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arXiv2026

Formation of adducts of C$_6$H with Na$^+$, Mg$^+$ and Al$^+$ metal cations by radiative association

The Mg-bearing cations MgC$_4$H$^+$, MgC$_6$H$^+$, MgC$_3$N$^+$, and MgC$_5$N$^+$ have been recently observed in the carbon-rich envelope IRC\,+10216. These species are thought to form upon radiative association between Mg$^+$ and the corresponding neutral radical. This work aims to determine the radiative association rate coefficients for the cations Al$^+$, Mg$^+$, and Na$^+$ reacting with carbon chain radicals to estimate the relative importance of metal-bearing carbon cations for each of these metals. For this purpose we use statistical methods in combination with highly accurate ab initio calculations to obtain the radiative association rate coefficient. Moreover, anisotropic effects beyond mono-dimensional capture model are considered, providing a more reliable description of the simulated processes.} The radiative association rate coefficients to form Mg-, Al- and Na-C$_6$H$^+$, as well as MgC$_4$H$^+$, MgC$_3$N$^+$, and MgC$_5$N$^+$, are calculated with the new restrictions considered in this work. These new rate coefficients are included in a chemical model of the C-rich AGB envelope IRC\,+10216. The abundances of MgC$_4$H$^+$, MgC$_6$H$^+$, and MgC$_5$N$^+$ are consistent with observations, with differences no greater than one order of magnitude, corroborating radiative association as a plausible formation mechanism for these adducts. However, the calculated abundance of MgC$_3$N$^+$ is about two orders of magnitude lower than observed, which indicates that either the chemistry of this species is significantly different from the others or the calculated rate coefficient is too low. The abundances obtained for Na-C$_6$H$^+$ and Al-C$_6$H$^+$ are around two orders of magnitude lower than for Mg, making very difficult to detect the analogous metal-bearing cations in IRC\,+10216.

astro-ph.SR↗
arXiv2026

Pomeranchuk-like electronic localization above 100 K in twisted MoS$_{2}$

Twisted transition-metal dichalcogenides (TMDs) have manifested a rich variety of emerging physical phenomena, yet experimental studies have so far been largely limited in their valence bands (p-doped). Here, we show correlated electronic states in the conduction bands (n-doped) of near-AA-twisted bilayer MoS$_2$ with twist angles ranging from $\sim2.3^\circ$ to $\sim3.5^\circ$, down to the mK temperature regime. A strongly reconstructed correlated phase diagram as a function of twist-angle has been observed - correlated gaps persist to temperatures approaching $160$ K at small twist angles, but collapse to only $\sim20$ K at intermediate angles, where a richer landscape of interaction-driven states emerges. At the largest twist-angle $\sim 3.5\,^{\circ}$, correlated resistance at 1 electron per moiré unit cell is enhanced upon heating, consistent with thermally assisted localization, or, a Pomeranchuk-like behaviour. Its magnetic-field response, however, is highly anisotropic, which differs markedly from that of canonical isospin moiré Pomeranchuk effect in graphene systems. Strikingly, such signature can persist even above 100 K around a filling of 2 electrons per moiré, despite of its weak resistive nature. Our results establish the twisted MoS$_2$ as a platform for studying the complexity of charge localization, internal flavour degrees of freedom, and band topology in conduction bands of semiconducting moiré systems.

cond-mat.mes-hall↗
arXiv2026

Structure of irreducible homomorphisms to/from free and injective modules

Let $R$ be a commutative noetherian local ring. We extend the work of the author and Takahashi by investigating the structure of irreducible monomorphisms originating from free modules in the category of finitely generated $R$-modules. In the case where $R$ is complete, we further study the structure of irreducible monomorphisms and epimorphisms to and from injective modules in the category of artinian $R$-modules.

math.AC↗
arXiv2026

A nonoverlapping spectral additive Schwarz method for interior penalty discontinuous Galerkin discretizations of Anisotropic Elliptic Problems

We design and analyze a nonoverlapping additive Schwarz preconditioner for interior penalty discontinuous Galerkin discretizations of anisotropic elliptic problems. The preconditioned method coupled with a Krylov subspace iteration is shown to be independent of the highly discontinuous (and anisotropic) jump coefficients as well as the subdomain size. To increase efficacy, various auxiliary spaces are considered to reduce the size of the coarse grid operator. We demonstrate how to modify the additive Schwarz preconditioner such that it is applicable to the nonsymmetric IPDG schemes. Several numerical experiments verify the theory and validate the robustness of the preconditioner.

