like reading a sentence [3], and Transformers, a recent dominant approach, which look at the entire sequence at once to spot important connections [4]. We examined whether Transformers still outperform recurrent neural networks (RNNs) when the data includes noise [5]. We found that while Transformers excelled at tracking stable, slow-moving processes, they tend to overreact to chaotic data, mistakenly taking sensor noise for meaningful signals [6]. We also found that the hybrid method that combines a Long Short-Term Memory (LSTM) layer with a Transformer layer is more resilient to noisy data from factory shops [7]. Functioning as a noise filter, the LSTM smooths out data volatility, allowing the Transformer to focus on the bigger picture without being distracted [8]. The hybrid model did not just improve accuracy; it proved to be significantly more consistent than complex models, delivering reliable predictions regardless of how chaotic the underlying system became.
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All authors Zhengyang Gu, Joseph E. Hernandez, Thomas Cook, John Burtenshaw, Sean Scott, Chris Couch

Computer Vision

Beyond the Leaderboard: Counterfactual Diagnosis of End-to-End and VLA Driving Policies Under Domain Shift

Ruolin Yang, Zilin Huang, Buoyue Wang et al. (+4 more)

End-to-end and vision-language-action (VLA) driving policies are compared by leaderboard rank, but a rank reports an outcome, not the behaviour behind it, so it predicts poorly how a policy will behave at a new site. On six released policies, rank on nuScenes open-loop error or on NAVSIM's leaderboard does not carry over to scenes with a pedestrian near the ego corridor at a new site. We propose a counterfactual check-up: a few hundred real frames, each edited two ways (pedestrian removed, or re-lit by a night-style perturbation), every edit verified by an independent detector, and the change in the planned trajectory read as a diagnosis rather than a score. From these edits two causal axes are read, and five exams built on them separate what a score merges: how far the policy plans to drive, whether seeing the pedestrian buys safety, whether that response scales with danger, whether the plan moves when nothing requires it, and how much an irrelevant lighting change moves it. On 246 NAVSIM near-pedestrian scenes, in the cells where the pedestrian lies on the planned path only 1.9% of responses are genuine avoidance, and under our open-loop protocol the median clearance change is at most 0.03 m and the median change in planned distance at most 0.08 m for every policy. In a pre-registered test from left- to right-hand drive, the exposure and specificity orderings, the lighting verdict and the collision outcome transfer, while point values and the hazard-sensitivity verdict do not. Read as a selection report, the profiles say which policy is safe because it plans short, which covers a human-like distance without yielding, and which is unsteady under a change that requires no reaction, and they price each verdict: most settle within a few dozen frames, hazard sensitivity needs hundreds. Code and edited frames will be released.
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All authors Ruolin Yang, Zilin Huang, Buoyue Wang, Zhengyang Wan, Yuhao Luo, Zihao Sheng, Sikai Chen

Cosmology and Nongalactic Astrophysics

Hunting Thermal Relics in the DESI DR1 Ly$\alpha$ Forest

Emanuelly Silva, Artur Ladeira, Rafael C. Nunes et al. (+1 more)

We investigate constraints on additional relativistic species and thermal sterile neutrinos using the DESI DR1 one-dimensional Lyman-$\alpha$ forest power spectrum, combined with Planck 2018 CMB and DESI DR2 BAO measurements. We consider both the $\Lambda$CDM+$N_{\rm eff}$ extension and a thermal with a different-temperature sterile-neutrino (DTS) scenario, in which the sterile relic can be colder than the standard neutrino background. We first validate the DESI two-parameter $P_{\rm 1D}$ compression for the DTS model, finding that the residual cosmological dependence not captured by the compressed parameters remains below 0.15%. No significant evidence for additional radiation or a sterile component is found. For $\Lambda$CDM+$N_{\rm eff}$, we obtain $N_{\rm eff}<3.41$ at 95% credibility from CMB+DESI-BAO+DESI-$P_{\rm 1D}$. In the DTS scenario, the full CMB+DESI-BAO+DESI-$P_{\rm 1D}$ combination yields the stringent bound $m_s^{\rm eff}<0.061\,{\rm eV}$, highlighting the complementarity of BAO and Lyman-$\alpha$ information in constraining the massive sterile abundance. We further interpret the allowed $\Delta N_{\rm eff}$ in terms of thermal light relics, deriving lower limits on their decoupling temperatures that reach the QCD epoch.
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All authors Emanuelly Silva, Artur Ladeira, Rafael C. Nunes, Eleonora Di Valentino

