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01.
arXiv (CS.AI) 2026-06-16

Automated ultrasound doppler angle estimation using deep learning

arXiv:2508.04243v2 Announce Type: replace-cross Abstract: Angle estimation is an important step in the Doppler ultrasound clinical workflow to measure blood velocity. It is widely recognized that incorrect angle estimation is a leading cause of error in Doppler-based blood velocity measurements. In this paper, we propose a deep learning-based approach for automated Doppler angle estimation. The approach was developed using 2100 human carotid ultrasound images including image augmentation. Five pre-trained models were used to extract images features, and these features were passed to a custom shallow network for Doppler angle estimation. Independently, measurements were obtained by a human observer reviewing the images for comparison. The mean absolute error (MAE) between the automated and manual angle estimates ranged from 3.9{\deg} to 9.4{\deg} for the models evaluated. Furthermore, the MAE for the best performing model was less than the acceptable clinical Doppler angle error threshold thus avoiding misclassification of normal velocity values as a stenosis. The results demonstrate potential for applying a deep-learning based technique for automated ultrasound Doppler angle estimation. Such a technique could potentially be implemented within the imaging software on commercial ultrasound scanners.

02.
arXiv (CS.AI) 2026-06-11

Reliability-Calibrated Edge-IoT Early Fault Warning for Rotating Machinery with a Physics-Guided Tiny-Mamba Transformer

arXiv:2601.21293v3 Announce Type: replace-cross Abstract: Industrial Internet of Things (IIoT) systems increasingly rely on distributed vibration sensing to support predictive maintenance of rotating machinery. In practical deployments, however, raw signal upload is costly and alarm decisions must be made locally under limited computation, changing operating conditions, and strict nuisance-alarm budgets. This paper presents a reliability-calibrated edge-IoT early-warning framework, in which a compact Physics-Guided Tiny-Mamba Transformer (PG-TMT) acts as the representation module and an extreme value theory (EVT) layer converts streaming anomaly scores into event-level alarm episodes. PG-TMT combines a depthwise-separable convolutional stem, a Tiny-Mamba state-space branch, and a lightweight local Transformer to capture transient, long-horizon, and multichannel degradation cues under batch-size-one inference. To improve auditability, temporal attention is projected to the frequency domain and softly aligned with analytical bearing fault-order bands. EVT calibration, dual-threshold hysteresis, and trimmed-tail fitting provide controllable false-alarm intensity even when healthy calibration data are imperfect. Experiments on CWRU, Paderborn, XJTU-SY, and an industrial pilot demonstrate that the proposed framework improves PR-AUC, reduces detection delay under a controlled nuisance-alarm budget, and remains robust to structured interference, metadata uncertainty, compound fault mixtures, and domain transfer. With a sub-1 MB footprint and Jetson p99 latency below 7 ms, the framework supports calibrated and interpretable early warnings for IIoT predictive maintenance.

03.
arXiv (CS.LG) 2026-06-12

To GAN or Not To GAN: Segmentation Analysis on Mars DEM

arXiv:2606.13252v1 Announce Type: new Abstract: To better understand Martian Surface, which is needed to enable Rovers navigate Mars with ease, it is necessary to be able to determine the location of mounds. Detecting and studying these morphologies can also help us find evidence of extraterrestrial life, in this case, more specifically, water or signs of life conducive environments. Detection of mounds was done by manually mapping morphological parameters onto Digital Elevation Models. This paper solves the problem by automatically detecting and or predicting mounds on Mars using Neural Network based Semantic Segmentation methodologies. This is done by using supervised semantic segmentation model and generative adversarial approach. A comparison of the approaches shows that adding extra artificially generated data did not improve the result.

