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01.
medRxiv (Medicine) 2026-06-15

Investigation of Intra-Fraction Stability and Inter-Fraction Reproducibility of Deep Inspiration Breath-Hold Across Two Hypofractionated Radiotherapy Regimens in the HYPORT Adjuvant Study.

Background: Deep Inspiration Breath Hold (DIBH) is a widely used respiratory motion management technique for minimizing cardiac dose in left-sided breast radiotherapy. In the Breast HYPORT Adjuvant study, DIBH was employed for cardiac sparing in patients without nodal irradiation using a standardized institutional protocol with the Varian Real-time Position Management (RPM) system. Both moderate-hypofractionation (control arm - 40Gy in 15 fractions) and one-week hypofractionation (experimental arm - 26 Gy in 5 fractions) regimens were delivered using this protocol. This study aimed to evaluate the robustness of DIBH by analyzing intra-fraction stability and inter-fraction reproducibility of breath-hold amplitude across the two treatment regimens. Methods: Respiratory waveforms acquired during each treatment session were analyzed to determine the median breath-hold amplitude and its standard deviation during beam delivery. Intra-fraction stability was assessed from vari- ations within individual treatment sessions, while inter-fraction reproducibility was evaluated relative to the simula- tion waveform amplitude across all treatment sessions. These parameters were compared between the two HYPORT regimens to examine breath-hold consistency during treatment delivery. Moreover, an additional comparison was made between the one-week hypofractionation regimen and the first five fractions of the moderate-hypofractionation regimen to evaluate the effect of treatment duration . Lung volumes from free-breathing and DIBH CT scans were analyzed to assess the effectiveness of patient breath-hold training. Results: Both arms demonstrated an average 1.7-fold increase of air volume in lung during the breath-hold position, confirming the effective implementation of DIBH during treatment planning and delivery. Structured training resulted in increased breath-hold amplitudes, with gains of 22.87% and 24.16% with respect to the first trial session in the experimental and control arms, respectively. Both regimens receive equivalent doses for approximately the same air volume in lung . Despite the different prescription doses in the two arms (26 Gy vs. 40 Gy), the experimental arm achieved an equivalent mean heart dose of 2.91% (75.6 cGy) compared with 2.95% (118.51 cGy) in the control arm, suggesting a similar cardiac preservation protocol adopted during treatment planning. Intra-fraction stability was similar between the control arm and the experimental arm, with median amplitude variations of 1.006 mm (95% CI: [0.998-1.015]) and 1.079 mm (95% CI: [1.067-1.097]), respectively. In contrast, inter-fraction reproducibility improved in the experimental arm, with lower deviation from simulation amplitude (0.44 {+/-} 0.24 mm vs. 0.66 {+/-} 0.25 mm) for the entire treatment schedule. The stability and reproducibility of experimental arm were further compared with the first five fractions of the control arm. The results were similar to those of the experimental arm. Conclusion: In this study, we compared two treatment regimens in terms of intra-fraction stability and inter-fraction reproducibility during DIBH radiotherapy. Both regimens demonstrated comparable intra-fraction stability, indicating effective motion management irrespective of treatment duration. However, the experimental arm showed better inter- fraction reproducibility, suggesting more consistent breath-hold performance throughout the treatment course. Based on stability and reproducibility, a reasonable narrowing of the DIBH gating window may be implemented with minor changes to the institutional protocol. The observed trend highlights the potential for improved consistency with the experimental approach and supports further investigation to better understand the underlying factors and strengthen these findings in future studies.

02.
arXiv (math.PR) 2026-06-12

Voronoi Percolation: Topological Stability and Giant Cycles

arXiv:2601.00793v2 Announce Type: replace Abstract: We study the topological stability of Voronoi percolation in higher dimensions. We show that slightly increasing p allows a discretization that preserves increasing topological properties with high probability. This strengthens a theorem of Bollobás and Riordan and generalizes it to higher dimensions. As a consequence, we prove a sharp phase transition for the emergence of i-dimensional giant cycles in Voronoi percolation on the 2i-dimensional torus.