math.NA↗
arXiv2026

Towards more plausible point-identifying assumptions in two-sample Mendelian randomization

Two-sample Mendelian randomization (MR) is a widely applied methodology in epidemiology. In two-sample MR, summary data (typically, regression coefficients and standard errors) quantifying the association between multiple genetic variants and the exposure and the outcome are used in an instrumental variable framework aimed at estimating the causal effect of the exposure on the outcome. Most two-sample MR methods were developed under data-generating models where the association of for each candidate genetic instrument with the exposure, as well as the causal effect of the exposure on the outcome, are constant in the additive scale. These assumptions are useful because they imply that, had all genetic variants been valid IVs, they would all estimate the same causal parameter - namely, the constant causal effect. We refer to this condition as summary-level homogeneity. However, these are rather strong homogeneity conditions which may raise concerns about the plausibility of these methods in practice. In this paper, we show that summary-level homogeneity is implied by the following conditions: the causal effect is additive linear, but not necessarily constant across, all strata of the population; and uncorrelatedness between heterogeneity in the causal effect and in the association between each genetic variant and the exposure. Under these conditions, typical two-sample MR methods can be interpreted as estimators of the average causal effect. These results clarify that point-identifying assumptions required for two-sample MR methods are weaker than previously anticipated, which contributes to their plausibility and interpretation in at least some practical applications.

stat.ME↗
arXiv2026

Deciphering the VHE gamma-rays spectra of Extreme High-Frequency peaked BL Lac Objects through a Photohadronic Model

Extreme high-frequency peaked BL Lac objects (EHBLs) have their synchrotron peak above $\sim 1$ keV and their inverse Compton peak extends up to several TeVs. Due to low luminosity of EHBLs, these objects are often undetected, and only a small number of them are thus known. As a result, they are poorly understood. Using a photohadronic model and including extragalactic background light correction we analyzed 22 very high-energy (VHE) gamma-ray spectra of 15 EHBL sources observed in different periods. We find that the photohadronic model used can adequately describe the observed VHE spectral energy distribution and furthermore, we classify them according to the value of the photon spectral index, $δ$. The redshift of the EHBL HESS J1943+213 is also tightly constrained using the same photohadronic model. Within the sample, a plurality of flaring epochs fall in the high-emission state which is followed by the low-emission state and the very-high-emission state respectively. These fractions of flaring epochs characterize only the present sample, not the EHBL population at large. Due to the anomalous behavior of the VHE gamma-ray spectra of the EHBL H 2356-309, we suggest it to be a new subclass of EHBL having hard and very soft intrinsic spectra during different flaring epochs.

astro-ph.HE↗
arXiv2026

A Framework for Identifying, Categorizing, and Explaining Bias in AI-Generated Code

As Large Language Models (LLMs) become integrated into software development workflows, concerns regarding unintentional biases in AI-generated code. Although evidence suggests these biases exist, limited research has systematically identified, categorized, and explained them. This study investigates bias in AI-generated code and evaluates whether LLMs can reliably identify and explain it through a taxonomy-driven framework. We extended an existing dataset of biased AI-generated Python code and manually annotated snippets with bias categories and human-authored justifications to establish a ground-truth dataset. Using this dataset, we evaluated proprietary and open-source LLMs as automated bias detection and justification systems through ICL. Finally, we analyzed similarity between LLM-generated explanations and human-authored justifications using structured justification and code identification metrics. Our findings demonstrate that LLMs can effectively support code bias identification and explanation. Gemini achieved 80.14% classification accuracy, with 84.0% precision and 95.7% recall, while the best open-source alternative, Qwen3-coder, achieved 82.45% accuracy, 68.64% precision, and 80.22% recall. Additionally, the models achieved justification similarity scores of 80.4% and 80.14%, respectively, relative to human-authored reasoning, and code identification similarity scores of 86.0% and 87.82%. These results suggest that LLMs can detect biased logic in generated Python code and produce explanations that substantially align with expert interpretations.

cs.SE↗
arXiv2026

MARCEDES: Score-based causal discovery under non-Gaussianity with continuous optimization

