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01.
arXiv (CS.CV) 2026-06-18

Forged Calamity: Benchmark for Cross-Domain Synthetic Disaster Detection in the Age of Diffusion

The rapid advancement of text-to-image diffusion models has enabled the creation of highly photorealistic synthetic images that closely resemble real photographs, making it increasingly difficult to distinguish authentic content from AI-generated fabrications. This poses challenges for cybersecurity, digital forensics, and disaster response, where fake imagery of floods, fires, or earthquakes can spread misinformation or disrupt emergency operations. To address this, we introduce Forged Calamity, a benchmark dataset for synthetic disaster detection containing 30,000 images, including 6,000 real and 24,000 synthetic samples generated by four diffusion models. Comprehensive experiments across fine-tuned and zero-shot settings reveal consistent weaknesses in current forensic approaches. Fine-tuned detectors perform well in-distribution but lose up to 50\% accuracy on unseen generators or disaster types, showing overfitting to model-specific artifacts. Zero-shot generalized detectors also struggle to maintain stable accuracy, with only limited resilience in a few representation-robust models. These findings highlight persistent generalization gaps and the urgent need for domain- and model-agnostic detection methods to ensure visual authenticity in the diffusion era.

02.
arXiv (quant-ph) 2026-06-16

Classical Explanations in (and of) General Probabilistic Theories

arXiv:2603.05627v2 Announce Type: replace Abstract: We introduce a notion of the ``explanation" of one (generalized) probabilistic model by another as particular kind of span in the category $\Prob$ of probabilistic models and morphisms. We show that explanations compose under a standard pullback construction (notwithstanding that $\Prob$ does not support arbitrary pullbacks). We then show that every locally-finite probabilistic model has a canonical, sharp classical explanation. The construction is functorial, so every locally-finite probabilistic theory has a canonical, sharp classical (though of course, usually non-local) representation.

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

TimeROME-DLM: Temporal Causal Tracing and Low-Rank Inference-Time Knowledge Editing for Masked Diffusion Language Models

arXiv:2606.12841v1 Announce Type: cross Abstract: Masked diffusion language models (MDLMs) such as LLaDA now rival autoregressive (AR) LLMs, but every existing knowledge-editing and unlearning method (ROME, MEMIT, etc.) targets AR transformers and either makes assumptions that fail under iterative denoising, or requires gradient updates whose backward-pass activations cost tens of GB of extra VRAM and which collapse MDLMs at standard learning rates. We introduce TimeROME-DLM, the first training-free, gradient-free, inference-time knowledge-editing framework for MDLMs. It couples two components: a Temporal Indirect Effect (TIE) causal-tracing protocol that identifies, for each fact, the coordinate whose intervention most strongly drives the object prediction at later denoising steps; and a closed-form, low-rank residual edit memory that aggregates subject keys and target deltas across all forget facts and applies a single ridge-regularised update at that coordinate at every diffusion forward, with sparsification to limit utility spillover. Backbone weights stay frozen; only three hyperparameters (alpha, lambda, q) are tuned on a small validation split. On TOFU forget01 with TOFU-finetuned LLaDA-8B-Base, TimeROME-DLM cuts forget-set log-probability by roughly 83 nats. The same configuration transfers to LLaDA-8B-Instruct, Dream-7B, MMaDA-8B, DiffuLLaMA-7B, and LLaDA-MoE-1.4B. It keeps retain-set log-probability nearly flat (within ~1 nat at the utility-safe operating point) across 50 sequentially inserted facts, delivers a four- to fourteen-fold wall-clock speedup with zero additional VRAM over the strongest converged training-time baseline, and scales sub-linearly to 400 facts. TimeROME-DLM closes the locate-then-edit gap between AR LLMs and MDLMs at a fraction of the computational cost.

