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01.
arXiv (CS.AI) 2026-06-12

A Mathematical Forum Platform for Collaborative Problem Solving and Dataset Generation for AI Reasoning

arXiv:2606.12976v1 Announce Type: new Abstract: Sharing mathematical content in online forums remains a significant friction point for students and educators: writing raw LATEX is error-prone, standalone optical character recognition tools require platform switching, and current forum software offers no integrated path from a photograph of a formula to a rendered post. We present a unified system that eliminates this friction by embedding an image to LATEX conversion pipeline directly inside a forum posting interface. A user uploads or captures an image of a mathematical expression; the system routes it through the Mathpix OCR API, detects whether the returned output is LATEX or plain text containing inline math, applies the appropriate delimiter normalisation, and renders a live preview in either LATEX or Markdown mode before the post is committed to the database. The architecture is organized in three loosely coupled layers: image processing, rendering, and storage, and supports both desktop and mobile clients. A provisional US patent application has been filed covering the core methods. We describe the full system design, each component in detail, the data schema, and the key technical innovations, and we position the work against existing standalone tools and forum platforms to demonstrate the practical gap it closes. Beyond immediate usability, we argue that a deployed platform of this kind constitutes a continuously growing, community-validated dataset of mathematical problems and step-by-step solutions, a resource that can be used to train and benchmark AI systems for accurate mathematical reasoning

02.
Nature (Science) 2026-06-10

Confirmation that bryozoan animals were present during the Cambrian explosion

作者: 未知作者

Bryozoans are marine invertebrates that live in colonies and have long been considered absent from the Cambrian explosion — a rapid evolutionary event that began around 538 million years ago. Newly discovered fossils from the Cambrian period reveal that the bryozoan phylum had already diversified by this time. Fossils of two forms of bryozoans show evidence of soft tissue still preserved inside their mineralized skeletons.

03.
arXiv (CS.CV) 2026-06-17

GASE: Gaussian Splatting-Based Automated System for Reconstructing Embodied-Simulation Environments

Training embodied agents in the real world requires skilled operators and expensive hardware. Simulation environments offer a compelling alternative by enabling large-scale, cost-effective data augmentation. Consequently, rapidly constructing high-fidelity simulation scenes with a minimal sim-to-real gap has become a critical objective in robot learning. While reconstruction-based methods provide superior visual quality, current workflows are hindered by inefficient data acquisition and subpar foreground object extraction. We thus propose GASE, a highly automated system for simulation scene construction. GASE leverages multi-view video streams from panoramic camera arrays to enable rapid environment scanning. To ensure high-quality asset generation, our pipeline introduces a camera-pose-based strategy that robustly extracts objects across frames in the 2D domain, followed by high-fidelity scene inpainting. Foreground objects and the static background are then reconstructed independently and seamlessly imported into physics simulators for policy training. Extensive experiments demonstrate that GASE outperforms existing 3D Gaussian-based methods in segmentation accuracy by over 10\% while achieving state-of-the-art inpainting quality. Furthermore, real-robot deployments across manipulation and navigation tasks maintains a performance gap of less than 10\% compared to policies trained purely on real-world data. These results confirm that GASE provides an efficient and highly effective solution for bridging the sim-to-real gap. Code will be released.

04.
arXiv (CS.CL) 2026-06-24

Meet UD_Czech-PDTC: A Large and Genre-Rich Treebank in Universal Dependencies

Czech has been part of Universal Dependencies since its first release in 2015. It has also been one of the best represented languages, with the Prague Dependency Treebank being order of magnitude larger than most other UD treebanks. More recently, three other datasets from the Prague family were added and the annotations thoroughly revisited, forming the "Prague Dependency Treebank-Consolidated" (PDT-C). In comparison to the original PDT, PDT-C is more than twice as large, but it is also much more diverse in terms of genres and domains. In this paper, we describe the conversion of the new resource to Universal Dependencies. While the two annotation schemes are relatively similar at the first sight, there are numerous small differences in topology of the dependency structures and in granularity of the POS and relation type inventories. We demonstrate a selection of such differences on examples, discuss the diverging motivations, as well as ways to overcome the differences during conversion. We argue that while PDT is less "universal" and more tightly bound to one language, its multi-layer annotation is rich and provides all information needed for basic UD trees, and much more.