04.
arXiv (CS.CV) 2026-06-17

When LLMs Analyze Scars: From Images to Clinically-Meaningful Features

Medical image classification faces a fundamental dilemma: while deep learning models achieve remarkable performance at scale, real-world clinical scenarios often suffer from severe data scarcity due to annotation costs, privacy constraints, and disease rarity. This challenge is particularly pronounced in pathological scar classification, where differentiating keloids from hypertrophic scars requires subtle expert knowledge and labeled images are extremely limited. We propose a novel paradigm that repositions large language models (LLMs) as knowledge-driven feature engineers rather than end-to-end classifiers. We call this framework ScaFE (Scar Feature Engineering). Our key insight is that LLMs encode rich medical knowledge that can be externalized as executable feature extraction code, enabling the transformation of high-dimensional images into low-dimensional, clinically interpretable representations. Specifically, we prompt an LLM with established scar assessment criteria to generate deterministic Python code that extracts features aligned with clinical scoring systems such as the Vancouver Scar Scale. Our approach offers three key advantages: (1) data efficiency, achieving robust performance with limited training samples by decoupling knowledge acquisition from statistical learning; (2) privacy preservation, as raw images are processed locally without exposure to external LLMs; and (3) interpretability, through explicit features grounded in clinical reasoning. Extensive experiments on scar classification demonstrate that our method consistently outperforms end-to-end deep learning baselines or using LLMs as black-box classifiers under limited data conditions, establishing a promising direction for integrating LLMs into data-efficient and clinically transparent medical AI systems.

05.
Nature Medicine 2026-06-10

Brain Health for Economic Resilience: a data-driven framework for the brain-positive economic transition

Announced in this Comment and in collaboration with Nature Medicine is the convening of the Brain Health for Economic Resilience Commission, a global, transdisciplinary effort to define, measure and operationalize brain health and cognitive capacity as foundational drivers of economic resilience.

06.
arXiv (math.PR) 2026-06-16

Super-Arrhenius relaxation of the triangular plaquette model in any dimension

arXiv:2606.16259v1 Announce Type: new Abstract: Consider the following plaquette model from statistical physics: a lamp lies at every vertex of the triangular lattice and a switch lies at every even vertex of the (bipartite) dual hexagonal lattice. Each switch toggles the three lamps on its face. The energy of a configuration is the number of ON lamps. For the Glauber dynamics associated with the Gibbs measure defined by this Hamiltonian at any inverse temperature $\beta>0$, we show that, in any dimension $d\ge 2$, the infinite volume relaxation time satisfies \[e^{\beta^2/C}/C \le T_{\mathrm{rel}}\le Ce^{e^{C\beta}}\] for some $C>0$. Our result entails that the Gibbs measure is unique. The $e^{\beta^2}$ scaling was conjectured by Newman and Moore in 1999 and matches the behaviour of supercritical rooted kinetically constrained models such as the East model, thus recovering fragile glass phenomenology in the absence of kinetic constraints. More precisely, we show that, on a torus of side length $2^k$, when $\beta\to\infty$ and $k/\beta\to0$, we have $T_{\mathrm{rel}}=e^{2\beta k(1+o(1))}$. Quite surprisingly, however, we also prove that, on non-periodic finite domains of size $n\le e^{\beta/C}$ for large $C>0$, we have the much larger asymptotics $\ln T_{\mathrm{rel}}=\beta n^{\Theta(1)}$. The main ingredients of the proofs are new results in extremal and enumerative combinatorics and rely on renormalisation ideas for the dynamics and its groundstates also known as the Ledrappier subshift. We note consequences of our results to geometric group theory (more precisely to the complexity of the word problem for the Baumslag finitely presented group) and to ergodic theory.

