On Two Open Problems by Johnson and Koll\'ar
We resolve two problems left open by Johnson and Koll\'ar in their paper Arcology: Question 21 and the openness issue arising in Example 14.
math.AG↗
arXiv subjects
Zhiming Li
Publications and source records attributed to Zhiming Li.
Parameter estimation and application in two types of uncertain single-index models
Uncertain data often arises in complex environments because of frequency instability and subjective judgment. This paper establishes two types of uncertain single-index models to capture the inherent properties of such data. Based on the semiparametric least-squares principle, the Nadaraya-Watson kernel and B-spline methods are used to estimate the unknown coefficients in various scenarios with both crisp and imprecise explanatory variables. Residual analysis and hypothesis testing under uncertainty assess the fit of the proposed models. Furthermore, simulation studies verify the models' validity, and a real-data application demonstrates their effectiveness in practical settings.
stat.ME↗
Confounding analysis of s-level designs with multi-block variables
In practical experiments, block variables often arise from multiple sources of heterogeneity. To address the confounding problem, this paper proposes a blocked aliased component-number pattern (B$^2$-ACNP) to analyze the confounding properties of s-level designs with multi-block variables. We calculate the values of (B$^2$-ACNP) via a blocked wordlength distribution matrix. The classification patterns of existing criteria can be expressed as functions of specific elements within the B$^2$-ACNP, thereby stablishing connections within a unified framework. Further, we provide confounding algorithms and visualization methods of the B$^2$-ACNP. Finally, case analysis clarifies the significant role of the B$^2$-ACNP. The Python code is available in the Appendix.
stat.ME↗
Understanding the Intermittency Signal in RHIC-STAR Data through Modeling
Intermittency analysis provides a promising probe of scale-invariant density fluctuations near the QCD critical point. The intermittency measurements reported in the STAR BES-I data call for a quantitative assessment of the signal strength and a clearer physical understanding of its collision-energy dependence. In this work, we perform such a study for the STAR measurements using an improved hybrid UrQMD+CMC model, in which critical-like fluctuations are embedded into a realistic non-critical background through event-level, particle-level, and combined replacement schemes. By directly comparing the second-order factorial moment $\Delta F_{2}(M)$ between model calculations and experimental data on a point-by-point basis, we constrain the effective critical-like contribution compatible with the STAR measurements without relying on scaling exponents. The STAR data at $\sqrt{s_{\mathrm{NN}}}=7.7$--$27~\mathrm{GeV}$ used for model comparison can be consistently described only by small and nearly energy-independent effective critical-like fractions. These results indicate that the current BES-I intermittency signal is weak and exhibits little collision-energy dependence, thereby favoring only a limited critical-like contribution rather than a strong critical-point-induced enhancement localized near a specific collision energy.
nucl-th↗
Analysis of uncertain fixed-effects model for Latin square designs
Uncertain data without frequency stability often arises in experimental design. Classical fixed-effects models can only analyze precise experimental data. Based on an uncertain measure, this paper establishes uncertain fixed-effect models for Latin-square designs. First, we propose three methods with uncertainty to estimate the treatment and blocked effects and construct their confidence intervals. Then, uncertain homogeneity and common tests are conducted to assess the significance of treatment effects. In the numerical simulations, the three estimation methods are compared based on bias, mean squared error, mean absolute error, overall standard deviation, coverage probability, and average interval length. Several examples are given to illustrate the process of estimation and hypothesis. Finally, the uncertain fixed-effects model is applied to real education data, demonstrating its practical value.
stat.ME↗
Estimate Collapsibility of Causal Effects in Completed Partial DAGs via Strong d-Convex Hulls
This paper proposes a collapsible method for estimating causal effects that maintains the estimator's consistency before and after marginalization over some variables in completed partially directed acyclic graphs (CPDAGs). We first introduce the estimate collapsibility for CPDAGs and characterize the minimal collapsible sets as strong d-convex hulls. An efficient algorithm is devised to obtain such sets in DAGs and is generalized to CPDAGs. Then, we combine the graph reduction procedure with the IDA framework. Finally, experiments and empirical analysis show the effectiveness of the collapsibility for causal estimations in CPDAGs. Code is available at https://github.com/Jamyang-D/strongly-convex.