05.
arXiv (quant-ph) 2026-06-16

Magnetic control of an exciton-polariton condensate in a van der Waals magnet

arXiv:2506.06010v3 Announce Type: replace-cross Abstract: Quasiparticle condensates are among the most spectacular solid-state manifestations of quantum physics. Coupling macroscopic real-space wavefunctions to additional degrees of freedom, such as the electron spin, would add valuable control knobs for quantum applications. While creating spin-carrying superconducting condensates has attracted enormous attention, man-made condensates of light-matter hybrids known as exciton-polaritons have lacked an analogous spin-based perspective. Here we open a new door by demonstrating magnetically tunable exciton-polariton condensation in the van der Waals magnet CrSBr. Under photoexcitation, CrSBr microwires embedded in an optical cavity show the hallmarks of polariton condensation: a dramatic increase of the emission intensity from an excited laterally confined polariton state by multiple orders of magnitude, spectral narrowing of the emission line, and a continuous shift of the peak energy. Interferometry evidences an increase in spatial and temporal coherence. Owing to the strong coupling between the spin order and excitonic correlation, the energy of the condensate can be tuned by up to 10.5 meV by an external magnetic field of only 2 Tesla. Our results establish CrSBr microcavities as a powerful platform for exploring magnetic control of polariton condensates and mark a significant step toward spin-controlled coherent quantum light sources.

07.
medRxiv (Medicine) 2026-06-10

Healthy Heart Actions Right Time (HHART): Co-design priorities to connect Aboriginal and Torres Strait Islander community and clinic activities for healthy hearts

Aim: Healthy Heart Actions Right Time (HHART) is a multi-phased research project that seeks to identify, implement and evaluate strategies to connect community and clinical activities to reduce the burden of heart disease for Aboriginal and Torres Strait Islander people. The aim in Phase One was to identify priority activities for two participating services. Background: The ongoing effects of colonisation drive a disproportionate burden of heart disease for Aboriginal and Torres Strait Islander people. Clinical and community groups both have established strengths in reducing the risk of heart disease, but these are not always well connected. Methods: Using a case study methodology in two locations we partnered in a 12-month co-design process to identify priority activities to connect clinical and community activities. Findings: Three priorities emerged from the Phase One co-design process: (i) community-led gardening as a strategy to promote heart health through connection and healthy lifestyles; (ii) community days to increase engagement in heart checks and strengthen community-clinic relationship; and (iii) clinic-led development of culturally relevant education resources to promote clinician confidence and community heart health knowledge.

08.
arXiv (CS.CV) 2026-06-16

From Static Inference to Dynamic Interaction: A Survey of Streaming Large Language Models

Standard Large Language Models (LLMs) are predominantly designed for static inference with pre-defined inputs, which limits their applicability in dynamic, real-time scenarios. To address this gap, the streaming LLM paradigm has emerged. However, existing definitions of streaming LLMs remain fragmented, conflating streaming generation, streaming inputs, and interactive streaming architectures, while a systematic taxonomy is still lacking. This paper provides a comprehensive overview and analysis of streaming LLMs. First, we establish a unified definition of streaming LLMs based on data flow and dynamic interaction to clarify existing ambiguities. Building on this definition, we propose a systematic taxonomy of current streaming LLMs and conduct an in-depth discussion on their underlying methodologies. Furthermore, we explore the applications of streaming LLMs in real-world scenarios and outline promising research directions to support ongoing advances in streaming intelligence. We maintain a continuously updated repository of relevant papers at https://github.com/EIT-NLP/Awesome-Streaming-LLMs.