07.
arXiv (CS.CV) 2026-06-18

Transformer Geometry Observatory TGO-I: Spectral Geometry Observatory

Despite the widespread adoption of Vision Transformers (ViTs) and their success across numerous computer vision applications, the fundamental understanding of their dimensional and representational geometry remains relatively underexplored. To address this gap, we introduce Transformer Geometry Observatory (TGO), a systematic framework of experiments and analysis pipelines designed to investigate the representational geometry and dynamics of Vision Transformers. TGO-I, the first installment of the framework, focuses on the spectral geometry of ViT representations. Using a ViT-Small/16 model trained on ImageNet-100, we analyze Effective Rank, Stable Rank, Participation Ratio, Spectral Entropy, Spectral Flatness, Spectral Anisotropy, covariance structure, eigenspectra, and singular value spectra throughout training. Our results reveal a consistent increase in dimensional utilization, accompanied by decreasing anisotropy, increasing spectral entropy, increasing participation ratio, and progressively flatter eigenspectra. Contrary to the common intuition that training should concentrate information into a small number of dominant directions, we observe a progressive redistribution of variance across representational dimensions. This phenomenon is particularly pronounced in the final CLS token representation, which exhibits the highest effective dimensionality and lowest anisotropy within the network.

08.
arXiv (math.PR) 2026-06-11

A Hybrid LSMC-PDE Method for Bermudan Option Pricing under the Gatheral Double Mean-Reverting Model

arXiv:2606.11237v1 Announce Type: cross Abstract: We study Bermudan option pricing under the Gatheral Double Mean-Reverting (GDMR) stochastic volatility model. The model features a variance process together with a stochastic long-run mean variance process and allows Constant Elasticity of Variance (CEV)-type exponents in the diffusion coefficients. This model is attractive since it provides a flexible specification for volatility dynamics. However, the pricing of early-exercise derivatives under the GDMR model remains largely unexplored in the literature. To address this challenge, we adapt a Hybrid Least-Squares Monte Carlo-Partial Differential Equation (LSMC-PDE) framework to the GDMR model and provide a detailed model-specific implementation. Conditioning on simulated variance paths, the pricing problem reduces to a one-dimensional problem in the asset price, which is solved by a Fourier-based approach, while the remaining dependence on the variance variables is approximated by least-squares regression. Our numerical experiments demonstrate that the Hybrid LSMC-PDE approach yields accurate pricing estimates and often lower pricing errors than plain LSMC, particularly for low and moderate numbers of simulation paths, showing the benefit of using the model structure in early-exercise option pricing.

09.
arXiv (CS.LG) 2026-06-12

Ride, Track, and Recover: Pilot Randomized Trial of a Wearable Digital Self-Management Intervention During a Veteran Endurance-Cycling Program

arXiv:2606.13529v1 Announce Type: cross Abstract: Post-traumatic stress disorder (PTSD) in veterans is characterized by persistent hyperarousal and comorbid anxiety and depressive symptoms that are difficult to monitor and manage outside clinical settings. Thirteen veterans participating in a Project Hero cycling event in Texas were randomized by computer-generated sequence in a naturalistic setting to two arms: (1) digital intervention plus physical activity, or (2) physical activity only, plus a third at-home monitoring control cohort consisting of 7 veterans selected from the broader Project Hero veteran community. Continuous smartwatch sensing combined heart rate and accelerometer features to detect hyperarousal events, which were confirmed in real time by participants. Weekly self-report measures of anxiety, depression, and PTSD severity were collected. Generalized additive mixed models characterized nonlinear trajectories over time. Baseline-normalized hyperarousal trajectories differed significantly across conditions, with the digital intervention group (n=7) showing structured stabilization compared to late-study escalation in the physical-only group (n=3). Both cycling groups exhibited acute symptom improvements during the endurance event; however, the digital intervention group demonstrated a higher overall maintenance of gains. The at-home control group (n=4) showed gradual symptom declines. Perceived precision of ML detections varied substantially across individuals and was positively associated with symptom severity, with higher-severity participants confirming a greater proportion of detected events. These results suggest that coupling wearable detection with digital self-management tools may support stabilization of hyperarousal and symptom improvement while emphasizing the importance of personalization and human-centered design in wearable mental health systems.

10.
arXiv (quant-ph) 2026-06-24

Teleportation-based quantum state tomography

arXiv:2511.18621v2 Announce Type: replace Abstract: We explicitly show that the quantum teleportation protocol can be employed to completely reconstruct arbitrary two- and three-qubit density matrices. We also extend the present analysis to n-qubit density matrices. The only quantum resources needed to implement the teleportation-based quantum state tomography protocol are the ability to make Bell measurements and the ability to prepare a few different single qubit states to be teleported from Alice to Bob.