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

BindEdit: Taming Attention Leakage for Precise Multi-Object Image Editing

Real image editing enables precise manipulation of visual content, yet existing methods often fail in complex multi-object scenarios, causing semantic blending, object duplication, or incomplete edits. We attribute these failures to attention leakage, where signals across spatial regions and text tokens become entangled during the denoising process. Specifically, we identify two distinct forms of leakage: Edit-Token Leakage, where ambiguous token-region alignment leads to object blending, and Source Dominance Leakage, where tokens of unchanged source objects overwhelm the attention intended for target entities. To resolve these leakages, we propose BindEdit, which enforces attention-level constraints within a single diffusion trajectory. To suppress Edit-Token Leakage, BindEdit jointly regularizes cross- and self-attention so that each target token group is bound to its corresponding spatial region while maintaining instance-level separation. To suppress Source Dominance Leakage, a cross-attention re-balancing mechanism amplifies target token influence and attenuates residual source semantics within editable regions. Moreover, a region fidelity term ensures that each target concept is expressed coherently across the entire editing mask. Additionally, we propose a comprehensive multi-object benchmark encompassing diverse object counts and categories. Extensive experiments demonstrate that BindEdit consistently outperforms existing methods within a single diffusion trajectory, maintaining robust performance across both single- and multi-object editing scenarios.

05.
arXiv (quant-ph) 2026-06-17

Induced Resource Theories and Harvesting via Quantum Probes

arXiv:2606.17287v1 Announce Type: new Abstract: We consider scenarios in which a quantum system with a well-defined resource theory is used as a probe to interact with an environment, such as a quantum field, for which a resource-theoretic description is absent or incomplete. We clarify if and how the harvesting of a resource in the probe can tell us about the state of the environment. This is particularly ambiguous when the probe-environment interaction is not a free operation, or the concept of such free operations cannot be defined altogether. We propose a framework and precise conditions under which it becomes possible to interpret resource generation on the probe as evidence of resources in the environment, thereby introducing an effective notion of resources for the latter. Our results clarify in which sense resources can be said to be harvested from the environment and provide a systematic way to analyse such processes beyond fully controlled resource-theoretic settings. More generally, this work may provide a step towards a more general understanding of the interplay of different quantum resources.

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

Hidden Ghost Hand: Unveiling Backdoor Vulnerabilities in MLLM-Powered Mobile GUI Agents

Graphical user interface (GUI) agents powered by multimodal large language models (MLLMs) have shown greater promise for human-interaction. However, due to the high fine-tuning cost, users often rely on open-source GUI agents or APIs offered by AI providers, which introduces a critical but underexplored supply chain threat: backdoor attacks. In this work, we first unveil that MLLM-powered GUI agents naturally expose multiple interaction-level triggers, such as historical steps, environment states, and task progress. Based on this observation, we introduce AgentGhost, an effective and stealthy framework for red-teaming backdoor attacks. Specifically, we first construct composite triggers by combining goal and interaction levels, allowing GUI agents to unintentionally activate backdoors while ensuring task utility. Then, we formulate backdoor injection as a Min-Max optimization problem that uses supervised contrastive learning to maximize the feature difference across sample classes at the representation space, improving flexibility of the backdoor. Meanwhile, it adopts supervised fine-tuning to minimize the discrepancy between backdoor and clean behavior generation, enhancing effectiveness and utility. Extensive evaluations of various agent models in two established mobile benchmarks show that AgentGhost is effective and generic, with attack accuracy that reaches 99.7\% on three attack objectives, and shows stealthiness with only 1\% utility degradation. Furthermore, we tailor a defense method against AgentGhost that reduces the attack accuracy to 22.1\%. Our code is available at \texttt{anonymous}.