We consider the problem of learning the underlying causal directed acyclic graph (DAG) structure corresponding to a structural equation model (SEM) with non-Gaussian errors. Motivated by an intentionally misspecified non-Gaussian SEM with all Laplace errors, we first introduce the mean absolute residual risk, defined over the space of all real matrices, and show that, asymptotically, the risk of the true weighted causal DAG matrix is strictly smaller than that of any other matrix. Nevertheless, to enhance generality and account for high-dimensional and finite-sample settings, we further incorporate row-specific sparsity penalties along with a soft DAG constraint to derive a continuous score function over the space of real matrices. Accordingly, we propose a score-based DAG learning method, named MARCEDES, formulated as an unconstrained score minimization problem, which can be efficiently solved using gradient-based optimization techniques, thereby circumventing the challenges associated with constrained optimization. Furthermore, we develop a computational algorithm to handle the non-smoothness of the score objective and to enable optimal tuning of row-specific sparsity penalties under a generalized Bayes framework. Finally, we demonstrate the efficiency and improved performance of the proposed method over existing approaches through an extensive simulation study.

stat.ML↗
arXiv2026

MR. POP: Multi-Robot Parallel Optimizing Planner for Almost-Surely Asymptotically Optimal Planning

Finding globally optimal paths remains a fundamental challenge in multi-robot motion planning. Despite acceleration of almost-surely asymptotically optimal (a.s.a.o.) planners via CPU-based parallelism, achieving both probabilistic convergence guarantees and strong computational performance, these algorithms still struggle to scale to multi-robot settings. As such, we introduce MR. POP, a GPU-based a.s.a.o. multi-robot planner based on dRRT and the AO-x meta-algorithm. MR. POP uses large-scale GPU-based SIMT-parallelism to simultaneously run hundreds of roadmap construction and tree search iterations with underlying parallel nearest neighbor search and collision checking operations. We show that this enables MR. POP to become the only planner achieving a 100% solve rate while being faster than state-of-the-art a.s.a.o. planners in multi-robot systems up to 35-DOF. MR. POP also raises the success rate of downstream motion optimizers (e.g., from 4% to 72%), by creating high-quality, diverse seeds that help avoid local minima.

cs.RO↗
arXiv2026

Special Cohen--Macaulay sheaves on partial resolutions of rational surfaces singularities

We introduce the categories $\CM(X)$ and $\SCM(X)$ of reflexive sheaves on a minimal partial resolution $f\colon X \to \Spec R$ of a rational surface singularity $\Spec R$. The main result of this paper establishes that $\SCM(X)$ possesses a natural Frobenius structure, serving as a geometric counterpart to the algebraic Frobenius structure on special Cohen--Macaulay $R$-modules, introduced by Iyama--Wemyss and Iyama--Kalck--Wemyss--Yang. Utilizing this geometric framework, we establish an exact equivalence between $\SCM(X)$ and the category of special Cohen--Macaulay $R$-modules equipped with a specific exact structure, which induces a triangle equivalence between their stable categories. Consequently, this provides a direct, geometric proof of the Iyama--Kalck--Wemyss--Yang equivalence and yields a Buchweitz-type equivalence $\underline{\SCM}(X) \simeq D_{\sg}(X)$.

math.AG↗
arXiv2026

Amortized Bayesian Disease Mapping and Boundary Detection on Heterogeneous Spatial Graphs

Spatial disease maps help public-health researchers identify geographic inequalities, but standard Bayesian smoothing can obscure localized disparities when neighboring communities have sharply different socioeconomic or behavioral profiles. Analysts therefore need to determine where smoothing should be interrupted and repeat that analysis as maps, adjacency structures, and outcomes change. We develop a covariate-informed Bayesian boundary model and an amortized posterior approximation trained across heterogeneous areal graphs. The model distinguishes local interruptions in smoothing from broader residual spatial dependence; the trained approximation handles maps with different numbers of regions. Simulations examine posterior calibration, boundary-probability recovery, replicated-data behavior, and MCSE-controlled agreement with prior-matched MCMC. In contrast to traditional approaches that analyze these data separately, we demonstrate the effectiveness of using a single trained deep learning network to analyze respiratory hospitalizations in Greater Glasgow; lung cancer incidence in California; and tracheal, bronchial, and lung cancer mortality in South Korea, comprising 58 to 241 regions. Selected boundary density is greatest in Glasgow and lowest in South Korea despite substantial residual spatial dependence in both, showing that local interruption and broader spatial persistence need not vary together. Across all three applications, edge-level boundary probabilities agree substantially with dataset-specific analyses, although posterior spread and thresholded boundary sets differ. These results support reusable Bayesian boundary analysis across the evaluated disease-map class and identify the validation needed before deployment to new applications.

