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01.
bioRxiv (Bioinfo) 2026-06-16

Evidence for recombination in dengue virus genomes

Recombination is a key driver of RNA virus evolution, yet its extent and evolutionary implications in dengue virus (DENV) remain incompletely understood. We conducted a comprehensive, genome-wide recombination screen across 6,905 complete DENV genomes representing all four serotypes, 82 countries, and eight decades of sampling (1944-2023) retrieved from the Bacterial and Viral Bioinformatics Resource Center. Using seven complementary recombination detection methods implemented in RDP5, we identified 66 recombination events across 53 unique recombinant sequences, of which 29 are newly described. Events included intra-genotypic (n = 18), inter-genotypic (n = 32), and inter-serotypic (n = 16) exchanges spanning 14 genotypes and four continents, with no meaningful serotype-level enrichment (Cramer's V = 0.054). Recombination was concentrated in non-structural genes, most frequently NS3 (19 events), NS5 (17), and NS2 (12), while the capsid gene contained no recombination events, consistent with strong functional constraint. Single-nucleotide polymorphism analyses confirmed low divergence between recombinants and their inferred parents in both recombinant and non-recombinant regions. Phylogenomic analysis of 6,642 sequences revealed that recombinants cluster significantly closer to their major parents (p = 8.9 x 10-6 ) and that their removal does not significantly alter tree topology (p = 0.898), suggesting that the short length of recombinant regions limits phylogenetic conflict. We also introduce RECOSIM, an unsupervised machine-learning tool for recombination detection that achieved higher precision than RDP5 on both simulated (93.4% vs. 80.0%) and empirical (98.1% vs. 39.3%) datasets. Collectively, these results establish recombination as a widespread, pan-serotypic phenomenon in DENV with implications for genomic surveillance, vaccine evaluation, and evolutionary inference.

02.
medRxiv (Medicine) 2026-06-18

Rare Coding Variants Reveal Distinct Genetic Architectures Across Multidimensional Sleep Phenotypes

Sleep and circadian traits have been widely studied using common variants, but the contribution of rare coding variation remains unclear. We analyzed rare coding variants in 397,065 whole-exome sequenced UK Biobank participants across 36 sleep phenotypes from self-report, diagnoses, sleep medication use and accelerometry, and meta-analyzed results with 171,536 whole-genome sequenced All of Us participants of diverse ancestries, with replication in the Mass General Brigham Biobank (N = 31,275). We identified 260 genes associated with sleep phenotypes, including novel associations with sleep medication use in 29 genes and 24 out of 29 have not previously been reported with any sleep phenotypes. We observed modest but significant rare variant heritability and strong genetic correlations between sleep medication use, insomnia and fatigue. Temporal gene expression trajectory analyses indicate that genes associated with self-reported sleep traits show constant high prenatal expression, whereas genes linked to sleep medication phenotypes exhibit peak expression in the late prenatal period. These findings highlight distinct biological mechanisms captured by different measurement sources of sleep phenotypes and reveal rare-variant-informed targets for therapeutic discovery.

03.
arXiv (quant-ph) 2026-06-24

Symmetric mass generation of interacting chiral fermions on a one-dimensional lattice without fermion doubling

arXiv:2606.24713v1 Announce Type: cross Abstract: Symmetric mass generation is the interaction-induced opening of a fermion gap without spontaneous symmetry breaking. The anomaly-free 3-4-5-0 model of Wang and Wen provides a minimal one-dimensional setting for this phenomenon, but a direct lattice realization faces two obstacles: fermion doubling for local chiral discretizations and perturbative irrelevance of the six-fermion gapping interaction. We address both obstacles. First, we formulate the model on a strictly one-dimensional tangent-fermion lattice, where a nonlocal hopping produces a single chiral branch without a mirror partner while retaining an efficient tensor-network representation. Second, we add a Hubbard-type density-density interaction (Luttinger parameter $K$) that reduces the scaling dimension of the 3-4-5-0 interaction from $5$ to $5K$, making it relevant for $K