Mesoscale and Nanoscale Physics

Vanadium doping induced valley asymmetries in WS$_2$ monolayers

Frederico B. Sousa, Boyang Zheng, Elizabeth Grace Houser et al. (+10 more)

Transition metal dichalcogenide (TMD) monolayers offer an innovative platform for encoding and manipulating information through the valley degree of freedom. While unique valley-related physical phenomena have been reported so far, practical applications still require advanced control over the valley polarization efficiency and the valley Zeeman effect. Recently, the introduction of spin-polarized metal atoms as substitutional defects was reported to break the time-reversal symmetry in TMD monolayers, consequently inducing a room-temperature ferromagnetic ordering and enhancing the valley-dependent optical responses. Here, we report valley asymmetries for vanadium-doped WS$_2$ monolayers. With a given magnetic polarization, one valley exhibits larger Zeeman slope and degree of circular polarization than the other valley. Additionally, the overall degree of circular polarization in the doped samples is approximately twice that of the pristine WS$_2$ monolayer. Density functional theory calculations in the doped structure show that different energy shifts in conduction band edges due to spin-dependent hybridization lead to different exciton energies between valleys, which is consistent with the experimental observations. Our results pave the way for valleytronic technologies based on defect-engineered two-dimensional materials.
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All authors Frederico B. Sousa, Boyang Zheng, Elizabeth Grace Houser, Paulo E. Faria Junior, Zhuohang Yu, Alessandra Ames, Gabriel A. D. Souza, Mingzu Liu, Gilmar Eugenio Marques, Leandro M. Malard, Mauricio Terrones, Vincent H. Crespi, Marcio D. Teodoro

Cellular Automata and Lattice Gases

Gliders on Aperiodic Monotilings: Cellular Automata on the Hat and Spectre

James Edmond

The hat and spectre monotiles, discovered in 2023, tile the plane only aperiodically. Cellular automata are studied here on patches generated by finite-state transducers, so that every experiment regenerates deterministically from a small record. Within edge-adjacency semi-totalistic rules, exhaustive and evolutionary searches find only mortal travelers: gliders are absent. Guided by a reproduction of the known Penrose-tiling glider, the rule space is extended to vertex neighborhoods and to priority-table rules whose non-quiescent states are visible to neighbors. Evolutionary search then discovers gliders on both monotilings; tracked by a sliding window that regenerates the patch along the flight, they travel one million rings at constant speed and heading. All headings are quantized, to millidegrees, onto a six-spoke compass: the fast axes of the tiling's graph metric. An ablation shows both rule-space extensions are individually necessary. All results replay exactly in an accompanying interactive essay.
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2609.22579 · 18 Sep · 32 pages, 11 figures, 8 tables. v2: priority claim withdrawn; a note added credits Trevorrow's HatLife (2023), whose worms are gliders in this paper's sense. Companion interactive essay (every result replayable live): https://offlattice.org/monotile/essay/ . Code and records: https://github.com/jamesedmond/monotile-ca (archived at doi:10.5281/zenodo.22836247)

Abstract PDF

Physics Education

Artificial Intelligence Driven Physics Assignments using Context Prompts

Miguel Rodriguez and Peter Wulff

Generative artificial intelligence (Gen AI) is increasingly shaping how students access information and engage with physics content, yet many instructional approaches still assume a pre-AI classroom. In this paper, we describe a practical framework for integrating Gen AI into physics instruction through the use of context prompts: instructor-designed prompts that define the role, task, and boundaries of the AI interaction. We focus on AI-supported exploration assignments implemented in an asynchronous introductory physics course enrolling approximately 70 students. In these activities, students used AI as a guided tutor to explore selected topics, ask follow-up questions, request explanations and analogies, and connect physics concepts to their personal interests and everyday experiences. We argue that this structure can help move students beyond answer-seeking and toward more dialogic and personally meaningful engagement with course content. We also discuss reflection as a natural extension of the same framework, while distinguishing it from the implemented exploration activities described here. Finally, we highlight practical considerations that emerged in use, including uneven access to AI platforms, grading workload, the need to teach students how to engage AI conversationally, and the growing importance of AI literacy in physics education.
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High Energy Astrophysical Phenomena