11.
arXiv (quant-ph) 2026-06-16

Quantum enhancement and Doppler suppression of Kasevich-Chu atom interferometer with motional squeezing states

arXiv:2606.16632v1 Announce Type: new Abstract: Hybridization of internal and external atomic degrees of freedom in a Kasevich-Chu interferometer enables the possibility to enhance the sensitivity significantly even under quantum-standard limit. By introducing motional squeezing state as an input, we systematically derive the computational framework of quantum and classical Fisher information of two measurement protocols for arbitrary strength of Doppler effects. Through maximizing the corresponding classical Fisher information, we obtain the optimal control parameters and the corresponding quantum Fisher information. For population measurement, the largest sensitivity can be as large as four times than the semi-classical limit through enlarging the atom coherence length. For joint measurement of population and position, the competition between quantum enhancement and Doppler suppression induces two three behaviors, in one regime, the quantum enhancement dominates even in presence of strong Doppler broadening effects where the sensitivity is significantly enhanced; while in another regime, an optimal squeezing parameter is observed where the classical Fisher information reaches the maximum. Our results clearly demonstrate the robustness of external quantum enhancement against Doppler suppression. Our proposal can be readily applied to gravimeter of mobile platform where decoherence from noise will damage the many-body entanglement of internal spin squeezing.

12.
arXiv (CS.LG) 2026-06-11

Hybrid Iterative Neural Low-Regularity Integrator for Nonlinear Dispersive Equations

arXiv:2605.04853v2 Announce Type: replace Abstract: We propose HIN-LRI, a hybrid framework that augments a classical numerical solver with a neural operator trained to correct the solver's structured truncation error. A base low-regularity integrator provides a consistent first-order approximation to nonlinear dispersive PDEs, while a lightweight neural network, operating on a low-dimensional latent manifold, learns the residual defect that analytical methods cannot close. An explicit time-step scaling on the neural correction ensures that its Lipschitz contribution remains $\mathcal{O}(\tau)$, yielding a Gronwall stability factor bounded uniformly in the step size and independent of the spatial resolution. The network is trained end-to-end through a solver-in-the-loop objective that unrolls the full iteration and penalises trajectory error in a Bourgain-type norm, aligning learning with multi-step solver dynamics rather than isolated one-step targets. Under stated assumptions, the global error satisfies $C(\varepsilon_{net}+\delta)\,\tau^\gamma\ln(1/\tau)$, where $\varepsilon_{net}$ measures the network approximation quality and $\delta$ the training shortfall. Experiments on three dispersive benchmarks with rough data show that HIN-LRI improves accuracy over analytical integrators, splitting methods, and neural PDE surrogates, with stable spatial refinement, effective out-of-distribution transfer, and modest online overhead.

14.
arXiv (CS.AI) 2026-06-24

SAFARI: Scaling Long Horizon Agentic Fault Attribution via Active Investigation

arXiv:2606.24626v1 Announce Type: new Abstract: As autonomous agents tackle increasingly complex multi-step, multi-agent tasks, their execution trajectories have scaled beyond the constraints of even the largest context windows. Current methods for effectively diagnosing agent failures load the full trajectory into an LLM's context window, which suffers from attention dilution and fails when agentic traces inevitably exceed context limits. To address this, we introduce SAFARI (Scaling long-horizon Agentic Fault AttRibution via active Investigation), a framework that replaces linear context loading with a tool-augmented diagnostic loop. By equipping LLMs with a specialized toolbox to read and search trajectory segments alongside a persistent Short-Term Memory (STM) for cross-turn reasoning, SAFARI effectively decouples diagnostic accuracy from architectural context limits. Our experiments demonstrate that SAFARI outperforms state-of-the-art results by 20% on the Who&When dataset within a 1M token budget, and by 19% on TRAIL GAIA subset on a 25K token budget. Most significantly, SAFARI maintains a 0.58 precision even when the target fault resides 5x beyond the model's native context window, a scenario where traditional evaluators fail entirely.