04.
arXiv (CS.LG) 2026-06-16

MultiMolecule: a modular ecosystem for biomolecular sequence-model workflows

作者:

arXiv:2606.16540v1 Announce Type: cross Abstract: Biomolecular sequence models are increasingly reused outside the studies in which they were introduced, but public checkpoints rarely preserve the execution context needed to inspect source-defined behavior, adapt models to new assays, compare models under shared task definitions or deploy biological predictions. MultiMolecule is an open-source Python ecosystem that turns heterogeneous RNA, DNA and protein sequence-model releases into complete, source-checked model-family implementations with shared loading, workflow and prediction interfaces. The Resource state reported here includes 53 complete model-family implementations with 112 standardized model checkpoints, together with 16 curated dataset resources released through 39 public dataset repositories and 10 user-facing prediction pipelines. Standardized components are linked to source provenance, conversion or preparation code, source-reference checks, Extended Data summaries and public documentation, allowing users to inspect what was standardized, what behavior was checked and how each component enters training, evaluation, inference or deployment. By shifting reuse from repository-specific checkpoints to executable implementations connected to standardized checkpoints, curated datasets, Runner workflows and biological prediction pipelines, MultiMolecule provides common infrastructure for preserving source-defined model behavior, adapting models to new assays, enabling controlled evaluation and deploying biomolecular predictions.

05.
arXiv (math.PR) 2026-06-18

Denoising Distances in Metric Measure Spaces

arXiv:2606.18301v1 Announce Type: cross Abstract: Recent work studied the problem of finding clusters and denoising pairwise distances from noisy distances of points sampled on a manifold. We study the same problems in more general metric measure spaces under \lowerphiregularity{}. We give an algorithm that extracts large localized clusters around every sampled point and uses them to denoise distances to any fixed accuracy, with near-linear running time in the dense fixed-accuracy regime. We also show how to achieve much higher accuracy with a non-efficient algorithm. This suggests that unlike the Riemannian case, denoising to higher accuracy in more general metric spaces has a statistical-computational gap.

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

Green SARC: Predictive Cost and Carbon Governance for Agentic AI Systems

arXiv:2606.15954v1 Announce Type: cross Abstract: Agentic AI systems act through tools and sub-agents, yet the controls meant to bound their financial and environmental cost still sit on dashboards evaluated beside or after execution. Green SARC applies the SARC governance-by-architecture framework – four enforcement sites in the agent loop – to FinOps and GreenOps, contributing the theory of what to enforce and how to predict it. We report four policy-independent results. (i) The unconstrained "State Snowball" is $\Theta(n^2)$ in loop depth; on 3,000 real multi-step plans (SWE-rebench) it holds on 100%, with median curvature $\hat{c}_2=216$ exceeding the linear-accretion prediction $p/2=134$ – real plans accrete faster than the model. (ii) On real residuals the Normal-$\sigma$ gate under-covers (92% at nominal 95%); split-conformal calibration holds (95.2%). (iii) A soft Lagrangian penalty tuned to the budget in expectation breaches it on 91.5% of seeds; the architectural gate breaches 0%. (iv) Under binding budgets the gate's over-budget incidence is 0% on synthetic and real (BurstGPT) arrivals. End-to-end token/USD/carbon savings (47–55%) are real but policy-dependent in magnitude – set by a scope-cap knob, not by gate rejections. The library is open-source, dependency-free, and ships a regeneration script for every cited number.

07.
arXiv (CS.AI) 2026-06-24

Multimedia and Visual Analytics in the Agentic Era

arXiv:2504.06138v3 Announce Type: replace-cross Abstract: Professional users need tools to help them gain actionable insights from large multimedia collections. Foundation models and AI agents have rapidly changed the playing field, and improving their accuracy, trustworthiness, and reasoning capabilities are active topics in the computer vision, machine learning, and multimedia communities. Most current research focuses on benchmark driven algorithmic improvements. The multimedia community is the place to go beyond algorithms and consider complete multimedia analytics systems that support professional users in their complex tasks and achieve a true teaming of humans and AI. Supporting users with machine learning and visualizations has been studied for decades in the visual analytics field. In this paper, we propose a framework to bring multimedia and visual analytics together and indicate how it could impact current and new multimedia analytics solutions. Additional information can be found at https://staff.fnwi.uva.nl/m.worring/analytics-model.html