stat.ME↗
arXiv2026

Conditional Predictive Sufficient Statistics for Visual Representation Learning

A useful visual representation is a statistic of the observed past that retains the latent factors shared with the future and discards patch-private noise. We formalize this requirement as a conditional predictive sufficient statistic (CPSS). Under a shared-factor model of image patches, the mutual information between the past and the next patch equals the information the past carries about the shared factor, up to a remainder that the next patch itself fails to reveal. Predicting the next patch embedding with a cosine loss is maximum likelihood for a von Mises-Fisher model of that embedding's direction, and is therefore a tractable surrogate for the predictive information. The same population loss is also minimized by a constant embedding, so stop-gradient does not by itself select the sufficient statistic; it only blocks the symmetric gradient that implements the constant solution in one step. The regression target is a shallow embedding, which forces the network output back into that shallow range and leaves the sufficient statistic in intermediate blocks. Small causal Transformers on MNIST and CIFAR-10 are used as diagnostics, not as a leaderboard. On MNIST the future shift and the stop-gradient move probe accuracy by tens of points, and the CPSS readout peaks before the output. On CIFAR-10, with the same short budget and no augmentation, every objective lands near a linear classifier on pixels. What still matches the derivation is the geometry: the CPSS output is a worse readout than its best intermediate block, next-pixel regression does not pay that penalty, and removing the stop-gradient collapses the effective rank of the embedding even when the pretext loss looks perfect.

cs.CV↗
arXiv2026

Random walk in a non-homogeneous random environment on some random trees and the non-negative integers

In this paper, we consider a random walk in a non-homogeneous random environment on two types of random trees and non-negative integers. The random trees here have progeny distributions that depend on the parent's generation. We provide a sharp threshold for the type of the random walk in a random environment on the random trees and the non-negative integers, up to the critical case. Then, we find the speed of the random walk on the non-negative integers and on random spherically symmetric trees. We use the method based on the relationship between the mean exit time from a vertex and speed. Meanwhile, we discuss several special cases that could be derived from those results. We also include many limiting formulas for sequences and series in the appendix, which are helpful for this study and others.

math.PR↗
arXiv2026

A VLA Study of the Disturbed Massive Cluster PLCK G165.7 + 67.0 and Its Two Narrow Angle Tail Galaxies

Since spectroscopic measurements provide only the line-of-sight velocity, transverse motions are difficult to constrain. As a result, transverse velocities have so far been measured only for local galaxies. Radio galaxies whose jets are bent back by ram pressure into nearly parallel Narrow-Angle Tails (NATs) offer a way to extend such measurements to higher redshifts. Here, we present proprietary 15 GHz (Ku-band) and archival 6 GHz (C-band) continuum observations from the Very Large Array (VLA) of seven radio galaxies in the galaxy cluster field PLCK G165.7+67.0 (G165). VLA imaging resolves two of the cluster galaxies into NATs whose tails both extend toward the Southwest, away from the cluster center of mass. Spectral index maps made at matched angular resolution resolve a steepening gradient consistent with radiative aging along the length of the tails. Physical properties of the NATs are measured and used to constrain two independent models: a Mach cone model and a nonrelativistic hydrodynamic flow model based on Euler's equation. The models returned space velocities of $\sim 2000 ~\rm km~ \rm s^{-1}$ for both galaxies. One NAT is the brightest cluster galaxy (BCG) and has a measured radial velocity of $-3300 ~\rm km ~\rm s^{-1}$, resulting in an even higher space velocity. The high inferred 3D velocity of the BCG may be explained if it is intercepted close to core passage.

astro-ph.GA↗
arXiv2026

Causal Retention in Interactive Agents: Interface Factorization and Selective Adaptation