15.
PLOS Medicine 2026-06-23

Comparisons of core component delivery in cardiac rehabilitation programs by country income classification and decade based on the 2025 Global Audit Update: A survey study

by Gabriela Lima de Melo Ghisi, Rachael P. Carson, Karam Turk Adawi, Rongjing Ding, Warner M. Mampuya, Mariya P. Jiandani, Jimena Martinez, Monserrat Cruz Rivero, Claudia V. Anchique, Dinah L. van Schalkwijk, Jonathan Gallagher, Buket Akinci, Dion Candelaria, Jirapa Champaiboon, Daniel F. Quesada-Chaves, Tone M. Norekvål, Iwona Szadkowska, Borut Jug, Evangelia Kouidi, Marta Supervia, Won-Seok Kim, Chamila Mettananda, Lilian Mbau, Gulsim T. Aimakova, Sherry L. Grace, on behalf of the ICCPR Global Cardiac Rehabilitation Audit Update Investigators Background Cardiovascular disease (CVD) remains a leading global health burden. Cardiac rehabilitation (CR) is essential to reducing morbidity and improving patient outcomes. Since the COVID-19 pandemic, CR delivery worldwide has evolved, yet these changes have not been systematically charactemkjrized. The objective of this study was to characterize globally: (1) the delivery of core CR components, including risk factors assessed, patient education practices, and program resources; (2) differences in these elements by country income classification and relative to the initial 2016 Global CR Audit. Methods and findings A cross-sectional Audit update was conducted. Program-level data were collected from May 1st to September 1st 2025 using a REDCap survey adapted from previous Audits. Eligible respondents were leads of phase II/post-discharge CR programs providing at least an initial assessment, structured aerobic exercise, and ≥1 additional core component. ICCPR associations and local leaders supported program identification. Main outcomes were core components delivered (10 assessed), risk factors assessed (14 assessed), patient education dose (hours/patient/program), and program resources (17 assessed). Generalized linear mixed models (GLMM) tested differences by income classification and (when applicable) changes since 2016. Of 7,025 programs identified globally, 1,505 (62% median country response rate) initiated a survey from 90/113 (80%) countries with CR. The median number of core components offered was 8/program (p25, p75 = 6, 10), with upper-middle income countries offering significantly more components overall (median = 9), and also high-income countries offering more than low-income countries (8 versus 6, p 

16.
arXiv (quant-ph) 2026-06-15

Efficient Simulation of Szegedy Quantum Walk Formulations and Algorithms

arXiv:2606.14226v1 Announce Type: new Abstract: Quantum walks provide a versatile framework for quantum algorithms across a wide range of applications. We develop efficient classical simulation methods for Szegedy quantum walks that avoid explicit construction of the full unitary evolution operator. Unlike previous approaches restricted to a particular walk formulation, our framework is built from fundamental update and reflection operators, enabling the simulation of a broader class of Szegedy walk formulations. We further extend these methods to phase-estimation-based algorithms coupled to the walk, including implementations suitable for large sparse graphs. The resulting methods achieve optimal $O(N^2)$ complexity for dense graphs with $N$ nodes. For sparse graphs, the computational cost scales linearly with the number of edges, which is $O(N)$ in many cases. We implement the framework in the Python package SQWLib and illustrate its capabilities through simulations of representative algorithms, including quantum simulated annealing and quantum search on graphs. These results provide a practical tool for studying Szegedy-walk-based algorithms numerically beyond purely analytical treatments.