07.
arXiv (CS.LG) 2026-06-19

Influence-Guided Concolic Testing of Transformer Robustness

arXiv:2509.23806v2 Announce Type: replace-cross Abstract: Concolic testing for neural networks alternates concrete execution with constraint solving to search for inputs that flip model decisions. We present a concolic tester for Transformer classifiers that uses SHAP estimates to rank pending path predicates by their impact on the current prediction. To support self-attention with multiple heads in execution backed by SMT solving, we implement attention semantics in pure Python that are compatible with the solver and make the softmax boundary explicit by concretizing exponentiation arguments. We evaluate our method on CIFAR-10 across three compact Transformer classifiers, ResNet18, and VGG16 under a one-pixel budget and a 900s horizon. Across the 500 model–input pairs in this matched comparison, our method achieves 60% success, compared with 15% for a differential evolution baseline that treats the model as a black box. In the primary two-layer Transformer branch-ordering study, SHAP-based predicate prioritization raises success from 56% to 60% and reduces median attack time by 51%. These results show that influence-guided path exploration can make concolic testing a practical way to find adversarial examples in Transformer models.

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

From Tokens to Faces: Investigating Discrete Speech Representations for 3D Facial Animation

The choice of speech representation is critical in speech-driven 3D facial animation. Representations differ in what they encode: SSL features emphasize segmental and semantic cues, neural codecs yield latents optimized for acoustic reconstruction, and ASR-style objectives produce label-based spaces. We evaluate four speech representation families for 3D facial synthesis, comparing their facial reconstruction quality across two facial decoders using objective metrics and a perceptual evaluation. We additionally conduct probing analyses that relate tokenized representations to phonetic units and to articulatory deformations. We found that encoding phonetic classes is beneficial for accurate facial animation prediction on both semantic and label-based representations with comparable facial animation quality. From the latter, we introduce an Audio Visual Text-to-Speech (AVTTS) pipeline that leverages, as a shared space, discrete representations to decode speech and 3D facial motion.

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

Demystifying Variance in Circuit Discovery of LLMs

arXiv:2606.16920v1 Announce Type: cross Abstract: Circuit discovery is a key technique in mechanistic interpretability to pinpoint the model components that are crucial for performing a given task. Although the current state-of-the-art method (EAP-IG) performs well on the metric of (un)faithfulness, it suffers from substantial variability. This includes resampling variance, where the circuit changes when we probe with a new batch of data from the same distribution; rephrasing variance, where the discovered circuit shifts when the prompts are rephrased; and sample-wise variance, where a circuit with low population unfaithfulness exhibits large fluctuations in unfaithfulness across individual samples. This paper studies the roots of these variances. We demonstrate that CEAP, our new circuit discovery method that improves upon EAP-IG with a theoretical guarantee, can substantially lessen resampling variance. We further show that rephrasing variance arises because prompts with different templates tend to activate different circuits in the model. This leads us to argue that it may be challenging to find a comprehensive circuit that explains and controls the model's behavior on a task, which can be expressed in countless templates, suggesting that LLMs may be inherently hard to steer. We show that sparsity, which has been claimed to form more compact and interpretable task circuits, fails to solve this problem. Regarding sample-wise variance, we argue that it is largely benign: extremely poor unfaithfulness scores often stem from how unfaithfulness is defined, rather than from defects in the measured circuits. We show that the magnitude of unfaithfulness is affected by selective contribution scaling, a neural mechanism that accounts for the extremely poor scores sometimes observed.

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

Disparate Impact in Synthetic Data Generation

arXiv:2606.13105v1 Announce Type: new Abstract: We revisit the fairness notion of disparate impact for synthetic data generation (SDG), that assesses whether the utility of generated records is the same across sensitive groups. Our approach departs from existing work on fair SDG, that address the problem of correcting for undue biases in the observed distribution, hence redefining SDG as learning a distribution that is not that of the real data. By contrast, non-disparate impact is notably achieved when the synthetic and real distributions are the same. We expose reasons why SDG may fail to reach that solution and discuss why approximation and estimation errors occur and can be disparate across groups. We notably look into the expressive power of SDG methods relative to distribution complexity, sampling errors due to group proportions, and estimation errors induced by differential privacy mechanisms. We illustrate cases of disparate impact on both artificial and real-world data, focusing on SDG methods that rely on probabilistic graphical models. We also introduce a strategy of learning group-wise SDG models and illustrate how it can improve both the overall utility and its parity in many settings.