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

FATE: Pillar Encoding and Frequency-Aware Training for Event-Based Object Detection

Event cameras are bio-inspired sensors that asynchronously capture logarithmic intensity changes, offering inherent advantages in high-speed and high-dynamic-range scenarios. However, the sparse and asynchronous nature of event streams poses a fundamental challenge for modern deep learning architectures. To enable compatibility with standard models, most existing approaches partition the accumulation window into fixed temporal sub-bins. While effective for spatial processing, this internal discretization discards fine-grained temporal structure and constrains inference to the low temporal frequencies imposed by training supervision. To address this limitation, we propose FATE, a unified framework built upon a novel Pillar Encoding (PE). While operating over discrete macro-accumulation windows dictated by the target frequency, PE avoids internal temporal sub-binning. It organizes events into spatial pillars and approximates their intra-window evolution via projection onto a continuous-time orthogonal polynomial basis. This formulation yields an L2-optimal representation that retains rich temporal dynamics in a dense pseudo-image, mitigating information loss under sparse event conditions. To fully leverage this representation, we introduce Frequency-Aware Training (FAT), a soft mean-teacher curriculum that generates temporally dense pseudo-labels, effectively bridging the mismatch between low-frequency supervision and high-frequency inference. Extensive experiments demonstrate that FATE generalizes across architectural paradigms and consistently outperforms strong baselines. It enables robust object detection at high temporal resolutions up to 200 Hz, while incurring minimal overhead in parameter count and inference latency

04.
arXiv (CS.CV) 2026-06-18

SC3-Eval: Evaluating Robot Foundation Models via Self-Consistent Video Generation

Evaluating generalist robot manipulation policies in the real world is expensive, slow, and difficult to scale. Action-conditioned video world models offer a scalable alternative by simulating policy rollouts. Autoregressive rollouts accumulate compounding errors, observations across multiple camera views must remain mutually consistent, and the evaluator must generalize to policies whose behaviors lie outside the training distribution. We address these challenges with SC3-Eval, a self-consistent video generation recipe that adapts a pre-trained video foundation model into an accurate policy evaluator by enforcing three complementary forms of consistency. First, forward-inverse dynamics consistency jointly trains the model to predict frames from actions and to recover actions from frames, anchoring generated rollouts to a physically plausible action manifold and counteracting the drift a forward-only model cannot penalize. Second, cross-view consistency trains the model to inpaint each camera view from the other, keeping the multi-camera observation coherent over long rollouts without any explicit memory mechanism. Third, test-time consistency reuses the inverse dynamics mode at inference as a per-action-chunk uncertainty signal that terminates rollouts whose generated frames drift away from the requested actions. We also demonstrate SC3-Eval rollouts reproduce the failure modes that policies exhibit in real-world rollouts, supporting fine-grained diagnostic comparison rather than aggregate ranking alone. Across seven real-world vision-language-action policies, SC3-Eval attains a closed-loop Pearson correlation of $0.929$ and MMRV of $0.119$, outperforming three strong prior video-model-based baselines, and generalizes to new tasks.

05.
PLOS Computational Biology 2026-06-22

Towards modeling phage therapy

by Rob J. de Boer, Robert Schooley, Alan S. Perelson Patients infected with life-threatening multi-drug resistant (MDR) bacteria have been treated with cocktails of bacteriophages. This is a complicated form of personalized medicine as the phages given to a patient have to be selected beforehand on the basis of their lytic capacity of the infecting bacteria. Because bacteria rapidly become resistant, the evolution of resistance to a diverse cocktail of phages is a complicated dynamical process, during which competing bacterial strains replace one another by accumulating several resistance mechanisms, each of which may involve a fitness cost. As a consequence, it is typically not known why a particular phage therapy succeeded or failed, and how one can optimize the composition of the cocktails to maximize the rate of success. To improve upon this, we extend an existing in vivo-calibrated mouse model into a novel mathematical model for the human situation, and include multiple phages infecting multiple bacterial strains, differing in their resistance to each of the phages. We adjust several parameter estimates of the bacterial model to the human situation, and use the model to describe a successful case of phage therapy involving several cocktails, each containing several phages. In the model, treatment success crucially depended on pretreatment resistance levels, and on the diversity and the timing of the cocktails. Once an appropriate cocktail is found, it is less important to further optimize the infection rates of the phages. Resistant bacterial strains expand rapidly when sensitive strains decline, and the higher the infectivity of the phages, the faster resistant strains expand. Because resistance evolves rapidly, it is best to provide a diverse set of phages right from the start of therapy, i.e., to hit hard and early, and create a high genetic barrier to bacterial resistance.