09.
arXiv (CS.AI) 2026-06-15

DIFF-ERO: A Conformance-Aware Loss for Deep Learning in Process Mining

arXiv:2606.14283v1 Announce Type: cross Abstract: Deep learning has driven many recent advances in process analytics, especially for predictive and prescriptive monitoring. However, standard objectives such as cross-entropy optimize local next-step likelihoods and only implicitly capture control-flow structure. As a result, models can achieve high token-level accuracy while permitting imprecise global behaviour. We introduce DIFF-ERO, a conformance-aware loss function for deep learning models on process data. DIFF-ERO is a differentiable formulation of entropy-based stochastic conformance that incorporates control-flow information during training. Our approach constructs batch-level stochastic transition matrices with soft edge memberships, allowing structural precision and recall signals to directly inform backpropagation. The loss is model-agnostic and can be applied whenever the final representation parametrizes stochastic transitions. We instantiate DIFF-ERO in transformer encoder-decoder pipelines for next-activity prediction and use it jointly with cross-entropy to analyse its theoretical components with respect to convergence. Across benchmarks comparing other loss functions and targets, DIFF-ERO shows improved predictive performance where structure matters most while maintaining parity elsewhere. At the same time, the learned stochastic automaton converges towards the structural ground truth, indicating that the network internalizes process model structure.

10.
bioRxiv (Bioinfo) 2026-06-12

Deciphering cross-omics complexity of tissues via diagonal integration of unpaired spatial multi-omics data

Recent spatial multi-omics technologies enable the simultaneous in situ profiling of multiple omics modalities on the same tissue section; however, they face challenges in experimental complexity and high costs. This technical limitation can be circumvented by diagonal integration methods, which integrate omics data from different modalities. However, existing single-cell diagonal integration approaches overlook spatial information, causing unreliable anchoring across omics layers. Here, we introduce STAMO, a graph attention neural network model for spatially aware integration of unpaired spatial slices from different omics. Systematic benchmarking on spatial epigenome-transcriptome slices proves that STAMO outperforms the state-of-the-art methods in generating aligned embeddings and identifying consensus spatial domains across omics. We apply STAMO to integrate unpaired data from diverse spatial omics types (transcripts, epigenetics, DNA, and proteins), including slices from spatial RNA and four different epigenomic modalities, spatial ATAC and RNA slices across embryonic stages, spatial protein and RNA slices, and spatial DNA and RNA slices. In addition, the integration capability of STAMO can be further used to achieve cross-omics generation, offering a solution for exploring spatial region-specific gene regulatory mechanisms.

11.
arXiv (CS.AI) 2026-06-18

Model Collapse Is Not a Bug but a Feature in Machine Unlearning for LLMs

arXiv:2507.04219v5 Announce Type: replace-cross Abstract: Current unlearning methods for LLMs optimize on the private information they seek to remove by incorporating it into their fine-tuning data. We argue this not only risks reinforcing exposure to sensitive data, but also fundamentally contradicts the principle of minimizing its use. As a remedy, we propose a novel unlearning method-Partial Model Collapse (PMC), which does not require unlearning targets in the unlearning objective. Our approach is inspired by recent observations that training generative models on their own generations leads to distribution collapse, effectively removing information from model outputs. Our central insight is that model collapse can be leveraged for machine unlearning by deliberately triggering it for data we aim to remove. We theoretically analyze that our approach converges to the desired outcome, i.e. the model unlearns the data targeted for removal. We empirically demonstrate that PMC overcomes four key limitations of existing unlearning methods that explicitly optimize on unlearning targets, and more effectively removes private information from model outputs while preserving general model utility. Overall, our contributions represent an important step toward more comprehensive unlearning that better aligns with real-world privacy constraints. Code available at https://www.cs.cit.tum.de/daml/partial-model-collapse/.

12.
medRxiv (Medicine) 2026-06-22

Modelling the decadal expansion of West Nile virus in Italy: the role of climatic, anthropogenic, and macroecological drivers