17.
arXiv (CS.LG) 2026-06-12

Fourier Multi-Component and Multi-Layer Neural Networks: Unlocking High-Frequency Potential

arXiv:2502.18959v3 Announce Type: replace Abstract: The architecture of a neural network and the choice of its activation function are both fundamental to its performance. Equally important is ensuring that these two elements are well matched, as their alignment is key to effective representation and learning. In this paper, we introduce the Fourier Multi-Component and Multi-Layer Neural Network (FMMNN), a model that combines sine-type activations with the multi-component and multi-layer structure of MMNNs. In an FMMNN, each component is represented as a trainable linear combination of fixed random sine-type basis functions, while multi-layer composition generates more complex and adaptive high-frequency features. We establish that FMMNNs retain exponential expressive power for function approximation even under a low-rank architectural structure. We also analyze the optimization landscape of FMMNNs and find it to be substantially more favorable than that of standard fully connected neural networks, especially for high-frequency targets. In addition, we propose a scaled random initialization method for the first-layer weights in FMMNNs, which accelerates training and improves final performance when sufficient samples are available. Extensive numerical experiments support our theoretical insights, showing that FMMNNs achieve strong accuracy and favorable convergence behavior on oscillatory function-approximation benchmarks.

18.
bioRxiv (Bioinfo) 2026-06-17

In silico characterization of lysis and host-recognition modules in Staphylococcus aureus bacteriophage genomes

Background/aim: Antimicrobial resistance in methicillin-resistant Staphylococcus aureus (MRSA) requires precision non-antibiotic therapeutics, yet phage lytic efficacy is poorly predicted by phenotypic assays, as shown by paradoxical biofilm responses. This study characterized the genomic architecture of lytic S. aureus bacteriophages, focusing on the conservation of the lysis module and the variability of host-recognition modules, to provide a rational basis for phage candidate selection. Materials and methods: Twenty-two complete S. aureus phage genomes were retrieved from NCBI GenBank. Genomic features were extracted with custom Biopython scripts. Lysis (endolysin, holin) and host-recognition (tail fiber/receptor-binding protein) modules were annotated and validated by InterPro domain analysis, with disrupted endolysins resolved by tBLASTn. Phylogeny was reconstructed from large terminase subunit (TerL) sequences using maximum likelihood. Results: Genome size spanned three classes, from 17.5 to 148.6 kb. The LysK-type endolysin (CHAP, Amidase, SH3b) was highly conserved, whereas tail fiber/RBP genes were detected in only 14 of 22 phages. Domain analysis reclassified two proteins annotated as endolysins as virion-associated peptidoglycan hydrolases, and identified two independent mechanisms, HNH endonuclease insertion and intron splitting, that interrupt lysis-module genes and confound automated annotation. Maximum likelihood analysis recovered a strongly supported, highly conserved core clade with EW and SA13 as divergent lineages. Conclusion: Lysis modules are conserved whereas host-recognition modules are variable, indicating that host recognition rather than the lytic enzyme is the principal determinant of host range and the more rational target for phage selection and engineering.

19.
arXiv (CS.LG) 2026-06-12

Learning with Simulators: No Regret in a Computationally Bounded World

arXiv:2606.13576v1 Announce Type: new Abstract: Understanding the minimal assumptions necessary for generalization is the fundamental question in learning theory. Unfortunately, most results rely heavily on independence (or some proxy thereof) of the data-generating process, while results for strongly dependent data are far more limited. Towards addressing this gap, we introduce the framework of simulatable processes, where the learner has access to a simulator that approximates the distribution generating the data (which may be an arbitrarily complex and dependent process). Surprisingly, given access to such a simulator, we show that we can recover the same learning guarantees as in the classical setting with independent data, namely, error bounds that depend on the VC dimension. Further, we use this framework to study the power of conditional sampling and show strict statistical and computational advantages in this setting. As a highlight of our framework, we exhibit a single algorithm that simultaneously learns any given VC class under all processes samplable in bounded polynomial time, with regret controlled by the time-bounded Kolmogorov complexity of the process. This provides a significant conceptual broadening of the classical PAC model.