Resolving the Galactic Center Region's Gamma-Ray Emission and Searching for its Neutrino Counterpart with HAWC and IceCube

R. Alfaro, M. Araya, J. Arteaga-Velázquez et al. (+501 more)

The Galactic Center (GC) is a prime candidate for petaelectronvolt cosmic-ray acceleration, with gamma-ray emission observed by the High Altitude Water Cherenkov (HAWC) Observatory extending beyond 100~TeV. Using $\sim$2860 days of HAWC data with improved machine-learning gamma/hadron separation, we present the first spatially resolved model of the GC region at the highest gamma-ray energies. The emission is resolved into a point source, HAWC J1745-2857, and a Galactic diffuse emission component that was not significant in previous HAWC analyses. With the diffuse emission accounted for, the point-source spectrum extends beyond 100~TeV with no evidence of a cutoff, showing that the PeVatron interpretation of the GC does not arise from unresolved diffuse emission. Assuming a hadronic origin, we construct the corresponding neutrino signal template and search for it in 12 years of IceCube muon-track data. No significant neutrino excess is found, and we report the first upper limit on the high-energy neutrino flux associated with the multi-component spatial model of the GC derived from HAWC data. The limit is approximately 12 times the nominal neutrino flux predicted from the HAWC gamma-ray model under a hadronic interpretation. Although the limit does not yet test the optically thin hadronic scenario, it quantifies the sensitivity required to test the hadronic origin of the GC PeVatron with future neutrino observations.
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All authors R. Alfaro, M. Araya, J. Arteaga-Velázquez, R. Babu, P. Bangale, A. Bernal, K. Caballero-Mora, T. Capistrán, A. Carramiñana, F. Carreón, S. Casanova, U. Cotti, J. Cotzomi, S. Coutiño de León, C. de León, E. De la Fuente, N. Di Lalla, R. Diaz Hernandez, M. DuVernois, K. Engel, T. Ergin, C. Espinoza, N. Fraija, J. García-González, F. Garfias, N. Ghosh, S. Giri, A. Gonzalez Muñoz, M. González, J. González, J. Goodman, S. Groetsch, J. Gyeong, J. Harding, I. Herzog, D. Huang, F. Hueyotl-Zahuantitla, P. Hüntemeyer, A. Iriarte, S. Kaufmann, D. Kieda, K. Leavitt, J. Lee, H. León Vargas, A. Longinotti, G. Luis-Raya, K. Malone, O. Martinez, J. Martínez-Castro, H. Martínez-Huerta, J. Matthews, P. Miranda-Romagnoli, P. Mirón-Enriquez, J. Morales-Soto, E. Moreno, M. Mostafá, M. Najafi, L. Nellen, Y. Niroula, M. Nisa, R. Noriega-Papaqui, M. Osorio-Archila, E. Ponce, Y. Pérez