Abstract BACKGROUND West Nile virus (WNV) is a growing health burden in Italy. Anticipating human infection risk is hampered by the pathogen's complex ecology, highlighting the need for comprehensive early-warning tools. AIM We aimed to model municipal-level WNV risk in Italy and characterize its decadal expansion in Italy, providing a comprehensive ecological understanding of viral emergence. METHODS We applied a machine learning framework to annual human WNV case data from 2014 to 2024. The model integrated a suite of environmental, socio-economic, and macroecological predictors to generate risk projections. We evaluated the model's performance through multiple validation settings. We also performed an anticipation test for the 2025 epidemic season, using 2024 environmental data to assess the model's predictive accuracy against observed 2025 human cases. RESULTS Our model achieved robust performance (True Skill Statistic > 0.4) and captured WNV progressive expansion from 184 predicted positive municipalities in 2014 to 2,012 in 2024 (an 11-fold increase in 11 years). Seasonal minimum temperature was the primary risk driver, followed by monitoring year and population density, indicating active spatial spread. Environmental suitability consistently preceded clinical detection. Municipalities with cases in 2023-2024 exhibited significantly higher predicted suitability during 2018-2022 than those without cases (average risk 0.58 vs 0.20). Our model successfully identified emerging risk hotspots along the Adriatic coast and southern Italy before the official human spillover of 2025. CONCLUSION Embedding macroecological drivers into WNV risk modelling provides an improved understanding of drivers of rapid WNV expansion. Our model enables proactive risk mapping, surveillance efforts, and targeted public health measures.

13.
arXiv (CS.CL) 2026-06-24

To Compare, or Not to Compare: On Methodological Practices in Evaluating Social Bias

As Large Language Models are increasingly deployed in critical applications, robustly evaluating their social biases is paramount. However, the current literature suffers from widespread methodological fragmentation, which yields contradictory conclusions. This stems largely from ignoring the structural framing of benchmark-level evaluations. To resolve this, we introduce a unified and controllable framework that standardizes heterogeneous benchmarks to systematically contrast isolated demographic assessments with forced-choice comparative settings. Crucially, this allows us to disentangle the confounding effects of Chain-of-Thought reasoning, neutral fallback options, and other structural artifacts in social bias evaluations. Our evaluation across multiple model families reveals a massive, systematic paradigm gap: while isolated assessments limit prejudice activation, comparative settings act as aggressive catalysts for latent discrimination, a shift primarily driven by underspecified contexts. Alarmingly, CoT reasoning exacerbates social biases under comparative settings, and this systemic bias persists as a deterministic prejudice even when models are provided neutral fallback options or claim to answer randomly. Finally, we demonstrate that this comparative prejudice is a generalized phenomenon that scales positively with model size. Ultimately, we offer a crucial methodological guideline: while researchers must leverage comparative settings to robustly audit hidden biases, practitioners cannot safely rely on comparative deployments in ambiguous real-world tasks.

14.
medRxiv (Medicine) 2026-06-16

Higher Population Coverage with Typhoid Conjugate Vaccine is Needed to Induce Herd Protection: Evidence from a Cluster-Randomized Trial in Urban Bangladesh

Introduction: A cluster randomized trial (CRT) in Bangladesh found that Vi-tetanus toxoid (Vi-TT) vaccine conferred 85% protection to vaccinees at 18 months of follow-up; however, it failed to confer significant herd protection to non-vaccinees. Methods: In the CRT, children aged 9 months to

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

History estimation in random recursive trees: Pointwise approach via iterated Jordan centralities

arXiv:2606.24465v1 Announce Type: new Abstract: We study the problem of estimating the arrival times of vertices in a uniform random recursive tree from its unlabeled structure. We adopt a pointwise perspective and analyze the distribution of the relative estimation error, and derive tail bounds that are uniform in both the vertex and the tree size. For the ranking induced by Jordan centrality, the probability that the estimate exceeds the true arrival time by a factor $S$ decays on the order of $1/S$, while the probability of underestimating the arrival time by a factor $1/S$ decays exponentially in $S$. We introduce a refined centrality measure whose overestimation tail decays on the order of $(\log S)/S^{2}$, at the cost of a heavier lower tail of order $1/S^{2}$. These results reveal a tradeoff between upper- and lower-tail performance in arrival-time estimation that is invisible to the previously studied risk functional. Nevertheless, the refined centrality measure attains the optimal order of the risk for all its parameter values.