06.
bioRxiv (Bioinfo) 2026-06-20

A network approach to DNA methylation clocks

Biological age predicts health and lifespan better than chronological age, but remains difficult to measure. One leading molecular proxy for biological age is DNA methylation, which underlies age predictors known as "clocks". These clocks use penalized linear regression to predict chronological age from methylation levels using selected cytosine–guanine pairs (CpGs) along DNA. Although they predict chronological age within a few years and track mortality risk, there are several issues. Different clocks share a vanishingly small number of CpG sites, many of which show weak associations with age. Also, the clocks often do not transfer across methylation array platforms. This paper takes a network approach to better understand these issues. By using 12 public datasets from human blood, we build a co-methylation network of the sites that show the strongest age correlation. After pruning weak links, we find that it has a small number of large modules of covarying CpGs surrounded by many small modules and singleton sites. These modules are biologically interpretable, as they are associated with CpG island contexts and enriched for distinct Gene Ontology functions. We also map five established clocks onto this network (Horvath, Hannum, AltumAge, Skin & Blood, and Han) and find that they select some CpGs from the same module. This suggests that they are more similar than they appear. The network structure also suggests new ways to build clocks. A simple clock that retains one CpG per module matches the performance of established clocks. A second one, built from module-level principal components, outperforms all five established clocks in three validation cohorts and is transferable across array platforms (Illumina Infinium Methylation 450K or EPIC arrays). Overall, the network perspective shifts attention from individual CpG sites to modules of covarying sites. This perspective helps explain why DNA methylation clocks perform so well despite their differences and provides a more systematic approach for developing the next generation of aging biomarkers.

07.
arXiv (CS.LG) 2026-06-17

Recursive Scaling in Masked Diffusion Models

arXiv:2606.18022v1 Announce Type: new Abstract: Masked diffusion models (MDMs) have recently emerged as a promising paradigm for sequence generation. Scaling MDMs is conventionally achieved by increasing the parameter count or the number of denoising steps. We introduce Recursive Masked Diffusion Models (R-MDMs), which add recursive depth as a third scaling axis by repeatedly applying the same denoising transformer within each diffusion step. Recursion enables iterative refinement of the output through parameter reuse, increasing effective model depth without increasing parameter count. Across structured generation tasks, including Sudoku and Countdown, we show that R-MDMs achieve substantially improved parameter efficiency: a model with $L$ recursive iterations often matches the performance of non-recursive baselines with roughly $L\times$ more parameters. Moreover, recursive refinement can partially substitute for additional denoising steps, allowing recursive models to reach the same generation quality with fewer forward passes at inference time. These results suggest that recursive depth is a practically useful scaling mechanism for MDMs, improving both parameter efficiency and the allocation of test-time compute.

08.
arXiv (CS.LG) 2026-06-15

Online Convex Optimization with Sublinear Noisy Probes

arXiv:2606.14640v1 Announce Type: new Abstract: We study Online Convex Optimization (OCO) over a convex set $K\subseteq \mathbb R^d$, where in each round $t$ the learner selects $x_t\in K$ and then observes a convex loss $f_t:K\to[0,1]$, with the goal of minimizing regret to the best fixed decision in hindsight. We introduce a unified probing model that generalizes two recent lines of work: sublinear best-expert queries in the experts setting, and pairwise (comparison-based) feedback available every round in OCO. In our framework, the learner has a budget of $k\le T$ pairwise probes; on a probed round it may query two points and learn which one has smaller loss. Our main result shows that even a sublinear and noisy probe budget can provably improve worst-case regret in the full feedback OCO regime. With $k$ $\delta$-noisy pairwise probes, we obtain: $ Reg_T \le O\left(\min\left\{\sqrt{dT\ln T},\; \frac{dT\ln T}{k|1-2\delta|}\right\}\right) $, which is tight (up to logarithmic factors in $T$) across $T$, $k$ and $\delta$. Specifically regarding the noise parameter $\delta \in [0,1]$, the regret guarantee smoothly degrades as the oracle response approaches a coin flip, i.e., $\delta$ is close to $\frac{1}{2}$. When applying the same techniques to a finite $K$ for the prediction with $d$ experts setting, the resulting rates are instead completely tight in all parameters, including $d$. Our analysis gives a streamlined treatment of pairwise probing in OCO by quantifying the benefit of probing via a variance reduction effect, combined with a second-order (variance-based) analysis of Continuous Exponential Weights.