08.
arXiv (CS.CV) 2026-06-12

VideoMDM: Towards 3D Human Motion Generation From 2D Supervision

We introduce VideoMDM, a diffusion-based framework that trains 3D human motion priors directly from accurate 2D poses extracted from monocular videos, without any 3D ground truth. A pretrained 2D-to-3D lifter provides approximate 3D pose sequences that serve as a noisy teacher: these are diffused, denoised by the model in 3D, and supervised in 2D by reprojecting the prediction and comparing against accurate keypoints. We show that, under mild assumptions, a depth-weighted 2D reprojection loss is equivalent in expectation to direct 3D supervision, and we adapt standard 3D motion regularizers - velocity consistency and over-parameterized representation alignment - to this 2D setting. Unlike methods that lift 2D to 3D only at inference, VideoMDM learns a coherent 3D motion manifold during training. On HumanML3D it nearly closes the gap to fully 3D-supervised MDM (FID 0.88 vs 0.54); On real video datasets Fit3D and NBA the method learns to generate motions consistently preferred by humans, with strong quantitative results.

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

ASRU: Activation Steering Meets Reinforcement Unlearning for Multimodal Large Language Models

Multimodal large language models (MLLMs) may memorize sensitive cross-modal information during pretraining, making machine unlearning (MU) crucial. Existing methods typically evaluate unlearning effectiveness based on output deviations, while overlooking the generation quality after unlearning. This can easily lead to hallucinated or rigid responses, thereby affecting the usability and safety of the unlearned model. To address this issue, we propose ASRU, a controllable multimodal unlearning framework that incorporates generation quality as a core evaluation objective. ASRU first induces initial refusal behavior through activation redirection, and then optimizes fine-grained refusal boundaries using a customized reward function, thereby achieving a better trade-off between target knowledge unlearning and model utility. Experiments on Qwen3-VL show that ASRU significantly improves unlearning effectiveness (+24.6%) on average and generation quality (5.8X) on average while effectively preserving model utility, using only a small amount of retained supervision data.

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

GePBench: Evaluating Fundamental Geometric Perception for Multimodal Large Language Models

Geometric shapes play important roles in both physical world and human cognition. While multimodal large language models (MLLMs) have made significant advancements in visual understanding, their abilities to recognize geometric shapes and their spatial relationships, which we term geometric perception, are not explicitly and systematically explored. To address this gap, we introduce GePBench, a novel benchmark specifically designed to assess the geometric perception capabilities of MLLMs. Our extensive evaluations reveal that even the current state-of-the-art MLLMs exhibit significant deficiencies in geometric perception tasks. Furthermore, we show that models trained with GePBench data demonstrate considerable improvements on a wide range of downstream tasks, highlighting the critical role of geometric perception in enabling advanced multimodal applications. Our code and datasets are available at \href{https://github.com/Changhao-Xiang/GePBench}{https://github.com/Changhao-Xiang/GePBench}.

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

HACMatch Semi-Supervised Rotation Regression with Hardness-Aware Curriculum Pseudo Labeling

Regressing 3D rotations of objects from 2D images is a crucial yet challenging task, with broad applications in autonomous driving, virtual reality, and robotic control. Existing rotation regression models often rely on large amounts of labeled data for training or require additional information beyond 2D images, such as point clouds or CAD models. Therefore, exploring semi-supervised rotation regression using only a limited number of labeled 2D images is highly valuable. While recent work FisherMatch introduces semi-supervised learning to rotation regression, it suffers from rigid entropy-based pseudo-label filtering that fails to effectively distinguish between reliable and unreliable unlabeled samples. To address this limitation, we propose a hardness-aware curriculum learning framework that dynamically selects pseudo-labeled samples based on their difficulty, progressing from easy to complex examples. We introduce both multi-stage and adaptive curriculum strategies to replace fixed-threshold filtering with more flexible, hardness-aware mechanisms. Additionally, we present a novel structured data augmentation strategy specifically tailored for rotation estimation, which assembles composite images from augmented patches to introduce feature diversity while preserving critical geometric integrity. Comprehensive experiments on PASCAL3D+ and ObjectNet3D demonstrate that our method outperforms existing supervised and semi-supervised baselines, particularly in low-data regimes, validating the effectiveness of our curriculum learning framework and structured augmentation approach.