16.
arXiv (CS.AI) 2026-06-17

C2FL: Clustered Continual Federated Learning under Spatial and Temporal Drift

arXiv:2606.18003v1 Announce Type: cross Abstract: Collective Adaptive Systems (CAS) increasingly rely on machine learning to let each node learn from locally sensed data, aligning its behavior with the surrounding environment. Scaling this intelligence, however, raises fundamental challenges: sensed data is often privacy-sensitive, preventing centralized collection; nodes are mobile, traversing regions where nearby nodes perceive similar phenomena while distant ones observe radically different conditions, creating natural spatial clusters; and these distributions evolve over time due to mobility, introducing temporal drift that makes local models progressively stale. These dynamics arise across domains - vehicular sensing, drone-based monitoring, smartphone crowdsensing - yet the interplay of privacy, spatial heterogeneity, and temporal drift severely undermines conventional learning strategies. Therefore, we propose C2FL, a fully distributed Federated Learning (FL) approach where nodes self-organize into learning groups through spatial clustering, reflecting the geographic structure of the environment. To counteract temporal drift, each node combines experience replay with a dwell-time-aware adaptive averaging step, progressively incorporating the regional consensus as it remains longer within the same area, while preserving previously acquired knowledge under evolving distributions. We evaluate our approach on synthetic experiments that systematically reproduce spatial and temporal shifts, showing that standard federated strategies degrade significantly under these conditions and that our method restores robust collective adaptation.

17.
arXiv (CS.AI) 2026-06-19

StaminaBench: Stress-Testing Coding Agents over 100 Interaction Turns

arXiv:2606.19613v1 Announce Type: cross Abstract: We introduce StaminaBench, a benchmark that measures the stamina of coding agents: how many consecutive interaction turns (change requests) they can handle before failing. Unlike the prevailing fraction-of-tasks-solved metric, this matches real vibe-coding where sessions run dozens or hundreds of turns. In StaminaBench, agents implement a REST API server and modify it across a tunable number of procedurally generated follow-up change requests - 100 in our experiments, resulting in codebases of up to 6,000 lines. Tests are generated fully programmatically without LLM involvement, ensuring reproducibility and reliability; change sequences are drawn from either a hardcoded or LLM-driven sampler, both constrained to a structured action space to ensure changes are valid. The agent and the server run in an isolated environment and communicate with the benchmark through HTTP, making testing fully black-box and language-agnostic. We evaluate six agent harnesses paired with seven open-source LLMs across 20 scenarios of 100 turns each and find that: (1) all the tested models fail within 5-6 turns, confirming that vibe-coding-style programming without thorough testing produces bugs; (2) passing test feedback back to the agent and allowing it to retry improves passed turn count by up to 12x; and (3) a good harness is required for strong performance: stronger models exhibit up to a 6x gap between their best and worst harness, while weaker models fail with any harness. We release the benchmark and the generated tasks to enable further research into multi-turn coding agent behavior. Benchmark code and data: github.com/amazon-science/StaminaBench.

18.
arXiv (quant-ph) 2026-06-12

Fibonacci Steady-States and Persistent Oscillations in an Ordered Multimode Dicke Model

arXiv:2606.13072v1 Announce Type: new Abstract: Ultracold atoms in multimode optical cavities provide a rich testbed for many-body phenomena enabled by light-mediated interactions. Recent experiments include realizations of spin glasses and associative memories, as described by multimode Dicke models with disordered couplings. However, the properties of multimode Dicke models with ordered coupling geometries remain largely unexplored. In this work, we investigate the stable steady-states of the multimode Dicke model with an ordered nearest-neighbor coupling geometry, where $n_c$ atomic clusters are coupled via $n_c-1$ cavity modes. We show that the number of mean-field stable steady-states in the superradiant phase exhibits Fibonacci scaling with the number of atomic clusters, and that a subset of these steady-states exhibit persistent oscillations. Using both the truncated Wigner approximation and the numerically-exact hierarchy of pure states, we further demonstrate that these features of the stable steady-state solutions persist for finite cluster sizes. Ordered multimode Dicke models, such as the nearest-neighbor coupling geometry considered here, are accessible with current experimental technologies and point toward a broader class of strongly interacting dissipative systems with similarly rich behavior.