09.
arXiv (CS.AI) 2026-06-11

CoVar: Confidence-Variance-Guided Pseudo-Label Selection for Semi-Supervised Learning

arXiv:2601.11670v3 Announce Type: replace-cross Abstract: Pseudo-label selection in semi-supervised learning is commonly driven by maximum-confidence thresholds, yet confidence alone can be unreliable under model overconfidence and class imbalance. We propose CoVar, a confidence–variance framework that assesses pseudo-label reliability by jointly modeling Maximum Confidence (MC) and Residual-Class Variance (RCV). Starting from entropy minimization, we derive a second-order cross-entropy approximation showing that low-loss pseudo-labels are favored when MC is high and RCV is low, with a confidence-dependent penalty that becomes stronger for near-certain predictions. Based on this criterion, CoVar embeds predictions into a two-dimensional confidence–variance space and uses SVD-based spectral relaxation to separate reliable and unreliable predictions without hand-tuned confidence thresholds. Cluster-wise Gaussian weighting then converts this separation into per-sample training weights. The resulting weights can be integrated into existing semi-supervised segmentation and classification pipelines during training and introduce no inference-time overhead. Experiments on PASCAL VOC 2012, Cityscapes, CIFAR-10, CIFAR-100, SVHN, and STL-10 show clear gains on VOC and Cityscapes under matched backbones, as well as competitive or improved error rates on standard classification benchmarks. These results indicate that residual-class dispersion provides a useful signal complementary to confidence for robust pseudo-label selection.

10.
arXiv (CS.CL) 2026-06-16

Ling and Ring 2.6 Technical Report: Efficient and Instant Agentic Intelligence at Trillion-Parameter Scale

Efficient and scalable agentic intelligence requires models that can deliver both low-latency responses and strong reasoning capabilities while remaining practical to train, serve, and deploy. In this report, we present Ling-2.6 and Ring-2.6, a family of models designed to address this challenge at scale. Ling-2.6 is optimized for instant response generation and high capability per output token, whereas Ring-2.6 is tailored for deeper reasoning and more advanced agentic workflows. Instead of training from scratch, we upgrade the Ling-2.0 base model through architectural migration pre-training and large-scale post-training. This upgrade is guided by a unified co-design of model architecture, optimization objectives, serving systems, and agent training environments, enabling improvements in both model capability and deployment efficiency. At the architectural level, we introduce a hybrid linear attention design that integrates Lightning Attention with MLA, improving the efficiency of long-context training and decoding. To further enhance token efficiency, we optimize capability per output token through Evolutionary Chain-of-Thought, Linguistic Unit Policy Optimization, bidirectional preference alignment, and shortest-correct-response distillation. For agentic capabilities, we propose KPop, a reinforcement learning framework designed to support stable training of Ring-2.6-1T on large-scale environment-grounded data. KPop improves training efficiency through asynchronous scheduling across coding, search, tool use, and workflow execution, enabling scalable learning from complex agent-environment interactions. Together, Ling-2.6 and Ring-2.6 provide a practical pathway toward efficient, scalable, and open agentic systems. We open-source all checkpoints in the 2.6 family to support further research and development in practical agentic intelligence.