Task performance need not determine which intervention mechanism an agent retains. We study causal retention: whether a frozen learned state answers a mechanism-probe map fixed independently of training, including action, context, direct target, value, and delay. For finite structural causal model classes, the optimal probe error is a Bayes decision risk. It vanishes exactly when every learning-interface fiber lies within one probe-answer fiber; any state obtained by post-processing that interface inherits the same lower bound. A posterior-coverage theorem characterizes budgeted retesting, while an exact edit decomposition shows that the shifted set is the unique support of an error-free target update. Causal Core implements these conditions through evidence-gated writing, readout filtering, temporal credit, hidden-context setup, and local diagnostic updates. Experiments cover finite causal systems, continuous simulators, an official TD-MPC2 world model, and Qwen2.5-7B-Instruct. A frozen Qwen last-layer probe reaches 0.958 balanced accuracy on source mechanisms but 0.583 on changed delays; the gated mechanism state reaches 1.000 and accepts only 0.056 of synchronized-readout candidates. In TD-MPC2, five target states per actuator recover effect-sign accuracy from 0.057 to 0.948 without degrading stable responses. Causal retention is therefore distinct from task sufficiency and source-domain decodability.

cs.LG↗
arXiv2026

Verification of Compiler-to-Accelerator Mappings for Machine Learning Accelerators

To meet the performance needs of modern machine learning (ML) applications, ML compiler frameworks support compiler-to-accelerator mappings that offload parts of application code to operations in specialized hardware accelerators. However, most of these frameworks do not verify these mappings down to the hardware level, potentially resulting in functional mismatches. In this paper we propose BOLT, the first framework for formally verifying the correctness of compiler-to-accelerator mappings for coarse-grained intrinsics in ML accelerators, with respect to a formal hardware semantics. BOLT does not require additional information from the compiler, and verifies the functional equivalence of the application code and the code for the mapped hardware accelerator intrinsic, including handling of complex loop nests and tensor data layouts in hardware. It effectively utilizes a pattern of *aligning* software loops with the hardware, followed by *relating* corresponding data layouts, to enable verification using well-aligned product programs. To support these steps, we propose two custom templates --- the sync-skeleton and the layout-sketch --- to guide users in aligning loops and specifying data layout relationships, respectively. We have developed a proof-of-concept prototype for BOLT and use it to successfully verify the correctness of several complex mappings for two recent open-source ML accelerators.

cs.PL↗
arXiv2026

Recursive Self-Improvement via On-Policy Distillation for Reasoning

On-policy distillation (OPD) trains a student model by having it generate trajectories, then matching its next-token predictions with an external teacher's next-token predictions. This provides dense, token-level supervision to the student. On-policy self-distillation (OPSD) eliminates the need for the external teacher. Specifically, a second frozen copy of the student model, now given the ground truth in its context, serves as the teacher. The student model only receives the problem and learns to mimic the privileged teacher model, while the teacher remains frozen throughout training. Previous work showed that freezing the teacher is useful for training stability, but we argue that this can prevent the teacher from incorporating the improvements learned by the student during training. Our primary contribution is to address this limitation with a recursive framework built around two complementary components. First, we let the privileged teacher co-evolve with the student so that revision learned in one round can guide the next, a process we refer to as Dynamic Co-Evolution (DCE). Second, because stronger revision can also make responses too verbose and self-critical, we additionally train on shorter, verified rewrites of the model's own on-policy responses. We call this complementary objective Self-Refined Concise Learning (SRCL). Overall, our comprehensive evaluations show that DCE+SRCL outperforms OPSD across multiple model scales and four competition-level mathematics benchmarks. Specifically, on Qwen3-8B, DCE+SRCL reaches 65.97% Average@12, outperforming OPSD by 35.62 percentage points while reducing mean output length by 7.80% relative to DCE alone.

cs.CL↗
arXiv2026

Fully 3GPP-Compatible Long-Range Sensing for LEO-ISAC: A Window-Grid Processing Framework

This paper addresses the long-range sensing problem in bistatic low-Earth-orbit integrated sensing and communication (LEO-ISAC) systems. Conventional OFDM-based sensing schemes fail in LEO-ISAC due to excessive propagation delays, which cause cross-symbol misalignment and unequal signal durations. We propose a window-grid processing framework that leverages the deterministic target geometry to resolve both challenges as a pure receiver-side processing: the transmitted sensing signal is 3GPP-compatible. Simulations demonstrate meter-level ranging accuracy for two targets at bistatic ranges beyond 640 km with 100.8 MHz bandwidth.

cs.IT↗