19.
PLOS Medicine 2026-05-29

Availability, appeal, and addictiveness by design: Tobacco and nicotine industry deliberate targeting of youth

by Raglan Maddox, Becky Freeman, Charlotta Pisinger, Emily Banks Contemporary tobacco and nicotine products, particularly e-cigarettes, are deliberately designed, marketed, and distributed to maximize youth appeal, uptake, dependence, and use. Youth uptake is a predictable outcome of systems designed to maximize product availability, appeal, and addictiveness. In recognition of the World No Tobacco Day 2026 theme, "unmasking the appeal", this Perspective by Raglan Maddox and colleagues discusses how tobacco and nicotine products, particularly e-cigarettes, are deliberately designed and marketed to maximize youth appeal, and highlight the need for policies to ensure greater industry accountability and to tackle concerning uptake trends.

20.
arXiv (CS.LG) 2026-06-18

TIGER: Inverting Transformer Gradients via Embedding-Subspace Distance Optimization

arXiv:2606.18312v1 Announce Type: cross Abstract: Federated learning allows multiple clients to jointly train a shared model by sending gradient updates to a central server while keeping raw inputs local. However, prior gradient inversion attacks show that these updates can reveal enough information to reconstruct client inputs. Existing attacks on transformers either optimize dummy inputs to match the true client updates, which is costly and unstable for modern models, or exploit the low rank of attention gradients to identify a subspace containing the true layer embeddings, followed by a discrete membership test for candidate tokens. However, this token test is brittle under numerical noise, i.e., from quantization or Differential Privacy (DP), and scales poorly for encoder models with non-causal attention. We introduce TIGER, a continuous gradient inversion attack that turns this subspace signal into a differentiable objective. Instead of searching over tokens or matching full gradients, TIGER directly optimizes token embeddings to minimize their distance to the subspace. Our experiments demonstrate that on encoder-only models, TIGER substantially improves both reconstruction quality and runtime over existing attacks, while on decoder models, TIGER is more robust than prior subspace-based attacks, enabling the first successful reconstructions in DP-defended federated learning settings.

21.
arXiv (quant-ph) 2026-06-16

MAPS: A Novel Multi-Axial Projective Sphere for Geometrically Visualizing Higher d-Valued Quantum State-Space of Qudits

arXiv:2606.15801v1 Announce Type: new Abstract: Visualizing the d-valued quantum state-space of quantum systems serves as a foundational pillar for the scientific research and practical applications in quantum computing and information science, where d >= 2. The 2-valued quantum states of a qubit are elegantly visualized on the three-dimensional Bloch sphere. In contrast, expanding this geometrical paradigm to visualize higher d-valued quantum states of a qudit (d >= 3), e.g., a qutrit (d=3), ququadit (d=4), and quintit (d=5), leads to severe structural and topological complexities. This paper introduces a new generalized three-dimensional framework to effectively visualize higher d-valued quantum states of a qudit, in the aspects of ease of illustration, structural simplicity, and natural representation for researchers and engineers. We called this new framework the "multi-axial projective sphere (MAPS)", which consists of n projectional intersecting spatial axes, where d-1

22.
arXiv (CS.LG) 2026-06-11

SpaTeoGL: Spatiotemporal Graph Learning for Interpretable Seizure Onset Zone Analysis from Intracranial EEG

arXiv:2602.11801v2 Announce Type: replace Abstract: Accurate localization of the seizure onset zone (SOZ) from intracranial EEG (iEEG) is essential for epilepsy surgery but is challenged by complex spatiotemporal seizure dynamics. We propose SpaTeoGL, a spatiotemporal graph learning framework for interpretable seizure network analysis. SpaTeoGL jointly learns window-level spatial graphs capturing interactions among iEEG electrodes and a temporal graph linking time windows based on similarity of their spatial structure. The method is formulated within a smooth graph signal processing framework and solved via an alternating block coordinate descent algorithm with convergence guarantees. Experiments on a multicenter iEEG dataset with successful surgical outcomes show that SpaTeoGL is competitive with a baseline based on horizontal visibility graphs and logistic regression, while improving non-SOZ identification and providing interpretable insights into seizure onset and propagation dynamics.

