This work characterizes the class of graphs for which the core equals the nucleus—that is, graphs where the intersection of all maximum independent sets coincides with that of all maximum critical independent sets. Building upon Larson’s independence decomposition, the graph is partitioned into a König–Egerváry part and a 2-bicritical part. By analyzing the boundary between these components and the structure of the corona, the study establishes, for the first time, a complete necessary and sufficient condition for core(G) = nucleus(G): the core of the 2-bicritical component must be empty, and no vertex of the corona may lie on the decomposition boundary. This condition is equivalent to diadem(G) = corona(G) ∩ L(G), offering deeper insight into the structural properties of independent sets and yielding several structural corollaries.

This paper identifies a temporal granularity inconsistency in the prevailing batch-wise evaluation paradigm for dynamic link prediction, leading to misaligned time windows and spurious temporal dependencies—causing up to 12.7% AUC estimation bias and undermining model comparability and generalizability. To address this, the authors first systematically characterize this distortion mechanism and then propose a novel time-aware evaluation framework centered on: (i) timestamp-aligned sequential modeling, (ii) dynamic graph neural network adaptation, (iii) temporal sliding-window resampling, and (iv) a counterfactual evaluation protocol. Extensive experiments across multiple benchmark datasets demonstrate that the proposed paradigm substantially mitigates evaluation bias, enhances fair model comparison, and improves cross-scenario generalization. The work provides both theoretical foundations and a practical framework for standardizing evaluation in temporal graph learning.

This work addresses the absence of principled value-based reinforcement learning algorithms for optimizing exponential utility under fixed risk aversion. It establishes, for the first time, a value-based framework tailored to discounted Markov decision processes in this setting. Building upon a Bellman-type equation for exponential utility, the paper introduces two Q-value-style operators and rigorously proves their contractivity and almost sure convergence under both the $L^\infty$ and sup-log (Thompson) metrics—without requiring a global contraction assumption for the single-timescale algorithm. Furthermore, it provides finite-time convergence rates and demonstrates that the induced greedy stationary policy is optimal in the sense of exponential utility.

This study systematically investigates selective judgment biases in large language models (LLMs) when simulating binary financial market decisions, and their detrimental impact on simulation fairness and accuracy. Methodologically, we compare response distributions across GPT variants—including GPT-4o-Mini-2024-07-18 and GPT-4-0125-preview—under varying conditions: one-shot versus few-shot prompting, temperature-sampling settings, and batch versus single API calls; we further employ negative recency effect tests and true-random sequence baselines. Key contributions include: (1) identifying inter-version “Yes/No” response disparities exceeding 60 percentage points; (2) demonstrating that GPT-4o-Mini achieves balanced “Yes” rates of 32–43%, markedly outperforming GPT-4’s extreme bias (98–99%); (3) showing few-shot prompting approximates 50% equilibrium distribution, whereas one-shot fails to satisfy both uniformity and Markovianity; and (4) revealing that certain models surpass human performance on negative recency tasks. These findings establish a critical bias diagnostic framework and enable controllable generation for LLM-based financial agent modeling.