12.
arXiv (CS.AI) 2026-06-18

Why SWAVE May Not Be All You Need:A Concept-Evolution Retrospective on Complex-Valued Recurrent Language Models

arXiv:2606.18324v1 Announce Type: cross Abstract: SWave is a complex-valued recurrent language model (169.26M parameters, D=384, L=16, T=2048) trained on FineWeb-Edu using 2xH100 NVL. It was designed around three founding premises: that representing language as complex waves rather than real-valued numbers enables richer information encoding; that a Cayley-parameterised unitary transition provides a mathematical guarantee against state decay or explosion; and that a hidden state which rotates rather than shrinks preserves signal integrity over arbitrarily long contexts. The core of SWave evolved substantially across three development phases. The Resonance Head was found to structurally admit imaginary-channel collapse as a global loss minimum (a failure mode we term cos-domination collapse) and was superseded by an untied head with independent real and imaginary embedding tables from the Phase-Associative Memory (PAM) architecture. This resolved the degenerate minimum and enabled stable 200,000-step training (best-step PPL 22.0 at step 89,861). ComplexNorm and the Wave Propagation Scan proved load-bearing throughout all three phases and were retained to the final architecture. ProtectGatedScan was reframed as a structural prior rather than a learned behaviour. The four multi-scale retention concepts showed no measurable improvement under controlled evaluation and were found non-load-bearing. The ComplexGatedUnit was superseded by a real-valued squared-ReLU channel mixer with fewer parameters. The auxiliary training objectives showed no benefit once structural constraints were resolved. The investigation yields a formal characterisation of cos-domination collapse, a parallel scan with a log-space backward pass for numerical stability, six transferable engineering principles for complex-valued recurrent training, and a plan-to-code traceability methodology for catching structural divergences that conventional test suites miss.

13.
arXiv (math.PR) 2026-06-11

An Information-Theoretic Analysis of Threshold Group Testing

arXiv:2606.11353v1 Announce Type: cross Abstract: We study the Threshold Group Testing (TGT) problem in the noiseless and non-adaptive setting, where the objective is to exactly recover a sparse binary vector from pooled tests, using as few tests as possible. In TGT, each test applied to a subset of items returns a positive outcome if the number of 1's (defective items) in that subset meets or exceeds a specified threshold, and has a negative outcome otherwise. We investigate how the complexity of TGT compares to that of Classical Group Testing (CGT), corresponding to the special case of the threshold equal to one, and analyse the impact of increasing the threshold on the required number of tests. Our main contribution is the derivation of a sharp information-theoretic phase transition at $c_{\mathrm{inf}}^{\mathrm{TGT}}k\log(n/k)$ (non-adaptive) tests for TGT within the constant-column test design. The threshold constant $c_{\mathrm{inf}}^{\mathrm{TGT}}$ is expressed as a function of the prevalence of defectives and the threshold value. Our upper bound is derived under an analytic assumption, and we verify that this assumption is satisfied for a threshold value of 2. The value of $c_{\mathrm{inf}}^{\mathrm{TGT}}$ reveals that TGT on the constant-column design has the same information-theoretic behaviour as CGT in the low-prevalence regime. Yet, strikingly, at higher prevalences, the threshold leads to a significant reduction in the number of tests. On the other hand, we provide evidence that when the asymptotic proportion of defective items is positive, TGT actually becomes strictly harder than CGT (excluding trivial reductions).

14.
arXiv (CS.LG) 2026-06-15

Muon$^p$: Muon with Fractional Spectral Powers

arXiv:2606.13867v1 Announce Type: new Abstract: Muon is an increasingly widely used optimizer that replaces a gradient $G=USV^\top$ with its polar factor $UV^\top$, thereby flattening the singular spectrum. However, full flattening discards singular-value information that may matter for adaptation. We introduce Muon$^p$, a Muon-style optimizer that instead uses fractional spectral-power updates $US^pV^\top$ for rational $p\in(0,1)$, interpolating between Muon and gradient descent. To make it practical, we prove that fractional spectral powers cannot be computed by any fixed univariate polynomial iteration, and furthermore derive low-degree odd bivariate recurrences that approximate $US^pV^\top$ using only matrix multiplications, preserving Muon's matrix-multiplication-only structure and compute complexity. We show that Muon$^p$ maximizes the linear improvement in loss under the Schatten $q$-norm for $q=1+\frac{1}{p}$. Empirically, Muon$^p$ is especially effective for finetuning: on billion-scale models, Muon$^p$ improves validation perplexity and downstream task performance. We further analyze when Muon$^p$ is less suitable, through the lens of spectral geometry. Our results reveal important insights on when preserving the singular spectrum can bring significant gains, and introduce a principled way to achieve them.