stat.ML↗
On the geometry of Certain Non-Basic Affine Deligne-Lusztig Varieties
Let $F$ be a non-Archimedean local field, let $L=\breve F$, and let $G=\mathrm{GL}_n$. Let $M\subset G$ be a standard Levi subgroup and let $b\in M(L)$ be basic in $M$, but not necessarily basic in $G$. For a dominant cocharacter $\mu$, we study the reduction-to-Levi morphism $\beta:X^G_\mu(b)\to \bigsqcup_{\mu_M\in S_M(\mu,\nu_b)}X^M_{\mu_M}(b)$ for affine Deligne--Lusztig varieties in the affine Grassmannian. Using an Iwasawa factorization relative to $P=MN$, we reduce the fiber condition to explicit Frobenius-twisted lattice equations in the off-block coordinates. In the Drinfeld case, where the base $X^M_{\mu_M}(b)$ is zero-dimensional, we prove that $\beta$ is globally trivial with constant affine-space fiber in the non-basic cases considered. More generally, in the minuscule case we develop a nonzero-slope lattice-theoretic criterion which shows that the fibers are affine spaces and that $\beta$ is Zariski locally a trivial affine-space bundle in the non-basic cases considered. We also give examples in the non-minuscule setting where the fibers need not be affine spaces.
math.AG↗
CoDA: Towards Effective Cross-domain Knowledge Transfer via CoT-guided Domain Adaptation
Large language models (LLMs) have achieved substantial advances in logical reasoning, yet they continue to lag behind human-level performance. In-context learning provides a viable solution that boosts the model's performance via prompting its input with expert-curated, in-domain exemplars. However, in many real-world, expertise-scarce domains, such as low-resource scientific disciplines, emerging biomedical subfields, or niche legal jurisdictions, such high-quality in-domain demonstrations are inherently limited or entirely unavailable, thereby constraining the general applicability of these approaches. To mitigate this limitation, recent efforts have explored the retrieval of cross-domain samples as surrogate in-context demonstrations. Nevertheless, the resulting gains remain modest. This is largely attributable to the pronounced domain shift between source and target distributions, which impedes the model's ability to effectively identify and exploit underlying shared structures or latent reasoning patterns. Consequently, when relying solely on raw textual prompting, LLMs struggle to abstract and transfer such cross-domain knowledge in a robust and systematic manner. To address these issues, we propose CoDA, which employs a lightweight adapter to directly intervene in the intermediate hidden states. By combining feature-based distillation of CoT-enriched reference representations with Maximum Mean Discrepancy (MMD) for kernelized distribution matching, our method aligns the latent reasoning representation of the source and target domains. Extensive experimental results on multiple logical reasoning tasks across various model families validate the efficacy of CoDA by significantly outperforming the previous state-of-the-art baselines by a large margin.
cs.AI↗
Towards Effective In-context Cross-domain Knowledge Transfer via Domain-invariant-neurons-based Retrieval
Large language models (LLMs) have made notable progress in logical reasoning, yet still fall short of human-level performance. Current boosting strategies rely on expert-crafted in-domain demonstrations, limiting their applicability in expertise-scarce domains, such as specialized mathematical reasoning, formal logic, or legal analysis. In this work, we demonstrate the feasibility of leveraging cross-domain demonstrating examples to boost the LLMs' reasoning performance. Despite substantial domain differences, many reusable implicit logical structures are shared across domains. In order to effectively retrieve cross-domain examples for unseen domains under investigation, in this work, we further propose an effective retrieval method, called domain-invariant neurons-based retrieval (\textbf{DIN-Retrieval}). Concisely, DIN-Retrieval first summarizes a hidden representation that is universal across different domains. Then, during the inference stage, we use the DIN vector to retrieve structurally compatible cross-domain demonstrations for the in-context learning. Experimental results in multiple settings for the transfer of mathematical and logical reasoning demonstrate that our method achieves an average improvement of 1.8 over the state-of-the-art methods \footnote{Our implementation is available at https://github.com/Leon221220/DIN-Retrieval}.