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

RegimeVGGT: Layer-Wise Spatially Preserving Redundancy Removal for Visual Geometry Grounded Transformer

Visual Geometry Grounded Transformer (VGGT) recovers dense 3D scene structure from multi-view images in one forward pass, but quadratic cross-frame attention limits its scalability. Existing training-free accelerators reduce computation uniformly along one axis, missing layer heterogeneity. Our spectral, probing, and causal analyses reveal three regimes: shallow layers lack cross-view structure, middle layers drive cross-view alignment, and deep layers are redundant for dense geometry yet their cross-frame attention remains essential for pose. RegimeVGGT applies layer-wise U-shaped compression along two axes: Saliency-Guided Banded Merging protects geometry- and edge-salient tokens, while Selectively Protected K/V Downsampling preserves cross-frame spatial coverage and the pose-critical path through a phase-shifted spatial grid, a reference-frame anchor, and uncompressed camera/register tokens. Training-free, RegimeVGGT achieves a 6.7x speedup over VGGT* at matched reconstruction quality.

13.
arXiv (CS.CV) 2026-06-19

Holo-World: Unified Camera, Object and Weather Control for Video World Model

Video world models are moving toward preserving an observed world under controllable camera and object motion while allowing its environmental state to change. Yet these controls remain isolated, and weather generation typically relies on a source video or reconstructed scene that already specifies future structure. We study a first-frame-anchored source-to-state setting, where the model starts from a single image and follows explicit camera and object controls and an optional weather instruction, then generates a video that either preserves the source world or transfers it to a target weather state. To address these challenges, we first build HoloStateData, a state video dataset that turns diverse videos into unified control samples for camera, object, and weather supervision. Second, we introduce Holo-World, a unified controllable video world model that jointly controls scene from a single image. Its Unified Scene Adapter factorizes world preservation and weather transfer into distinct parameter subspaces, using rendered background, geometry buffers, and object controls to maintain controlled scene structure while modeling weather-dependent appearance and particle effects. Additionally, Scene-Weather Decomposed CFG guides scene and weather residuals separately, strengthening target weather effects without over-amplifying the full condition. Quantitative and qualitative experiments demonstrate that Holo-World maintains precise camera and object control with consistent scene structure while transferring scenes into diverse target weather state, outperforming video-to-video weather editing baselines on weather-state generation. Our project page is available at \url{https://xiangchenyin.github.io/Holo-World/}.

14.
arXiv (CS.AI) 2026-06-17

IsabeLLM: Automated Theorem Proving Applied to Formally Verifying Consensus

arXiv:2606.18098v1 Announce Type: new Abstract: Advances in Artificial Intelligence (AI) have led AI for Theorem Proving to become a promising means of formally verifying computer systems. Whilst formal verification is traditionally reserved for safety-critical systems due to the required amount of expertise and effort, AI can help to automate a large amount of this workload and make it far more accessible. Blockchain-based systems are becoming increasingly popular and are frequently targeted by malicious actors, often resulting in huge financial losses, highlighting the need to better verify these systems and mitigate vulnerabilities. Arguably the most important component of these systems is the consensus protocol, which allows nodes to agree on decisions in a potentially adversarial environment. In this paper, we improve upon IsabeLLM, the automated theorem proving tool in Isabelle. Namely, we implement a Retrieval-Augmented Generation framework, Error tracing and counterexample generation for improved context supplied to the Large Language Model. Compatibility with the latest version of Isabelle and Sledgehammer is also implemented for improved efficiency. We compare the performance of the two versions of IsabeLLM in their ability to complete the verification of Bitcoin's Proof of Work consensus.