15.
bioRxiv (Bioinfo) 2026-06-10

GEOAgent: An AI-driven Autonomous Framework for Intelligent GEO Data Retrieval and Standardized Preprocessing

Datasets in the Gene Expression Omnibus (GEO) remain difficult to reuse at scale because sample annotations are heterogeneous and raw sequencing data require assay-specific preprocessing. We present GEOAgent, an AI-driven autonomous framework designed for intelligent dataset retrieval and standardized preprocessing by coupling autonomous semantic governance with an automated Nextflow pipeline named bioStream. Metadata from 181,760 sequencing series and 84,756 associated PubMed records were organized in a relational database and semantic index to support natural-language dataset retrieval. The framework automatically determines assay modalities, resolves experimental design pairings, and standardizes sample naming to minimize manual curation overhead. Based on these parsed attributes, the framework generates deployment-ready manifests to automatically execute containerized workflows across bulk and single-cell omics modalities. In expert-curated benchmarks, the workflow achieved 96% retrieval precision alongside 100% accuracy in assay classification and sample relationship resolution. The web platform is publicly accessible, while the source code and associated databases are openly available via GitHub and Zenodo.

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

S23DR 2026: End-to-End 3D Wireframe Prediction via DETR-Style Set Prediction with Contrastive Denoising

作者:

We present WireframeDETR, our submission to the Structured Semantic 3D Reconstruction (S23DR) 2026 Challenge, which requires predicting a 3D building wireframe from multi-view COLMAP point clouds. Our method applies DETR-style set prediction directly to 3D point clouds, producing wireframes as sets of edge coordinate pairs without any intermediate vertex detection stage. We introduce three technical contributions: (1) contrastive denoising training that stabilises noisy Hungarian matching in early epochs; (2) a multi-scale encoder that aggregates the last encoder layer outputs via learned scalar weights; and (3) progressive auxiliary loss weighting that concentrates gradient signal on the decoder layers that most benefit from it. Our model achieves a public test HSS of 0.575 (F1~=~0.664, IoU~=~0.516) and a best validation HSS of 0.534 on the cleaned val split.

17.
arXiv (quant-ph) 2026-06-19

Matrix Product Operator Encodings of the Magnus Expansion and Dyson Series

arXiv:2605.21597v2 Announce Type: replace Abstract: We introduce a matrix product operator (MPO) encoding of the Magnus expansion and the Dyson series for one-dimensional quantum lattice models with time-dependent Hamiltonians. The MPO construction can be made accurate up to arbitrary order in the time step, it can be applied to both finite and infinite systems, and it can handle long-range interactions. The resulting MPO can be combined with state-of-the-art time evolution algorithms based on matrix product states, allowing for drastic improvements in simulating evolution under time-dependent Hamiltonians. Our MPO construction can also be used for the optimization of quantum circuits in the context of quantum simulation of time-dependent Hamiltonians.

18.
PLOS Computational Biology 2026-06-22

A lactylation- and autophagy-associated prognostic signature reveals LSEC-derived CLEC3B as a novel mediator of hepatocellular carcinoma suppression

作者:

by Youai Song, Yinkuan Ning, Meihui Li, Jianwei Lan, Liangchen Lei, Yufei Han, Zhuo Meng, Binjie Li, Pengpeng Liu, Quanyan Liu The crosstalk between lactylation and autophagy within the hepatocellular carcinoma (HCC) microenvironment is a burgeoning field with profound implications. By integrating multi-omics data from public cohorts, we delineated two molecular subtypes of HCC with divergent clinical outcomes and established a lactylation-autophagy-related prognostic signature. This signature highlighted CLEC3B as a pivotal gene. Subsequent single-cell RNA sequencing and experimental validation unequivocally pinpointed liver sinusoidal endothelial cells (LSECs) as the principal cellular source of CLEC3B, which was significantly downregulated in HCC tissues. Functionally, conditioned media derived from CLEC3B-overexpressing LSECs potently inhibited HCC cell proliferation. Mechanistic investigations revealed that this tumor-suppressive effect was orchestrated through the concurrent suppression of autophagy and diminution of lactylation levels. Our findings position LSEC-secreted CLEC3B as a novel metabolic mediator in HCC, bridging two key pathways in tumor suppression, and endorse its clinical value both as a prognostic indicator and a promising therapeutic target.