cs.AI↗
Reason Analogically via Cross-domain Prior Knowledge: An Empirical Study of Cross-domain Knowledge Transfer for In-Context Learning
Despite its success, existing in-context learning (ICL) relies on in-domain expert demonstrations, limiting its applicability when expert annotations are scarce. We posit that different domains may share underlying reasoning structures, enabling source-domain demonstrations to improve target-domain inference despite semantic mismatch. To test this hypothesis, we conduct a comprehensive empirical study of different retrieval methods to validate the feasibility of achieving cross-domain knowledge transfer under the in-context learning setting. Our results demonstrate conditional positive transfer in cross-domain ICL. We identify a clear example absorption threshold: beyond it, positive transfer becomes more likely, and additional demonstrations yield larger gains. Further analysis suggests that these gains stem from reasoning structure repair by retrieved cross-domain examples, rather than semantic cues. Overall, our study validates the feasibility of leveraging cross-domain knowledge transfer to improve cross-domain ICL performance, motivating the community to explore designing more effective retrieval approaches for this novel direction.\footnote{Our implementation is available at https://github.com/littlelaska/ICL-TF4LR}
cs.AI↗
Estimation and Hypothesis Testing of Fixed Effects Models-Based Uncertainty for Factor Designs
To analyze the uncertain data frequently encountered in practice, this paper proposes novel fixed-effects models that incorporate an uncertain measure to investigate variables of interest and nuisance variables in factor designs. First, an uncertain fixed-effects (UFE) model of a single-factor design is established, and uncertain estimation and hypothesis testing are conducted. We then extend the UFE model to two-factor designs with and without interactions and classify them as balanced or unbalanced based on the equality of replicates within each combination. In the above UFE models, the effectiveness and practicality of estimation and hypothesis methods are demonstrated through three real-world cases, including both balanced and unbalanced designs. These examples highlight the models' ability to handle uncertain experimental data.
stat.ME↗
Microstructural origin of the simultaneous enhancements in strength and ductility of a nitrogen-doped high-entropy alloy
As one of the most abundant interstitial elements, nitrogen (N) is effective in improving yield strength of metallic materials, due to interstitial solid solution strengthening. Doping N can substantially enhance the yield strength but often leads to a decreased ductility, revealing a strength-ductility trade-off phenomenon. Here, we simultaneously enhance the strength and ductility in a non-equiatomic CrMnFeCoNi high-entropy alloy via N alloying and unravel the underlying microscopic mechanisms. The N-doped alloy (1 at.% N) shows an excellent combination of higher yield strength (104% increase) and larger ductility (38% increase), with a two-stage strain hardening behavior, compared to the N-free alloy. Detailed transmission electron microscopy (TEM) analysis reveals that N-doping introduces short-range order (SRO) domains within the microstructure, leads to pronounced planar slip, and promotes the formation of nano-spaced (6-15 nm) stacking faults and deformation twins. Continuous generation and interaction of the fine-spaced SFs act as a strong barrier for dislocation movement and provide ample room for dislocation storage. The interaction of SRO with dislocations and the evolution of SFs ascribe to the first strain hardening stage, and the disordering of the SRO along with the activation of deformation twins are attributed to the second strain hardening stage. Our work shows that N-doping is effective in simultaneously improving the strength-ductility synergy and provides novel insights into alloy design with slightly elevating the SFE, and manipulating the ordered structure within the HEA.
cond-mat.mtrl-sci↗
Model Study of Eigen-Microstate Signatures of Criticality in Relativistic Heavy-Ion Collisions
We present a comprehensive model study of the eigen-microstate approach (EMA) for identifying critical fluctuations in relativistic heavy-ion collisions. Using UrQMD and two stochastic baseline models, we demonstrate that EMA is insensitive to conventional short-range correlations and effectively filters out non-critical backgrounds. Critical fluctuations embedded via event-level or particle-level replacement with CMC events generate characteristic cluster-like eigen-microstate patterns and enhanced leading eigenvalues, with event-level criticality producing stronger responses. The eigen microstates exhibit the same pattern across different scales, demonstrating that the fractal nature of critical fluctuations is captured by the eigen microstates. Finite-size scaling of eigenvalue ratios exhibits fixed-point behavior, confirming the largest eigenvalue as an effective order-parameter-like quantity. These results demonstrate that EMA offers a robust and background-independent method for critical-point searches in the RHIC Beam Energy Scan and future heavy-ion experiments.
nucl-th↗
Dual-Axis RCCL: Representation-Complete Convergent Learning for Organic Chemical Space
Machine learning is profoundly reshaping molecular and materials modeling; however, given the vast scale of chemical space (10^30-10^60), it remains an open scientific question whether models can achieve convergent learning across this space. We introduce a Dual-Axis Representation-Complete Convergent Learning (RCCL) strategy, enabled by a molecular representation that integrates graph convolutional network (GCN) encoding of local valence environments, grounded in modern valence bond theory, together with no-bridge graph (NBG) encoding of ring/cage topologies, providing a quantitative measure of chemical-space coverage. This framework formalizes representation completeness, establishing a principled basis for constructing datasets that support convergent learning for large models. Guided by this RCCL framework, we develop the FD25 dataset, systematically covering 13,302 local valence units and 165,726 ring/cage topologies, achieving near-complete combinatorial coverage of organic molecules with H/C/N/O/F elements. Graph neural networks trained on FD25 exhibit representation-complete convergent learning and strong out-of-distribution generalization, with an overall prediction error of approximately 1.0 kcal/mol MAE across external benchmarks. Our results establish a quantitative link between molecular representation, structural completeness, and model generalization, providing a foundation for interpretable, transferable, and data-efficient molecular intelligence.