15.
arXiv (CS.LG) 2026-06-12

Earth Science Foundation Models: From Perception to Reasoning and Discovery

arXiv:2605.12542v2 Announce Type: replace-cross Abstract: Large foundation models (FMs) are transforming Earth science by integrating heterogeneous multimodal data, such as multi-platform imagery, gridded reanalysis data, diverse geophysical and geochemical observations, and domain-specific text, to support tasks ranging from basic perception to advanced scientific discovery. This paper provides a unified review of Earth science foundation models (Earth FMs) through two complementary dimensions: depth, which traces the evolution of model capabilities from perception to multimodal reasoning and agentic scientific workflows, and breadth, which summarizes their expanding applications across the atmosphere, hydrosphere, lithosphere, biosphere, anthroposphere, and cryosphere, as well as coupled Earth system processes. Using this framework, we review representative multimodal Earth foundation models and compile more than 200 datasets and benchmarks spanning diverse Earth science tasks and modalities. We further discuss key challenges in multimodal data heterogeneity, scientific reliability and continual updating, scalability and sustainability, and the transition from foundation models to agentic and embodied Earth intelligence, and outline future directions toward more integrated, trustworthy, and actionable AI Earth scientists. Overall, this paper offers a structured roadmap for understanding the development of Earth foundation models from both capability depth and application breadth.

16.
medRxiv (Medicine) 2026-06-15

A More-Than-Human Approach to Designing for Mental Health: Remixing Prototypes for the Contexts of Complex Healthcare Infrastructures

Digital mental health tools (DMHTs) often fail to be successfully implemented in clinical settings. While user- and human-centred design frameworks are frequently proposed for developing effective tools, they are insufficient to address the sociotechnical complexity of healthcare environments. This paper addresses this limitation by detailing the application of a more-than-human design framework to incorporate wider contextual factors into design decisions. To demonstrate the application of this more-than-human design framework, we present a case study showcasing the design of one specific feature within a DMHT intended to support Health Improvement Practitioners (HIPs) in New Zealand's Integrated Primary Mental Health and Addictions (IPMHA) service. Our process blends usage-context storyboards with interface prototypes, using think-aloud interviews to test the contextual fit of our prototypes. The initial design concept failed due to contextual factors such as inconsistent wait times and the administrative burden on clients and clinic staff. This led to a pivot to a more context-appropriate, practitioner-focused, in-session concept for digital psychometric administration and automated scoring. This case study demonstrates that for DMHTs to be viable within complex healthcare environments, design must focus on more than the needs of a single user, incorporating multiple stakeholders and contextual variables across the wider service-delivery context.

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

ThinkJEPA: Empowering Latent World Models with Large Vision-Language Reasoning Model

Recent progress in latent world models (e.g., V-JEPA2) has shown promising capability in forecasting future world states from video observations. Nevertheless, dense prediction from a short observation window limits temporal context and can bias predictors toward local, low-level extrapolation, making it difficult to capture long-horizon semantics and reducing downstream utility. Vision–language models (VLMs), in contrast, provide strong semantic grounding and general knowledge by reasoning over uniformly sampled frames, but they are not ideal as standalone dense predictors due to compute-driven sparse sampling, a language-output bottleneck that compresses fine-grained interaction states into text-oriented representations, and a data-regime mismatch when adapting to small action-conditioned datasets. We propose a VLM-guided JEPA-style latent world modeling framework that combines dense-frame dynamics modeling with long-horizon semantic guidance via a dual-temporal pathway: a dense JEPA branch for fine-grained motion and interaction cues, and a uniformly sampled VLM thinker branch with a larger temporal stride for knowledge-rich guidance. To transfer the VLM's progressive reasoning signals effectively, we introduce a hierarchical pyramid representation extraction module that aggregates multi-layer VLM representations into guidance features compatible with latent prediction. Experiments on hand-manipulation trajectory prediction show that our method outperforms both a strong VLM-only baseline and a JEPA-predictor baseline, and yields more robust long-horizon rollout behavior.