19.
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.

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

Diffusion-Proof: Recipe for Formal Theorem Proving Beyond Auto-Regressive Generation

arXiv:2606.19315v1 Announce Type: new Abstract: Enhancing the formal math reasoning capabilities of Large Language Models (LLMs) has become a key focus in both mathematical and computer science communities in recent years. While significant progress has been made in using state-of-the-art Auto-Regressive (AR) LLMs for formal theorem proving, these models suffer from inherent limitations. Their next-token prediction generation methods may yield suboptimal performance due to the challenges of long-range coherence and the compounding of errors over long sequences. Recent advancements in diffusion LLMs (dLLMs), which generate text through iterative denoising of a multi-token block, offer a promising alternative. However, the application of dLLMs to formal mathematics, where maintaining long-range coherence is critical, remains largely understudied. To address the challenges above, we propose **Diffusion-Proof**, to the best of our knowledge, the first framework to train and apply dLLMs for formal theorem proving. Our frameworks contain training and inference methods for two models. The first one is *dLLM-Prover-7B*, which performs whole-proof writing with long-range coherent tactic usage. The second one is *dLLM-Corrector-7B*, which is a novel large block diffusion-based correction model. It leverages the in-filling capabilities of dLLMs to perform local proof correction using bi-directional information. Extensive experiments demonstrate that **Diffusion-Proof** relatively significantly outperforms the AR LLM baseline trained under the same dataset. **Diffusion-Proof** achieves an absolute improvement of **1.61%** on ProofNet-Test and **6.14%** on MiniF2F-Test benchmarks compare to the baseline. Notably, **Diffusion-Proof** successfully resolves one IMO problem that more advanced thinking model DeepSeek-Prover-V2-7B could not solve, showcasing the unique advantage of dLLMs in formal theorem proving.

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

Fully Quantum Algorithm for the 1-dimensional linear Lattice Boltzmann Method

arXiv:2606.16514v1 Announce Type: new Abstract: A fully quantum algorithm for solving the one-dimensional linear advection-diffusion equation using the Lattice Boltzmann method as a numerical procedure is presented in this work. We start by presenting a state of the art of the current usage of quantum algorithms for solving ordinary and partial differential equations. We then describe two algorithms for the one-dimensional Lattice Boltzmann method with two degrees of freedom. The first one is an existing hybrid quantum-classical algorithm with measurements at each time step, and the second one is our improved version, viz. a fully quantum algorithm where only one measurement is needed at the end of the algorithm. The fully quantum algorithm is first executed on a quantum simulator and then compared with a classical approach. Subsequently, the fully quantum algorithm is run on a quantum system with 133 qubits to investigate the effect of noise and the depth of the circuit on the output state. We find fluctuations in the final result due to the decoherence noise of the qubits.

22.
medRxiv (Medicine) 2026-06-17

Preserved Medial Temporal Lobe Flexibility Predicts Memory Generalization Only in the Context of Good Sleep Quality among Older African Americans

Objectives: Poor sleep quality is a risk factor for Alzheimer's disease (AD). Older African Americans experience disproportionately high rates of sleep disturbance and AD. Medial temporal lobe (MTL) flexibility reflects dynamic neural reorganization and may be a marker of generalization performance. This study examined whether sleep quality moderates the association between MTL flexibility and memory generalization. Methods: Fifty older African Americans (MeanAge=69.7{+/-}6.21 years; 80% women) underwent rs-fMRI to quantify MTL flexibility, Rutgers Acquired Equivalence Task for memory generalization, and Pittsburgh Sleep Quality Index for sleep quality. Results: Greater MTL flexibility was associated with better generalization (r=0.367, p=.017). Good sleepers showed higher MTL flexibility (F(1,44)=8.11, p2=.156, p=.007) and superior generalization (F(1,46)= 12.33, p2=.211, p=.001). Sleep quality significantly moderated the MTL flexibility and generalization relationship ({beta}=-1.519, p=.012). Conclusions: Preserved MTL flexibility may confer generalization only in good sleepers, suggesting that sleep disturbance may disrupt the MTL neural resilience among older African Americans.