cs.LG↗
Analysis of hypothesis tests for multiple uncertain finite populations with applications to normal uncertainty distributions
Hypothesis test plays a key role in uncertain statistics based on uncertain measure. This paper extends the parametric hypothesis of a single uncertain population to multiple cases, thereby addressing a broader range of scenarios. First, an uncertain family-wise error rate is defined to control the overall error in simultaneous testing. Subsequently, a hypothesis test of two uncertain populations is proposed, and the rejection region for the null hypothesis at a significance level is derived, laying the foundation for further analysis. Building on this, a homogeneity test for multiple populations is developed to assess whether the unknown population parameters differ significantly. When there is no significant difference in these parameters among finite populations or within a subset, a common test is used to determine whether they equal a fixed constant. Finally, homogeneity and common tests for normal uncertain populations with means and standard deviations are conducted under three cases: only means, only standard deviations, or both are unknown. Numerical simulations demonstrate the feasibility and accuracy of the proposed methods, and a real example is provided to illustrate their effectiveness.
stat.ME↗
Eigen-microstate Signatures of Criticality in Relativistic Heavy-Ion Collisions
We develop the eigen-microstate framework as a new approach to identify criticality in relativistic heavy-ion collisions. We construct the original microstate, defined as the final-state particle fluctuations of a single event. By examining ensembles of such original microstates with and without critical signals, we demonstrate that the corresponding eigen-microstate can extract and reveal the dominant critical mode, with the largest eigenvalue serving as a robust order parameter. This framework avoids equilibrium assumptions and is insensitive to non-critical background, and the approach is directly applicable to RHIC Beam Energy Scan data, offering a powerful new tool in the search for the QCD critical point.
hep-ph↗
Investigating Training Data Detection in AI Coders
Recent advances in code large language models (CodeLLMs) have made them indispensable tools in modern software engineering. However, these models occasionally produce outputs that contain proprietary or sensitive code snippets, raising concerns about potential non-compliant use of training data, and posing risks to privacy and intellectual property. To ensure responsible and compliant deployment of CodeLLMs, training data detection (TDD) has become a critical task. While recent TDD methods have shown promise in natural language settings, their effectiveness on code data remains largely underexplored. This gap is particularly important given code's structured syntax and distinct similarity criteria compared to natural language. To address this, we conduct a comprehensive empirical study of seven state-of-the-art TDD methods on source code data, evaluating their performance across eight CodeLLMs. To support this evaluation, we introduce CodeSnitch, a function-level benchmark dataset comprising 9,000 code samples in three programming languages, each explicitly labeled as either included or excluded from CodeLLM training. Beyond evaluation on the original CodeSnitch, we design targeted mutation strategies to test the robustness of TDD methods under three distinct settings. These mutation strategies are grounded in the well-established Type-1 to Type-4 code clone detection taxonomy. Our study provides a systematic assessment of current TDD techniques for code and offers insights to guide the development of more effective and robust detection methods in the future.
cs.SE↗
Towards Universal & Efficient Model Compression via Exponential Torque Pruning
The rapid growth in complexity and size of modern deep neural networks (DNNs) has increased challenges related to computational costs and memory usage, spurring a growing interest in efficient model compression techniques. Previous state-of-the-art approach proposes using a Torque-inspired regularization which forces the weights of neural modules around a selected pivot point. Whereas, we observe that the pruning effect of this approach is far from perfect, as the post-trained network is still dense and also suffers from high accuracy drop. In this work, we attribute such ineffectiveness to the default linear force application scheme, which imposes inappropriate force on neural module of different distances. To efficiently prune the redundant and distant modules while retaining those that are close and necessary for effective inference, in this work, we propose Exponential Torque Pruning (ETP), which adopts an exponential force application scheme for regularization. Experimental results on a broad range of domains demonstrate that, though being extremely simple, ETP manages to achieve significantly higher compression rate than the previous state-of-the-art pruning strategies with negligible accuracy drop.
cs.CV↗