Araujo, E. Pérez-Pérez, D. Rosa-González, M. Roth, A. Sandoval, M. Schneider, J. Serna-Franco, S. Shankar, A. Smith, Y. Son, R. Springer, O. Tibolla, K. Tollefson, I. Torres, R. Torres-Escobedo, E. Varela, L. Villaseñor, H. Wu, X. Wang, Z. Wang, I. Watson, S. Yu, S. Yun-Cárcamo, X. Zhang, H. Zhou, for the HAWC collaboration, R. Abbasi, M. Ackermann, J. Adams, J. Aguilar, M. Ahlers, J. Alameddine, S. Ali, N. Amin, K. Andeen, C. Argüelles, S. Athanasiadou, S. Axani, X. Bai, A. Balagopal V., S. Barwick, V. Basu, R. Bay, J. Beatty, J. Becker Tjus, J. Beise, C. Bellenghi, S. Benkel, S. BenZvi, D. Berley, E. Bernardini, D. Besson, E. Blaufuss, L. Bloom, S. Blot, F. Bontempo, J. Book Motzkin, C. Boscolo Meneguolo, S. Böser, O. Botner, J. Braun, B. Brinson, Z. Brisson-Tsavoussis, L. Brusa, R. Burley, D. Butterfield, K. Carloni, J. Carpio, N. Chau, Y. Chen, Z. Chen, D. Chirkin, S. Choi, A. Chubarov, B. Clark, D. Coloma Borja, A. Connolly, J. Conrad, D. Cowen, C. De Clercq, J. DeLaunay, D. Delgado, T. Delmeulle, S. Deng, P. Desiati, K. de Vries, G. de Wasseige, T. DeYoung, J. Díaz-Vélez, S. DiKerby, T. Ding, M. Dittmer, A. Domi, L. Draper, L. Dueser, D. Durnford, K. Dutta, M. DuVernois, T. Ehrhardt, L. Eidenschink, A. Eimer, C. Eldridge, P. Eller, E. Ellinger, D. Elsässer, R. Engel, H. Erpenbeck, W. Esmail, S. Eulig, J. Evans, P. Evenson, K. Fan, K. Fang, K. Farrag, A. Fattorini, A. Fazely, A. Fedynitch, N. Feigl, C. Finley, D. Fox, A. Franckowiak, S. Fukami, P. Fürst, J. Gallagher, A. Garcia, M. Garcia, E. Genton, L. Gerhardt, A. Ghadimi, C. Glaser, T. Glüsenkamp, J. Gonzalez, S. Goswami, A. Granados, D. Grant, S. Gray, S. Griffin, S. Griswold, K. Groth, D. Guevel, C. Günther, P. Gutjahr, C. Ha, A. Hallgren, F. Halzen, M. Handt, K. Hanson, J. Hardin, A. Harnisch, P. Hatch, A. Haungs, J. Häußler, K. Helbing, J. Hellrung, B. Henke, L. Hennig, F. Henningsen, L. Heuermann, R. Hewett, N. Heyer, S. Hickford, A. Hidvegi, C. Hill, G. Hill, R. Hmaid, K. Hoffman, A. Hollnagel, D. Hooper, S. Hori, K. Hoshina, M. Hostert, W. Hou, M. Hrywniak, T. Huber, K. Hultqvist, K. Hymon, A. Ishihara, W. Iwakiri, M. Jacquart, S. Jain, O. Janik, M. Jansson, M. Jin, N. Kamp, D. Kang, W. Kang, A. Kappes, L. Kardum, T. Karg, A. Karle, A. Katil, M. Kauer, J. Kelley, B. Kern, M. Khanal, A. Khatee Zathul, A. Kheirandish, T. Kim, H. Kimku, F. Kirchner, J. Kiryluk, C. Klein, S. Klein, Y. Kobayashi, S. Koch, A. Kochocki, R. Koirala, H. Kolanoski, T. Kontrimas, L. Köpke, C. Kopper, D. Koskinen, P. Koundal, M. Kowalski, T. Kozynets, A. Kravka, N. Krieger, T. Krishnan, K. Kruiswijk, E. Krupczak, E. Kun, N. Kurahashi, C. Lagunas Gualda, L. Lallement Arnaud, M. Larson, F. Lauber, J. Lazar, K. Leonard