23.
arXiv (CS.AI) 2026-06-11

From Awareness to Action: Understanding and Overcoming the Research-Practice Gap in Algorithmic Fairness for Public Health

arXiv:2606.11214v1 Announce Type: cross Abstract: Algorithmic fairness is essential for responsible ML-driven public health research, yet its practical implementation remains limited. To investigate this awareness-action gap, we conducted a sequential mixed-methods study comprising expert interviews, an online survey, and systematic mapping. The expert interviews informed the design of the survey, which in turn revealed fragmented definitions of fairness, limited training and guidance, reliance on external sources, and rare use of formal assessment, mitigation, or monitoring. These findings were subsequently mapped onto three established research-practice gap lenses: the Knowledge-Practice Gap, the Knowledge-to-Action Cycle, and the Knowing-Doing Gap, each offering complementary perspectives. Building on this synthesis, we introduce the Fairness-to-Action framework, which integrates methodological, organizational, and systemic dimensions to identify where translation of algorithmic fairness knowledge stalls. Our analysis shows that fairness remains weakly institutionalized, translation mechanisms are externally driven, and system-level priorities continue to emphasize accuracy over fairness. These insights suggest critical leverage points for advancing safe, fair, and ethical ML-driven public health research practice.

24.
arXiv (CS.CV) 2026-06-16

Active Reference Acquisition in Few-Shot Font Generation

Few-shot font generation aims to synthesize the remaining glyphs of a font given one or a few reference glyphs while preserving stylistic consistency, thereby supporting font designers in efficiently completing a typeface. Existing methods primarily focus on improving generation quality given a fixed reference set. However, when the current reference glyphs are insufficient to represent the target style, few-shot font generation may fail to produce satisfactory results. In practical scenarios, additional reference glyphs can often be obtained from the designer when necessary. Accordingly, we propose a new framework, Active Reference Acquisition in Few-Shot Font Generation, in which the model sequentially decides which character to acquire next as an additional reference. Furthermore, we propose a reference part-coverage-based acquisition function to efficiently query the designer. Motivated by the observation that font styles are well characterized by local structural parts, we represent each glyph using a histogram of local features and select query characters that maximize the expected part coverage of the reference set. By prioritizing characters that contain parts not yet covered by the current references, the proposed method progressively expands the diversity of visual parts in the reference set. As a result, generation quality is improved with fewer queries. Experiments on the Google Fonts dataset demonstrate that the proposed method achieves higher generation quality than random querying and reference-agnostic baselines. The code is available at https://github.com/matsuo-shinnosuke/ActiveRef-FontGen.

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medRxiv (Medicine) 2026-06-22

The Unsteady Return of Command-Following: Recovery and Instability of Bedside Motor Command-Following After Acute Brain Injury

Background/Objective: Following a verbal command marks the bedside transition from unresponsiveness to overt recovery of consciousness after acute brain injury. Its timing across phenotypes, stability once present, and dependence on sedation are uncharacterized at scale. Methods: Retrospective cohort of adults with acute brain injury, first intensive care unit stay, MIMIC-IV. Command-following was the Glasgow Coma Scale motor response "Obeys Commands." Among patients not following commands at admission, cumulative incidence was estimated with death or hospice and discharge without recovery as competing events. Instability was quantified as transient first recovery and threshold crossings; examinations were tagged for concurrent sedation. Principal findings were externally validated in the multicenter eICU Collaborative Research Database. Results: Of 13,900 brain-injured patients with three or more motor examinations, 5,498 (39.6%) were not following commands at admission. The cumulative incidence of first command-following was 43.5% by 24 hours and 65.0% by 14 days, ranging at 14 days from 36.9% in anoxic injury to 77.2% in ischemic stroke (anoxic versus ischemic stroke at 72 hours, difference 0.41; adjusted P = .002). Among 3,573 patients who recovered, the first recovery was transient in 22.2%, and 62.4% crossed the threshold repeatedly. Non-following was strongly associated with sedation, consistent with an arousal-dependent examination. In eICU, the 14-day incidence was 64.8%, and transient first recovery was 22.7%, closely matching the primary cohort. Conclusions: After acute brain injury, overt bedside command-following returns early but unsteadily, with phenotype-dependent timing, threshold fluctuation, and strong dependence on sedation. A single charted observation is an unreliable index of the underlying state.