18.
arXiv (CS.CL) 2026-06-16

MosaicQuant: Inlier-Outlier Disaggregation for Unified 4-Bit LLM Quantization

4-bit quantization significantly reduces the memory footprint and accelerates the inference of large language models (LLMs). However, its limited bit-width representation struggles to faithfully capture both dense common values (inliers) and rare large-magnitude values (outliers), causing substantial accuracy degradation. Existing mixed-precision methods mitigate this by retaining outliers in high precision, but at the cost of breaking the uniformity of low-bit execution, introducing precision conversion and extra data movement that undermine practical speedup. We propose MosaicQuant, a unified 4-bit LLM quantization paradigm built on a novel principle of inlier–outlier disaggregation. Rather than elevating outlier precision, MosaicQuant quantizes the full weight matrix into a dense 4-bit base component, where inliers are captured faithfully while outlier are inevitably quantized. A sparse 4-bit residual component is then introduced to compensate for these quantization errors, selectively targeting the most error-critical weight blocks where output distortion is shown to be concentrated. However, a unified representation alone is insufficient, as naïvely executing the sparse residual as a separate kernel still breaks the unified low-bit inference pipeline. To bridge this gap, we introduce ZipperEngine, which fuses sparse block computation into the dense 4-bit GEMM kernel via an overlapped pipeline, unifying not only the representation but also the execution into a single coherent low-bit inference pipeline. Extensive experiments on LLaMA3 and Qwen3 demonstrate that MosaicQuant preserves near-FP16 accuracy while achieving up to $1.24\times$ speedup over the W16A16 baseline.

19.
arXiv (CS.AI) 2026-06-15

Benchmarking Vision-Language-Action Models on SO-101: Failure and Recovery Analysis

arXiv:2606.08881v2 Announce Type: replace-cross Abstract: Vision-Language-Action (VLA) models have demonstrated strong generalization in robotic manipulation, yet existing evaluations are primarily conducted in simulation or on expensive robotic platforms, leaving their robustness on affordable real-world robots largely unexplored. We present a standardized real-world benchmark for evaluating representative VLA and imitation learning policies on the low-cost SO-101 robotic platform. The benchmark comprises four representative manipulation tasks together with unified evaluation protocols, enabling systematic comparison under embodiment uncertainty. Using real-world teleoperated demonstrations, we fine-tune and evaluate $\pi_{0.5}$, SmolVLA, Wall-X, and ACT directly on the physical platform. Beyond conventional task success rates, the benchmark incorporates a structured failure taxonomy, semantic- and execution-level failure decomposition, and recovery-aware evaluation metrics to characterize policy robustness. Experimental results show that stronger pretrained VLA policies generally outperform the imitation learning baseline, although performance remains highly task-dependent under low-cost robotic deployment conditions. Execution instability emerges as the dominant failure source, while recovery capability varies substantially across architectures. These results highlight the importance of failure and recovery analysis beyond binary task success and establish SO-101 as a practical benchmark for evaluating embodied AI systems under realistic low-cost robotic deployment conditions.

20.
arXiv (CS.CV) 2026-06-17

SceneCompleter: Dense 3D Scene Completion for Generative Novel View Synthesis

Generative models have shown great promise for novel view synthesis (NVS) by leveraging strong image generation priors. However, existing approaches typically follow a 2D inpainting paradigm, first completing missing image regions and then performing 3D reconstruction. This strategy often causes geometry distortion and appearance drift, as 2D inpainting models cannot reliably infer the underlying 3D structure required for cross-view consistent generation. In this paper, we propose SceneCompleter, a geometry-aware framework that reformulates generative NVS as dense 3D scene completion. Instead of hallucinating isolated 2D views, SceneCompleter jointly completes geometry and appearance through a geometry-appearance dual-stream diffusion model in a spatially aligned RGBD latent space. To provide holistic scene context, we further introduce a Scene Embedder that conditions generation on global semantic and stylistic information from reference images. The completed RGBD predictions are then aligned and integrated into an expandable 3D scene representation, enabling iterative and coherent scene completion. Extensive experiments on in-domain and out-of-distribution datasets demonstrate that SceneCompleter produces visually plausible and geometrically consistent novel views across diverse scenarios. Project Page: https://chen-wl20.github.io/SceneCompleter