DeHolton, A. Leszczyńska, C. Li, J. Liao, C. Lin, Q. Liu, Y. Liu, M. Liubarska, C. Love, L. Lu, F. Lucarelli, W. Luszczak, Y. Lyu, M. Macdonald, E. Magnus, Y. Makino, E. Manao, S. Mancina, A. Mand, I. Mariş, S. Marka, Z. Marka, I. Martinez-Soler, R. Maruyama, J. Mauro, F. Mayhew, F. McNally, K. Meagher, A. Medina, M. Meier, Y. Merckx, L. Merten, J. Mitchell, L. Molchany, S. Mondal, T. Montaruli, R. Moore, Y. Morii, A. Mosbrugger, D. Mousadi, E. Moyaux, T. Mukherjee, M. Nakos, U. Naumann, R. Neshat, L. Neste, M. Neumann, K. Noda, A. Noell, A. Novikov, A. Obertacke, V. O'Dell, A. Olivas, R. Orsoe, J. Osborn, E. O'Sullivan, B. Owens, V. Palusova, H. Pandya, A. Parenti, C. Parisel, N. Park, V. Parrish, E. Paudel, L. Paul, C. Pérez de los Heros, T. Pernice, T. Petersen, J. Peterson, S. Pick, M. Plum, A. Pontén, V. Poojyam, B. Pries, R. Procter-Murphy, G. Przybylski, L. Pyras, C. Raab, J. Rack-Helleis, N. Rad, M. Ravn, K. Rawlins, Z. Rechav, A. Rehman, R. Reimann, I. Reistroffer, E. Resconi, C. Rho, W. Rhode, L. Ricca, B. Riedel, A. Rifaie, E. Roberts, S. Rodan, M. Rongen, A. Rosted, C. Rott, T. Ruhe, L. Ruohan, D. Ryckbosch, J. Saffer, D. Salazar-Gallegos, P. Sampathkumar, A. Sandrock, G. Sanger-Johnson, M. Santander, S. Sarkar, M. Scarnera, M. Schaufel, H. Schieler, S. Schindler, L. Schlickmann, B. Schlüter, F. Schlüter, N. Schmeisser, T. Schmidt, F. Schmitt, A. Scholz, F. Schröder, S. Schwirn, S. Sclafani, D. Seckel, L. Seen, M. Seikh, S. Seunarine, P. Sevle Myhr, R. Shah, S. Shah, A. Sharma, S. Shefali, N. Shimizu, M. Shin, R. Singh, B. Skrzypek, R. Snihur, J. Soedingrekso, D. Soldin, P. Soldin, G. Sommani, D. Song, C. Spannfellner, G. Spiczak, C. Spiering, J. Stachurska, M. Stamatikos, T. Stanev, T. Stezelberger, T. Stürwald, T. Stuttard, G. Sullivan, I. Taboada, S. Ter-Antonyan, A. Terliuk, A. Thakuri, P. Thelen, M. Thiesmeyer, W. Thompson, J. Thwaites, W. Tian, S. Tilav, J. Torres, S. Toscano, D. Tosi, K. Upshaw, A. Vaidyanathan, N. Valtonen-Mattila, J. Valverde, J. Vandenbroucke, T. Van Eeden, N. van Eijndhoven, L. Van Rootselaar, J. van Santen, J. Vara, F. Varsi, M. Velazquez, M. Venugopal, M. Vereecken, S. Vergara Carrasco, S. Verpoest, A. Vijai, J. Villarreal, C. Walck, A. Wang, E. Warrick, C. Weaver, P. Weigel, A. Weindl, J. Weldert, A. Wen, C. Wendt, J. Werthebach, M. Weyrauch, N. Whitehorn, C. Wiebusch, D. Williams, L. Witthaus, J. Woodward, G. Wrede, X. Xu, J. Yanez, Y. Yao, E. Yildizci, S. Yoshida, F. Yu, S. Yu, T. Yuan, A. Zander Jurowitzki, A. Zegarelli, S. Zhang, Z. Zhang, P. Zhelnin, P. Zilberman, C. Zilleruelo Cañas, M. Zimmermann for the IceCube collaboration