12.
arXiv (quant-ph) 2026-06-17

Unveiling Hierarchical Invariants in Multiphoton Linear Optics

arXiv:2506.12857v2 Announce Type: replace Abstract: Linear optical networks driven by quantum states of light are important building blocks of photonic quantum technologies. They access large bosonic Hilbert spaces through multiphoton interference. At the same time, their dynamics are generated by single-particle mode transformations, thereby defining a highly structured subset of multiphoton unitaries and setting boundary on linear optics capability. To elucidate this boundary, we reveal an underlying fine-grained symmetry structure that partitions the multiphoton operator space into invariant subspaces and generates a hierarchy of invariants. We experimentally confirm the conservation of high-order invariants and demonstrate their operational utility in characterizing state reachability and the metrological capability of multiphoton probes. Our framework provides a symmetry-based perspective for understanding and harnessing structured multiphoton dynamics across photonic quantum technologies.

13.
arXiv (quant-ph) 2026-06-16

Sub-Poissonian Statistics and Quantum Non-Gaussianity from High-Harmonic Generation

arXiv:2602.10882v4 Announce Type: replace Abstract: Quantum technologies are powered by platforms to generate complex non-classical states of matter or light to realize applications. We investigate the non-classical properties of high-harmonic generation in semiconductors, an emerging photonic platform. Measuring the click statistics of three double-digit orders, we evaluate witness operators to certify the non-classicality of the generated states. We show that higher-order harmonics driven by a coherent laser are squeezed and entangled. The properties of the emission are well retrieved with an entangled Gaussian state model, obtained by numerical state optimization to multiple observables. Additionally, we perform inter-order heralded measurements to engineer the quantum state of the emission. The heralded states have distinct properties, showing sub-Poissonian photon statistics. Further, we witness the generation of a quantum non-Gaussian state, a resource highly relevant for quantum information. With this, we establish high-harmonic generation as a platform for generating quantum optical resources.

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

Shuttling Compiler for Trapped-Ion Quantum Computers Based on Large Language Models

arXiv:2512.18021v3 Announce Type: replace-cross Abstract: We present the first shuttling compiler based on large language models (LLMs) for trapped-ion quantum computers, where qubits are shuttled between segments for gate execution and qubit storage. We fine-tune pre-trained LLMs on examples from linear and branched one-dimensional shuttling architectures. Thus, we obtain a layout-independent compilation strategy that learns the required shuttling operations directly from data. Using benchmark circuits with up to 16 qubits, such fine-tuned LLMs can now generate valid schedules for shuttling architectures. Notably, we also obtain a valid schedule for a previously unseen four-way junction layout. This demonstrates that trained LLMs can generalize to layouts not encountered during training. For various architectures, LLM-based schedules improve upon state-of-the-art baseline compiler results, reducing the shuttling effort by up to 15%.

15.
arXiv (quant-ph) 2026-06-11

Scaling-optimal purification of noisy qubit unitary channels

arXiv:2606.12394v1 Announce Type: new Abstract: We consider the problem of purifying noisy qubit unitary channels. Given the ability to apply an unknown qubit unitary channel followed by depolarizing noise, we aim to construct a superchannel that purifies the noisy unitary back to the original unknown unitary. We first provide numerical evidence that sequential strategies can strictly outperform parallel strategies when the number of channel uses is finite, highlighting the fundamental distinction from state purification. We then provide a concrete $\mathrm{U}(2)$-covariant parallel protocol based on a novel entanglement-assisted quantum error-correcting code that suppresses the first-order noise strength as $O(1/n)$ with $n$ channel uses and show this scaling is asymptotically optimal in the low-noise regime, even when sequential strategies are allowed.