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

Eyring-Kramers asymptotics for infinite-dimensional stochastic gradient systems

arXiv:2606.16083v1 Announce Type: new Abstract: We study small-noise asymptotics for a class of reversible stochastic evolution equations in infinite dimensions. The dynamics are of the form \[ dX_t=-A\nabla F(X_t)\,dt+\sqrt{2\beta^{-1}A}\,dW_t, \] where $F$ is a regular multi-well potential, $A$ is a selfadjoint mobility operator, $W$ is a cylindrical Brownian motion and $\beta\gg 1$ is the inverse noise strength. The invariant measure is a Gibbs perturbation of a Gaussian reference measure, and the resulting framework covers, in particular, the stochastic Allen-Cahn and stochastic Cahn-Hilliard equations on bounded intervals. In the double-well case, we derive a sharp asymptotic formula for the first nonzero eigenvalue of the generator. This gives an infinite-dimensional Eyring-Kramers law for the spectral gap, with exponential rate determined by the communication height and leading prefactor determined by the local quadratic behavior at the relevant minima and saddle points. Our approach provides a general strategy for lifting finite-dimensional Eyring-Kramers analysis to infinite-dimensional stochastic gradient systems.

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

Queues with Correlated Service Times – the $M/M_D/c$ Model

arXiv:2606.24881v1 Announce Type: new Abstract: This paper studies multi-server queueing systems with correlated service times, modeled as the $M/M_D/c$ queue, which is a natural extension of the recent work by Thapa and Zhao [Thapa-Zhao:2026]. In this model, arrivals follow a Poisson process, while service times across servers exhibit dependence captured by the Marshall–Olkin multivariate exponential distribution (MO-MVED). We first develop a rigorous sample-path construction of the system and establish that the resulting queueing process is a continuous-time Markov chain. We then analyze the stationary behavior of the $M/M_D/c$ model. In the homogeneous case, we derive a complete solution via geometric tail structure and explicit boundary equations, recovering a tractable one-dimensional representation. In the heterogeneous case, we establish a general framework combining a geometric tail with a finite boundary system, and prove existence, uniqueness, and nonnegativity of the stationary distribution. The above results provide a unified analytic framework extending classical $M/M/c$ theory to correlated-service settings, and reveal how dependence among service times fundamentally affects system performance and structure. Beyond the $M/M_D/c$ model, We next study the interplay between Marshall–Olkin service dependence and queue-state Markovianity. On the one hand, Marshall–Olkin dependent service completions are shown to preserve Markovianity for a broad class of queueing systems. On the other hand, if a queueing process admits a Markovian state description without tracking service ages, residual service times, or service phases, then its service mechanism must satisfy a weak multivariate lack-of-memory property and consequently belongs to the Marshall–Olkin family. These results provide a probabilistic foundation for the use of Marshall–Olkin multivariate exponential service times in Markovian queueing models.

25.
arXiv (math.PR) 2026-06-16

Stein's method for the matrix normal distribution

arXiv:2601.11422v2 Announce Type: replace-cross Abstract: This work presents the first systematic development of Stein's method for matrix distributions. We establish the basic essential ingredients of Stein's method for matrix normal approximation: we derive an extended-generator-based Stein identity from a matrix Ornstein-Uhlenbeck diffusion with two-sided scales, provide an explicit semigroup representation for the solution of the Stein equation, and obtain regularity estimates for the solution. The new methodology is demonstrated in three examples: (i) smooth Wasserstein distance bounds to quantify the matrix central limit theorem (a didactic example), (ii) a Wasserstein distance bound for the matrix normal approximation of the centered matrix $T$ distribution, and (iii) a Stein's method-of-moments approach to estimating the row and column covariance factors of the matrix normal, yielding a flexible class of weighted flip-flop Stein estimators that generalize Dutilleul's classical flip-flop algorithm and naturally accommodate row/column importance weights, systematic missingness, and projection onto structured covariance families. The latter two examples are intrinsically matrix-valued and cannot be treated using naive vectorization.