Optimization and Control

Scalable Incremental Robustness Analysis of Neural Network Feedback Systems

Zichen Wang, Peter Seiler, Geir Dullerud et al. (+1 more)

Semidefinite programming (SDP) certificates for feedback systems containing deep neural networks (NNs) typically scale with the total number of neurons, whereas small-gain tests are scalable but can be highly conservative. This paper develops a unified and scalable framework for incremental robust stability and performance analysis of feedback interconnections involving high-dimensional NNs and unmodeled dynamics. By combining a structured decomposition of the full-order SDP condition with scalable Lipschitz constant estimation algorithms, we derive reduced verification conditions that certify incremental convergence and incremental $\ell_2$-gain bounds. The dimensions of the resulting control-analysis linear matrix inequalities (LMIs) depend only on the widths of the last two network layers and are independent of network depth. The framework preserves the coupling between the plant and the NN, with the incremental small-gain condition recovered as a special case. To further reduce conservatism, we develop a multi-round alternating update scheme that iteratively refines the coupling variables while preserving scalability. Numerical experiments show that the proposed framework achieves state-of-the-art incremental $\ell_2$-gain bounds for large-scale NN feedback systems.
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All authors Zichen Wang, Peter Seiler, Geir Dullerud, Bin Hu

Differential Geometry

Elastic BB knots are multifold circles

Philipp Reiter and Heiko von der Mosel

We study elastic knots obtained by minimizing the bending energy of a unit loop together with a small multiple of ropelength. We assume a generalized Fáry-Milnor inequality on the $C^1$-boundary of a knot class: every $H^2$-limit curve in the $C^1$-closure has total curvature at least $2\pi$ times the bridge index. Under this assumption we prove that every elastic knot in a one-component BB knot class, that is, a class whose bridge and braid indices coincide, is the round circle covered precisely that many times. The proof does not differentiate the nonsmooth ropelength functional. A minimal closed braid is contracted in the fibres of a solid torus, producing a family of comparison curves with quadratic bending-energy excess and thickness of linear order. This yields a lower thickness bound for the regularized minimizers. Variations on an intermediate scale then give free stationarity of the limiting curve for the normalized bending energy. Constant curvature and free stationarity reduce the classification to a linear distributional ordinary differential equation.
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Atmospheric and Oceanic Physics

Diffusion-Based Super-Resolution of Adriatic Sea Oceanographic Fields

Rajat Srivastava, Muhammad Sarmad, Emanuele Mele et al. (+3 more)

High-resolution oceanographic fields are critical for resolving mesoscale and sub-mesoscale coastal dynamics, yet their generation remains constrained by both computational cost and observational sparsity. We present OcDiffSR, a conditional denoising diffusion probabilistic model (DDPM) for oceanographic super-resolution that reconstructs high-resolution sea-surface fields from coarse-resolution reanalysis inputs. The model is trained on ten years (2011-2020) of paired low-resolution (GLORYS12V1, 1/12) and high-resolution (Mediterranean Sea Physics Reanalysis, Med MFC, 1/24) data, and evaluated on an independent test year (2009) over the Adriatic Sea. OcDiffSR employs a conditional U-Net augmented with multi-scale low-resolution encoders, cross-attention bottleneck layers, and sinusoidal seasonal embeddings via Feature-wise Linear Modulation (FiLM), enabling joint super-resolution of sea-surface temperature (SST), salinity (SSS), and horizontal velocity components with visually coherent circulation patterns. Benchmarked against bilinear interpolation and the state-of-the-art residual diffusion model CorrDiff, OcDiffSR achieves substantially lower reconstruction errors for scalar fields (RMSESST=0.477 C, RMSESSS=0.346 psu), near-unity Pearson correlation (PCC >= 0.999), and high structural similarity (SSIM >= 0.964). For dynamical vector fields, OcDiffSR outperforms both baselines in absolute error and spatial coherence, though moderate correlation (PCC = 0.64) reflects the intrinsic stochasticity of oceanic velocity fields. Daily and monthly evaluations confirm temporal robustness across all seasons. These results establish OcDiffSR as a reliable framework for high-fidelity oceanographic downscaling and reanalysis enhancement, producing fields that are visually consistent with known ocean dynamics.
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All authors Rajat Srivastava, Muhammad Sarmad, Emanuele Mele, Massimo Cafaro, Marco Pulimeno, Italo Epicoco

Cryptography and Security

Zero-Trust Authorization and Discovery for Enterprise MCP

Huan Li, Yuwei Wang and Srinivasan Manoharan

LLM agents translate natural-language context, which may include attacker-controlled text, into privileged tool calls, so authorization must remain effective even when an agent is prompt-injected or adversarially steered. The Model Context Protocol (MCP) has become a widely adopted interface for this boundary, yet its official SDKs' authentication and authorization primitives fall short of enterprise zero-trust requirements, most acutely a dual-persona model in which one server must serve human users (corporate SSO) and automated agents (service-account credentials on a different header). We conduct a systematic gap analysis of six surveyed MCP SDKs (Python, TypeScript, Go, Rust, C#, Swift) and identify three structural shortcomings: credential extraction bound to a single Authorization header, complicating dual-persona deployment without custom middleware; the absence of pre-authentication tool discovery; and the lack of fine-grained per-tool authorization in the base SDKs. We close these gaps with composable extensions to FastMCP: cross-header credential normalization for enterprise deployments serving both human and service-account callers, cached token verification across heterogeneous IdPs, an unauthenticated metadata endpoint for credential-free registry discovery, and permission-filtered tool visibility kept consistent with per-tool invocation enforcement by a single declarative annotation, all without modifying the protocol or SDK internals. Across four frontier LLMs over 2160 attempts, an in-body-check-only server still exposes forbidden tools (152/720, 21.1%), whereas permission-aware visibility drives the rate to 0/720; visibility-only filtering remained bypassable by scripted clients, while models referenced the hidden tool by name in up to 94% of settings when inferable from the prompt, confirming that discovery controls cannot replace invocation-time enforcement.
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Quantum Physics