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

Test-Time Training for Robust Text-Guided Open-Vocabulary Object Counting

Text-guided Open-vocabulary Object Counting (TOOC) enables counting arbitrary object categories specified by text prompts, offering substantially greater flexibility than conventional closed-set counting. However, existing TOOC methods are developed and evaluated primarily on ideal images, while real-world scenes often suffer from adverse conditions such as rain, fog, darkness, and sensor noise, which severely degrade visual quality and impair vision-language alignment. To bridge this gap, we introduce Robust-TOOC, the first benchmark for evaluating TOOC under diverse corruption conditions, which covers six representative degradation types: rain, fog, darkness, Gaussian noise, salt-and-pepper noise, and mixed corruption. To improve robustness while preserving the original counting architecture, we propose Dual-TTT, a dual-architecture test-time training framework for TOOC. Specifically, during test-time training, Dual-TTT updates only the Text-guided Lightweight Denoising module (TL-Denoiser), while keeping the original counting network frozen. Inspired by diffusion models, the TL-Denoiser is optimized to remove corruption-aware noise from image representations under degraded conditions. Since only the TL-Denoiser is trained at test time, Dual-TTT is annotation-free and can be seamlessly integrated into existing TOOC models without modifying their original architecture. Extensive experiments on multiple recent TOOC baselines demonstrate the effectiveness of our method.

17.
arXiv (CS.CV) 2026-06-18

DART: A design-aware microfluidic chip paradigm for real-time live-cell image analysis

High-throughput microfluidic live-cell imaging generates rich single-cell data. Yet semi-automated procedures for locating regions of interest (RoIs), each containing one cell population, and removing surrounding microfluidic structures from recorded images, scale with the number of RoIs. This prevents real-time image analysis and delays time-to-insight by hours to days. We introduce the Design-Aware and Real-Time capable (DART) paradigm for microfluidic cultivation chips, which aligns the CAD blueprint with the physical chip and thereby enables throughput-independent localization of all RoIs and fully automated image processing across diverse RoI geometries and chip layouts. DART establishes this alignment through embedded fiducial markers and deep-learning-based marker detection. We validate DART using the Swiss Army Knife chip, which combines eight structurally distinct RoI designs across 1164 RoI locations. DART localizes all RoIs in five minutes, removes microfluidic structures from raw microscopy images in 40 ms, and performs fully automated image analysis, including cell segmentation, in under 1.1 s per image. Together, these capabilities establish DART as an end-to-end hardware-software paradigm with real-time-capable analysis that paves the way toward closed-loop and outcome-driven smart microscopy.

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

Diversity-Driven Offline Multi-Objective Optimization via Nested Pareto Set Learning

arXiv:2606.15115v1 Announce Type: new Abstract: Multi-objective optimization (MOO) has emerged as a powerful approach to solving complex optimization problems involving multiple objectives. In many practical scenarios, function evaluations are unavailable or prohibitively expensive, necessitating optimization solely based on a fixed offline dataset. In this setting, known as offline MOO, the goal is to find out the Pareto set without access to the true objective functions. This setting suffers from the out-of-distribution (OOD) issue, where the surrogate model is not accurate for unseen designs. Due to the OOD issue, surrogate errors may cause the optimizer to select solutions that do not lie on the true Pareto front and are biased toward its extremes. To address this, this paper proposes Diversity-driven Offline Multi-Objective Optimization (DOMOO), which aims to find out a diverse and high-quality set of solutions. First, DOMOO incorporates an accumulative risk control module that estimates the potential risk of candidate solutions and alleviates the OOD issue between the training data and the generated solutions. In addition, a nested Pareto set learning (PSL) strategy is proposed to jointly learn preference and PSL parameters, then optimize them, enabling adaptation to diverse Pareto front geometries. To further enhance solution quality, we design a diversity-driven selection strategy that extracts a representative and well-distributed set of final solutions. To achieve this diversity-driven selection strategy, we propose $IGD_offline$, a tailored indicator for the offline setting that considers both diversity and convergence, and avoids the bias of hypervolume indicator. Extensive experiments on synthetic and real-world benchmarks show that DOMOO achieves the best average rank across tasks in both convergence and diversity among the compared methods.