20.
arXiv (CS.CV) 2026-06-11

TopoCap: Learning Topology-Agnostic Motion Priors for Monocular Video-to-Animation

The explosion of generative 3D assets has created a massive demand for animation, yet current motion capture methods remain brittle, restricted to species-specific templates (e.g., SMPL) or requiring labor-intensive manual rigging. We introduce TopoCap, the first unified framework capable of extracting motion from monocular video and retargeting it onto characters with arbitrary, unseen skeletal topologies, i.e., from bipeds to hexapods and inanimate objects, without test-time optimization. Our key insight is that while skeletal structures are combinatorial and discrete, the underlying physics of motion occupy a continuous, low-dimensional manifold. We materialize this insight via a two-stage generative pipeline. First, we learn a Universal Motion Manifold using a Graph CVAE that compresses heterogeneous kinematic chains into a shared, fixed-length latent code. By explicitly conditioning the decoder on a structural embedding of the target rig, we disentangle motion dynamics from skeletal topology. Second, we treat video-to-animation as a conditional flow matching problem, predicting these topology-agnostic codes from visual features. To learn this generalized prior, we introduce Mobjaverse, a massive-scale dataset curated from Objaverse-XL. Comprising over 5,000 unique skeletal topologies and 2 million frames, it exceeds the structural diversity of existing datasets by two orders of magnitude. Extensive experiments demonstrate that \MethodMotion outperforms specialist models on human and quadruped benchmarks while enabling zero-shot retargeting for the long tail of 3D creatures. Dataset is publicly available at https://huggingface.co/datasets/duckduckplz/Mobjaverse.

21.
arXiv (CS.CL) 2026-06-11

Judging Against the Reference: Uncovering Knowledge-Driven Failures in LLM-Judges on QA Evaluation

While large language models (LLMs) are increasingly used as automatic judges for question answering (QA) and other reference-conditioned evaluation tasks, little is known about their ability to adhere to a provided reference. We identify a critical failure mode of such reference-based LLM QA evaluation: when the provided reference conflicts with the judge model's parametric knowledge, the resulting scores become unreliable, substantially degrading evaluation fidelity. To study this phenomenon systematically, we introduce a controlled swapped-reference QA framework that induces reference-belief conflicts. Specifically, we replace the reference answer with an incorrect entity and construct diverse pairings of original and swapped references with correspondingly aligned candidate answers. Surprisingly, grading reliability drops sharply under swapped references across a broad set of judge models. We empirically show that this vulnerability is driven by judges' over-reliance on parametric knowledge, leading judges to disregard the given reference under conflict. Finally, we find that this failure persists under common prompt-based mitigation strategies, highlighting a fundamental limitation of LLM-as-a-judge evaluation and motivating reference-based protocols that enforce stronger adherence to the provided reference.

22.
arXiv (quant-ph) 2026-06-15

Bandstructure of a coupled BEC-cavity system: effects of dissipation and geometry

arXiv:2504.17730v2 Announce Type: replace-cross Abstract: We present a theoretical model for a transversally driven Bose-Einstein condensate coupled to an optical cavity. We focus on the interplay between different coherent couplings, which can trigger a structural phase transition, known as the superradiant phase transition. Our approach, based on band structure theory and a mean-field description, enables a comprehensive analysis of the nature of the system's excited modes, precursing the phase transitions. By incorporating dissipative couplings, intrinsic to these systems, we find non-Hermitian phenomena such as the coalescence of crossing precursor modes and the emergence of exceptional points (EPs). The general formulation of our model allows us to explain the role of an angle between transverse pump and the cavity deviating from $90^\circ$. This offers us a unified perspective on the plethora of different implementations of such systems.