Modular fault-tolerant quantum computing on a non-CSS code

Robert Freund, Friederike Butt, César Benito et al. (+6 more)

Modularization promises to break down the design and implementation complexity of large scale quantum processors into smaller manageable subtasks. In this approach, quantum channels, realized for instance through physical rerouting of qubits or quantum teleportation, connect multiple modules. Each of those modules hosts a subset of qubits, e.g. multiple logical qubits, and provides quantum operations on them. In this work, we implement for the first time all logical operations required for modular fault-tolerant universal quantum computing with a non-Calderbank-Shor-Steane (CSS) code, the perfect $[[5, 1, 3]]$ code, on a trapped-ion quantum computer. This code is the smallest quantum error-correcting (QEC) code capable of correcting any single-qubit error, making it a compact alternative to larger CSS codes. We demonstrate logical state teleportation and a full suite of fault-tolerant operations required for universal logical control, including logical state preparation, QEC with real-time feedback, logical measurements, magic-state preparation, logical entangling operations, and magic-state injection. Moreover, we characterize the logical spectator error picked up by idling logical qubits during quantum operations on distinct qubit registers and demonstrate a logical Pauli quantum process tomography that minimizes required sampling resources for logical tomography.
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All authors Robert Freund, Friederike Butt, César Benito, Ivan Pogorelov, Marcel Meyer, Alex Steiner, Alejandro Bermudez, Markus Müller, Thomas Monz

Dynamical Systems

Trace formula for billiard flow on surfaces with concave boundary

Alain Kangabire

We study grazing closed trajectories of the billiard flow $\varphi^t$ on a compact surface $(\Sigma,g)$ with concave boundary. Under a non-degeneracy condition, which is satisfied for example when $(\Sigma,g)$ has negative sectional curvature, we compute the trace of a regularized pullback $E_{\epsilon}(\varphi^t)^* E_{\epsilon}$ near a closed trajectory grazing once, which is an analogue of the Atiyah–Bott–Guillemin trace formula for closed billiard trajectories.
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High Energy Physics (Phenomenology)

Probing light axion-like particles in vector boson fusion at CMS with data parking and scouting

Sena Durgut, Mariel Peczak, Gonzalo Alonso-Álvarez et al. (+4 more)

Axion-like particles (ALPs) with masses between 10 MeV and 10 GeV and moderately small couplings sit in an experimental blind spot. They decay too fast for intensity-frontier experiments and are too feebly coupled and too light for conventional collider searches. The LHC produces them at substantial rates through vector boson fusion (VBF), the dominant production mode for electromagnetically coupled ALPs, but two obstacles keep this signal out of reach. The events are soft, so trigger thresholds discard most of them, and the Lorentz boost merges the two decay photons into a single calorimeter deposit. We show that the Compact Muon Solenoid (CMS) experiment can overcome both by combining its data-acquisition strategies with the tracker-based reconstruction of merged photon pairs. Data parking on the VBF jet topology in Run 3 (312 fb$^{-1}$) and trigger-level data scouting at the High-Luminosity LHC (HL-LHC, 3 ab$^{-1}$) remove the need for a threshold on the photons. Photons that convert to electron-positron pairs in the silicon tracker resolve the merged pair, since the tracker measures their direction far more finely than the calorimeter granularity. Reconstructing the ALP decay vertex from the conversion tracks removes the prompt backgrounds but not the long-lived $K_L\to\gamma\gamma$. In Run 3, where the full event is recorded, the merged diphoton invariant mass confines the $K_L$ to a narrow window around its own mass. In the scouting stream, where only trigger-level information survives, the diphoton $p_T$, the conversion tracks, and the hadronic activity in the event take over this role. We project that the parked Run 3 data, already recorded, reach a region of the $(m_a, g_{a\gamma\gamma})$ plane that no measurement has probed. Level-1 trigger data scouting at the HL-LHC extends that reach by roughly an order of magnitude in both coupling and mass.
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All authors Sena Durgut, Mariel Peczak, Gonzalo Alonso-Álvarez, Chiara Amendola, Matteo Cremonesi, Joerg Jaeckel, Matteo Marchegiani