19.
arXiv (CS.CV) 2026-06-11

Seeing What Matters: Perceptual Wrapper with Common Randomness for 3D Gaussian Splatting

While 3D Gaussian Splatting (3DGS) achieves impressive real-time rendering, it frequently struggles to synthesize high-frequency textures, a limitation heavily exacerbated in memory-constrained and rate-distortion-optimized (RDO) pipelines. To address this, we propose a versatile 2D perceptual wrapper that enhances the rendered outputs of existing 3DGS representations in a content- and view-dependent manner. Our method leverages a lightweight synthesis network conditioned on pseudo-random Gaussian noise to synthesize perceptually plausible textures. Supervised by Wasserstein Distortion, the network learns to match local feature statistics rather than strictly enforcing pixel-wise reconstruction fidelity, effectively mitigating the blurriness inherent in standard frameworks. We demonstrate the broad applicability of our plug-and-play approach across vanilla, memory-constrained, and RDO 3DGS methods. Comprehensive subjective and objective experiments confirm that our method significantly improves over existing baselines, yielding superior perceptual quality at sharply reduced file or model sizes.

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

SEDULity: A Proof-of-Learning Framework for Distributed and Secure Blockchains with Efficient Useful Work

arXiv:2512.13666v2 Announce Type: replace-cross Abstract: The security and decentralization of Proof-of-Work (PoW) have been well-tested in existing blockchain systems. However, its tremendous energy waste has raised concerns about sustainability. Proof-of-Useful-Work (PoUW) aims to redirect the meaningless computation to meaningful tasks such as solving machine learning (ML) problems, giving rise to the branch of Proof-of-Learning (PoL). While previous studies have proposed various PoLs, they all, to some degree, suffer from security, decentralization, or efficiency issues. In this paper, we propose a PoL framework that trains ML models efficiently while maintaining blockchain security in a fully distributed manner. We name the framework SEDULity, which stands for a Secure, Efficient, Distributed, and Useful Learning-based blockchain system. Specifically, we encode the template block into the training process and design a useful function that is difficult to solve but relatively easy to verify, as a substitute for the PoW puzzle. We show that our framework is distributed, secure, and efficiently trains ML models. We further demonstrate that the proposed PoL framework can be extended to other types of useful work and design an incentive mechanism to incentivize task verification. We show theoretically that a rational miner is incentivized to train fully honestly with well-designed system parameters. Finally, we present simulation results to demonstrate the performance of our framework and validate our analysis.

21.
bioRxiv (Bioinfo) 2026-06-10

Bias-mitigated microbiome inference refines coronary artery disease signature

Authors:

Roughly half the cells in the human body are microbial, and changes in these communities are increasingly implicated in cardiovascular, metabolic, and oncological diseases. Yet identifying which taxa truly differ in abundance, differential abundance (DA), is distorted by four major sources of bias: loss of total microbial load, taxa measurement efficiencies, arbitrary pseudocounts required to handle pervasive zeros, and contamination which has recently driven retractions. No existing DA method accounts for all four. Here we introduce BootDA, a non-parametric bootstrap-based method that explicitly models each bias source without data transformations, pseudocounts, parametric assumptions, or assuming that most taxa are non-DA. In semi-parametric simulations preserving the sparsity (>70% zeros) and correlation structure of real 16S amplicon data, BootDA achieved the highest sensitivity among tested methods, including ANCOM-BC2, LinDA, MaAsLin 3, and Wilcoxon tests, while controlling the false discovery rate. Performance was retained in low biomass settings when contamination contributed ~50% of counts, and without negative controls, indicating de novo decontamination capability. Applied to a coronary artery disease cohort, BootDA refined the original signature to two co-enriched genera, Klebsiella and Gemmiger, and excluded likely contaminants. BootDA is available as an R package and could generalise to other sparse, high dimensional biological data.