23.
arXiv (math.PR) 2026-06-16

An Analytical Methodology for Quantifying Airspace Conflict Rate and Complexity

arXiv:2606.14897v1 Announce Type: cross Abstract: Air traffic growth, advanced air mobility, and increasingly autonomous operations are driving the need for scalable and adaptive airspace design methodologies. Central to this challenge is quantifying how traffic flow structure and demand, governed in part by airspace geometry, influence conflict generation and operational complexity. This paper presents an analytical framework for computing conflict rate and conflict probability in structured airspace using stochastic flow models. Traffic streams are modeled as renewal processes with prescribed inter-arrival time distributions, while interactions between flows are captured through geometry-dependent minimum spacing constraints at merges and crossings. Within this formulation, closed-form upper bounds on the expected conflict rate and conflict probability per aircraft are derived as functions of flow configuration and demand. These metrics are interpreted as complementary measures of airspace complexity, reflecting controller workload and per-aircraft operational risk. The methodology is applied to representative hexagonal cell geometries with varying routing structures and flow distributions. Results reveal non-monotonic tradeoffs between routing flexibility, capacity, and conflict generation, with intermediate flow configurations outperforming both highly constrained and highly distributed cases. The proposed framework provides a tractable tool for evaluating airspace design alternatives and complexity-informed traffic management strategies.

24.
arXiv (math.PR) 2026-06-15

Universality for Products of Random Matrices with i.i.d. Entries and the Fuss–Catalan Number

arXiv:2606.14450v1 Announce Type: cross Abstract: Let \((w_{ij})_{i,j\ge1}\) be a single infinite array of independent identically distributed real- or complex-valued entries of mean zero, variance \(\sigma^2\), and finite fourth moment. Set \(W_n=(w_{ij})_{1\le i,j\le n}\) and \(X_n=n^{-1/2}W_n\). For every fixed \(k\ge1\), we identify the almost sure limiting operator norm of several fixed products built from this family. Define the \(k\)-th freeness coefficient by \[ \gamma_k:=\sqrt{\frac{(k+1)^{k+1}}{k^k}}. \] Then we prove \[ \|X_n^k\|\to\sigma^k\gamma_k \qquad almost surely. \] The same limit holds for products sampled with replacement from any fixed finite pool of independent copies of \(X_n\); in particular, it holds for the product of \(k\) independent copies. Thus, the freeness coefficient captures the non-commuting characteristic between large random matrices %powers and independent or fixed-pool sampled products under the finite fourth moment assumption. The improvement of the classical Bai–Yin-type power estimate from the scale \(\sigma^k(k{+}1)\) to \(\sigma^k \sqrt{k{+}1}\) is a direct corollary of our result. The main technical challenge is to prove the upper bound using a high-moment expansion of %the upper bound is proved by a high-moment expansion of \(\E\Tr((X_n^kX_n^{*k})^m)\). The leading zero-defect trace words are tree-like and are counted by the Fuss–Catalan number \[ F_{k,m}= \frac1{km+1}\binom{(k+1)m}{m}. \] The combinatorial tool helps to devise a defect-sensitive global enumeration: if \(L=km\) and \[ r=(L+1-v)+(L-q), \] then the number of admissible word classes with defect \(r\) is at most \(F_{k,m}(Cm)^{Dr}\). This polynomial-in-\(m\) loss, with degree proportional to the defect, is summable in the logarithmic moment range.

25.
arXiv (CS.AI) 2026-06-12

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems

arXiv:2509.03340v4 Announce Type: replace-cross Abstract: Bifurcation phenomena in nonlinear dynamical systems often lead to multiple coexisting stable solutions, particularly in the presence of symmetry breaking. Deterministic machine learning models are unable to capture this multiplicity, averaging over solutions and failing to represent lower-symmetry outcomes. In this work, we formalize the use of generative AI, specifically flow matching, as a principled way to model the full probability distribution over bifurcation outcomes. Our approach builds on existing techniques by combining flow matching with equivariant architectures and an optimal-transport-based coupling mechanism. We generalize equivariant flow matching to a symmetric coupling strategy that aligns predicted and target outputs under group actions, allowing accurate learning in equivariant settings. We validate our approach on a range of systems, from simple conceptual systems to physical problems such as buckling beams and the Allen–Cahn equation. The results demonstrate that the approach accurately captures multimodal distributions and symmetry-breaking bifurcations. Moreover, our results demonstrate that flow matching significantly outperforms non-probabilistic and variational methods. This offers a principled and scalable solution for modeling multistability in high-dimensional systems.