Data Structures and Algorithms

When Shall We $k$ Meet Again? Tight Algorithms for Diameter and Radius under the Meet Distance

Yael Kirkpatrick, John Kuszmaul, Merey Temirzinova et al. (+1 more)

Finding an optimal meeting point for a collection of agents on a directed graph is a classical problem studied in the context of network analysis, operations research and computational geometry. In this work, we use the two objectives of optimal meeting points examined in the literature to study two notions of meet-distance: $d^{\max}(u,v)$, the minimum over all meeting points $w$ of $\max(d(u,w), d(v,w))$; and $d^+(u,v)$, the minimum over all meeting points of $d(u,w) + d(v,w)$. These values measure the minimum time and minimum total distance required for two agents to meet. We initiate the fine-grained study of fundamental graph parameters under the two notions of meet-distance, namely the diameter, radius and eccentricities. For general directed graphs, we give an $\tilde{O}(m\sqrt{n})$ time algorithm for computing a 2-approximation to both notions of meet-diameter and show that this result is optimal under SETH. In contrast, we show that such a result is unattainable for the meet-radius as any finite approximation requires quadratic time under the Hitting Set Conjecture. For directed acyclic graphs, we obtain stronger results. We compute the meet$^{\max}$-diameter exactly in linear time and give a linear-time $2$-approximation for the meet$^{+}$-diameter. We complement the latter with a quadratic-time lower bound for any $(3/2-\varepsilon)$-approximation under SETH, yielding a separation between the two meet-distance objectives. Finally, we study the generalized meet-distance of $k$-tuples of vertices. For every positive integer $\ell$, we reduce the problem of $\ell$-approximating the $k$-point meet-diameter to computing an exact meet-diameter on smaller tuples, obtaining an $\ell$-approximation in time \[ O\!\left( mn+ \ell \left\lceil k^{1/\ell}\right\rceil n^{\left\lceil k^{1/\ell}\right\rceil+1} \right). \]
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All authors Yael Kirkpatrick, John Kuszmaul, Merey Temirzinova, Virginia Vassilevska Williams

Information Theory

Fourier Ratio and Restricted Isometry via Entropic Descent

Will Burstein, Alex Iosevich and Ben Krause

In this second paper on descent methods as proof mechanisms in harmonic analysis (the first treated Bourgain's $\Lambda(p)$ selection theorem), entropic mirror descent gives an improved restricted isometry bound, improving sampling and recovery bounds in the Fourier Ratio program. Let $H$ be a complex $n\times n$ matrix with $H^*H=nI$ and $|H_{ij}|=1$. For fixed $0<\varepsilon<\frac14$ and $A_0>0$, independent Bernoulli row selection with expected cardinality $C_{\varepsilon,A_0}r\log\frac{2en}{r}\log(2r)\leq m\leq n/2$ preserves, after normalization by $\sqrt m$, the squared norm of every complex vector $y$ with $\|y\|_1\leq\sqrt r\|y\|_2$ within a factor $1\pm\varepsilon$, with failure probability at most $Cn^{-A_0}$. This includes every $r$-sparse vector and also fully supported ones; support size enters only through this inequality. For $y=\widehat f$ the condition is exactly $\operatorname{FR}(f)^2\leq r$, where $\operatorname{FR}(f)=\|\widehat f\|_1/\|\widehat f\|_2$, giving uniform energy sampling and approximate recovery even for signals with full Fourier support. The same holds for a uniform subset of prescribed cardinality, and for discrete Fourier and real Hadamard matrices. At fixed accuracy the bound removes one sparsity logarithm from the earlier count and replaces $\log n$ by $\log\frac{2en}{r}$; for Walsh matrices it matches, up to constants, the lower bound of Błasiok et al.\ in their range. One relative-entropy potential controls the corrections of an amplitude predictor at every scale; counting them on the symmetric difference of two samples gives the uniform estimate. We also prove the sufficient bound $C_{A_0}\varepsilon^{-5}r\log\frac{2en}{r}\log\frac{2r}{\varepsilon}$, and stable sparse recovery from $Cs\log\frac{2en}{s}\log(2s)$ measurements, with error controlled by the noise and the best $s$-term approximation.
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