22.
arXiv (quant-ph) 2026-06-24

Quantum Entanglement Halves the Oblivious Update Bandwidth

作者:

arXiv:2605.19248v2 Announce Type: replace Abstract: We consider $(n,k)$ MDS-coded distributed storage over $\mathbb{F}_q$ with per-node storage $\alpha$ symbols. For the oblivious update problem, where a single message symbol changes and neither helpers nor the stale node know which, the classical lower bound is $\alpha k \log_2 q$ bits. We prove that when the $k$ contacted helpers share prior quantum entanglement, the update bandwidth is $\lceil \alpha/2 \rceil \cdot k \log_2 q$ bits-equivalent, a factor approaching 2 reduction. For $\alpha = 2$, a $[[k, k-2]]_q$ CSS code achieves bandwidth $k \log_2 q$ with one qudit per helper. For general $\alpha$, a $[[\lceil \alpha/2 \rceil k, \lceil \alpha/2 \rceil k - \alpha]]_q$ CSS code achieves the bound with $\lceil \alpha/2 \rceil$ qudits per helper. The matching converse uses the superdense coding bound: the stale node holds all transmitted qudits and hence the entangled partners, so each helper's channel supports at most $D^2$ distinguishable signals for dimension $D$. The result holds for all $(n,k)$ pairs with sufficiently large prime $q$.

23.
arXiv (math.PR) 2026-06-11

Micro-macro population dynamics models of benthic algae with long-memory decay and generic growth

arXiv:2505.04289v4 Announce Type: replace Abstract: Benthic algae as a primary producer in riverine ecosystems develop biofilms on the riverbed. Their population dynamics involve growth and decay processes, the former owing to the balance between biological proliferation and mortality, while the latter to mechanical abrasion because of the transport of sediment particles. Contrary to the assumptions of previous studies, the decay has experimentally been found to exhibit long-memory behavior, where the population decreases at an algebraic rate. However, the origin and mathematical theory of this phenomenon remain unresolved. The objective of this study is to introduce a novel mathematical model employing spin processes to describe microscopic biofilm dynamics. A spin process is a continuous-time jump process transitioning between states 0 and 1, and the continuum limit of these processes captures the long-memory decay and generates generic growth. The proposed framework leverages heterogeneous spin rates, achieved by appropriately superposing spin processes with distinct rates, to reproduce the long-memory decay. Computational simulations demonstrate the behavior of the model, particularly emphasizing rate-induced tipping phenomena. This mathematical model provides a computationally tractable interpretation of benthic algae dynamics and their long-term prediction, relevant to river-engineering applications.

24.
arXiv (math.PR) 2026-06-16

The Backward Stochastic Partial Differential Integral Equations: Solvability and Comparison Principle

arXiv:2606.16237v1 Announce Type: new Abstract: The paper is concerned with the well-posedness of backward stochastic partial differential equations with jumps, also called backward stochastic partial differential integral equations. We start from the proof for the existence and uniqueness of solution to backward stochastic evolution equation with jump in the Gelfand triple framework. Then the well-posedness of both weak solution and strong solution to backward stochastic partial differential integral equation is obtained with the Gelfand triple replaced by specific Sobolev spaces. Finally, the comparison principle for backward stochastic partial differential integral equation is proved, which has potential applications in financial mathematics.

25.
arXiv (quant-ph) 2026-06-16

Entanglement-Rank Duality in Quadratic Phase Quantum States

arXiv:2605.05167v2 Announce Type: replace Abstract: Absolutely maximally entangled (AME) states are fundamental resources in quantum information theory, yet their construction and certification remain a nontrivial problem. Within the family of quadratic phase quantum states, defined by symmetric matrices $P$ over finite fields $\mathbb{F}_{p^m}$, we show that the Rank-Purity Duality $\operatorname{Tr}(\rho_S^2) = |\mathbb{F}|^{-\operatorname{rk}_{\mathbb{F}}(P_{S,\bar{S}})}$ follows from additive character orthogonality and holds over all $\mathbb{F}_{p^m}$, yielding a polynomial-time AME certification criterion. For square-free dimensions $d = p_1\cdots p_r$, the Chinese Remainder Theorem induces a prime-field factorisation. This implies additivity of Rényi-2 entropy and yields sharp obstruction criteria that rule out cases such as $\operatorname{AME}(4,6)$ and constrain the open case $\operatorname{AME}(8,6)$. As a proof of concept, we construct an explicit $\operatorname{AME}(17,10001)$ state, certified across all $65{,}535$ bipartitions, demonstrating that the framework scales to large systems and previously inaccessible local dimensions.