22.
arXiv (CS.AI) 2026-06-16

Adaptive $k$NN graph model

arXiv:2601.16509v2 Announce Type: replace-cross Abstract: The $k$-nearest neighbors ($k$NN) algorithm is a cornerstone of non-parametric classification in artificial intelligence, yet its deployment in large-scale applications is persistently constrained by the computational trade-off between inference speed and accuracy. Existing approximate nearest neighbor solutions accelerate retrieval but often degrade classification precision and lack adaptability in selecting the optimal neighborhood size ($k$). Here, we present an adaptive graph model that decouples inference latency from computational complexity. By integrating a Hierarchical Navigable Small World (HNSW) graph with a pre-computed voting mechanism, our framework completely transfers the computational burden of neighbor selection and weighting to the training phase. Within this topological structure, higher graph layers enable rapid navigation, while lower layers encode precise, node-specific decision boundaries with adaptive neighbor counts. Benchmarking against eight state-of-the-art baselines across six diverse datasets, we demonstrate that this architecture significantly accelerates inference speeds, achieving real-time performance, without compromising classification accuracy. These findings offer a scalable, robust solution to the inherent inference bottleneck of $k$NN, laying an adaptive structural foundation for graph-based nonparametric learning.

23.
arXiv (math.PR) 2026-06-17

The Loss of Tension in an Infinite Membrane with Holes of Decaying Spatial Density

arXiv:2606.17792v1 Announce Type: new Abstract: What is the effect of randomly removing material from an infinite stretched membrane? Under what conditions can the membrane still sustain tension? This problem was introduced by Robert Connelly in connection with applications of rigidity theory in the natural sciences, and was later studied in M. V. Menshikov, K. A. Rybnikov, and S. E. Volkov, "The loss of tension in an infinite membrane with holes distributed according to a Poisson law" (2002); a discrete version was also considered in Robert Connelly, Konstantin Rybnikov, and Stanislav Volkov, "Percolation and the Loss of Tension in an Infinite Triangular Lattice" (2001). We study a mathematical framework based on a non-homogeneous Poisson point process whose intensity $\lambda$ tends to zero at infinity. The hole shapes are i.i.d.\ and independent of their locations. We show that if the intensity does not decay too quickly, then tension is still lost throughout the whole plane, as in the homogeneous model studied in 2002. Conversely, we give sufficient conditions under which complete loss of tension does not occur. Thus, both destruction and non-destruction regimes are possible even when the intensity tends to zero, indicating a phase transition in the model. The processes studied here are closely related to bootstrap percolation.

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

On the Energy Distribution of the Galactic Center Excess' Sources

arXiv:2507.17804v2 Announce Type: replace-cross Abstract: The Galactic Center Excess (GCE) may yet herald the discovery of annihilating dark matter. Weighing against that conclusion are analyses showing evidence for dim point sources within the spatial structure of the emission. Due to technical limitations these analyses are purely spatial with all spectral information that could disentangle the excess from astrophysical backgrounds discarded. Here, we demonstrate that a neural network simulation-based inference approach can jointly analyze the spatial and spectra data. The addition is profound: energy information drives the putative point sources to be significantly dimmer, indicating either the GCE is truly diffuse in nature or made of an exceptionally large number of sources. Quantitatively, for our best fit background model, the excess is essentially consistent with Poisson emission as predicted by dark matter. If due to point sources, our median prediction is $\mathcal{O}(10^5)$ sources, or more than 35,000 at 90\% confidence, both orders of magnitude larger than the hundreds preferred by earlier point-source analyses of the GCE, although variations allowed by background systematics could reduce the required number of sources by roughly an order of magnitude.

25.
arXiv (math.PR) 2026-06-17

Convergence rate of Euler–Maruyama scheme to the invariant probability measure under total variation distance for the SDEs

arXiv:2505.04218v3 Announce Type: replace Abstract: This article shows the geometric decay rate of Euler-Maruyama scheme for one-dimensional stochastic differential equation towards its invariant probability measure under total variation distance. Firstly, the existence and uniqueness of invariant probability measure and the uniform geometric ergodicity of the chain are studied through introduction of non-atomic Markov chains. Secondly, the equivalent conditions for uniform geometric ergodicity of the chain are discovered, by constructing a split Markov chain based on the original Euler-Maruyama scheme.