Urban rural common prosperity is the ultimate goal of narrowing the gap between urban and rural areas and promoting urban rural integration development, and it is an indispensable and important element in the common wealth goal of Chinese style modernization.

We study the existence of equilibrium when agents' preferences may not beconvex. For some specific utility functions, we provide a necessary and sufficientcondition under which there exists an equilibrium. The standard approach cannot be directly applied to our examples because the demand correspondence of some agents is neither single-valued nor convex-valued.

Darwinian spreading of vigor, in addition to quality distribution, is introduced in a tree growth model. The size of any tree, within an even-aged stand, is taken as a measure of an inherited productive capacity, and then combined with quality thinning. For sparse cultivation density, the result is forestry without commercial thinnings; large trees cannot be removed since they are the most productive, neither small trees because the unit price of harvesting would be large. For large cultivation density, thinning from above becomes combined with quality thinning of large trees. Darwinian spreading of growth rate may correlate with quality. Quality thinning may enhance growth rate. Such effects combined, large trees still become removed but quality thinning becomes implemented in almost all diameter classes. At financial maturity, Darwinian spreading treated with quality thinning, the weighted mean breast height diameter is in the vicinity of 20 cm within stands of high planting density, and somewhat higher with low planting density. Quality correlating with Darwinian spreading of growth, and growth rate correlating with observed quality, trees grow bigger, the maturity size becoming closer to 25 cm - bigger than in earlier studies without tree-size - dependency of vigor.

This study provides the first comprehensive assessment of consistency and reproducibility in Large Language Model (LLM) outputs in finance and accounting research. We evaluate how consistently LLMs produce outputs given identical inputs through extensive experimentation with 50 independent runs across five common tasks: classification, sentiment analysis, summarization, text generation, and prediction. Using three OpenAI models (GPT-3.5-turbo, GPT-4o-mini, and GPT-4o), we generate over 3.4 million outputs from diverse financial source texts and data, covering MD&As, FOMC statements, finance news articles, earnings call transcripts, and financial statements. Our findings reveal substantial but task-dependent consistency, with binary classification and sentiment analysis achieving near-perfect reproducibility, while complex tasks show greater variability. More advanced models do not consistently demonstrate better consistency and reproducibility, with task-specific patterns emerging. LLMs significantly outperform expert human annotators in consistency and maintain high agreement even where human experts significantly disagree. We further find that simple aggregation strategies across 3-5 runs dramatically improve consistency. Simulation analysis reveals that despite measurable inconsistency in LLM outputs, downstream statistical inferences remain remarkably robust. These findings address concerns about what we term "G-hacking," the selective reporting of favorable outcomes from multiple Generative AI runs, by demonstrating that such risks are relatively low for finance and accounting tasks.

We study the martingale property and moment explosions of a signature volatility model, where the volatility process of the log-price is given by a linear form of the signature of a time-extended Brownian motion. Excluding trivial cases, we demonstrate that the price process is a true martingale if and only if the order of the linear form is odd and a correlation parameter is negative. The proof involves a fine analysis of the explosion time of a signature stochastic differential equation. This result is of key practical relevance, as it highlights that, when used for approximation purposes, the linear combination of signature elements must be taken of odd order to preserve the martingale property. Once martingality is established, we also characterize the existence of higher moments of the price process in terms of a condition on a correlation parameter.

Recently, autonomous driving system (ADS) has been widely adopted due to its potential to enhance travel convenience and alleviate traffic congestion, thereby improving the driving experience for consumers and creating lucrative opportunities for manufacturers. With the advancement of data sensing and control technologies, the reliability of ADS and the purchase intentions of consumers are continually evolving, presenting challenges for manufacturers in promotion and pricing decisions. To address this issue, we develop a two-stage game-theoretical model to characterize the decision-making processes of manufacturers and consumers before and after a technology upgrade. Considering the unique structural characteristics of ADS, which consists of driving software and its supporting hardware (SSH), we propose different business strategies for SSH (bundle or unbundle with the vehicle) and driving software (perpetual licensing or subscription) from the manufacturer's perspective. We find that, first, SSH strategies influence the optimal software strategies by changing the consumers' entry barriers to the ADS market. Specifically, for manufacturers with mature ADS technology, the bundle strategy provides consumers with a lower entry barrier by integrating SSH, making the flexible subscription model a dominant strategy; while perpetual licensing outperforms under the unbundle strategy. Second, the software strategies influence the optimal SSH strategy by altering consumers' exit barriers. Perpetual licensing imposes higher exit barriers; when combined with a bundle strategy that lowers entry barriers, it becomes a more advantageous choice for manufacturers with mature ADS technology. In contrast, the subscription strategy allows consumers to easily exit the market, making the bundle strategy advantageous only when a substantial proportion of consumers are compatible with ADS.

The paper analyses trade between the most developed economies of the world. The analysis is based on the previously proposed model of international trade. This model of international trade is based on the theory of general economic equilibrium. The demand for goods in this model is built on the import of goods by each of the countries participating in the trade. The structure of supply of goods in this model is determined by the structure of exports of each country. It is proved that in such a model, given a certain structure of supply and demand, there exists a so-called ideal equilibrium state in which the trade balance of each country is zero. Under certain conditions on the structure of supply and demand, there is an equilibrium state in which each country have a strictly positive trade balance. Among the equilibrium states under a certain structure of supply and demand, there are some that differ from the ones described above. Such states are characterized by the fact that there is an inequitable distribution of income between the participants in the trade. Such states are called degenerate. In this paper, based on the previously proposed model of international trade, an analysis of the dynamics of international trade of 8 of the world's most developed economies is made. It is shown that trade between these countries was not in a state of economic equilibrium. The found relative equilibrium price vector turned out to be very degenerate, which indicates the unequal exchange of goods on the market of the 8 studied countries. An analysis of the dynamics of supply to the market of the world's most developed economies showed an increase in China's share. The same applies to the share of demand.

As artificial intelligence becomes increasingly integrated into professional and personal domains, traditional metrics of human intelligence require reconceptualization. This paper introduces the Artificial Intelligence Quotient (AIQ), a novel measurement framework designed to assess an individual's capacity to effectively collaborate with and leverage AI systems, particularly Large Language Models (LLMs). Building upon established cognitive assessment methodologies and contemporary AI interaction research, we present a comprehensive framework for quantifying human-AI collaborative intelligence. This work addresses the growing need for standardized evaluation of AI-augmented cognitive capabilities in educational and professional contexts.

In this paper, we investigate how individuals evaluate human and large langue models generated responses to popular questions when the source of the content is either concealed or disclosed. Through a controlled field experiment, participants were presented with a set of questions, each accompanied by a response generated by either a human or an AI. In a randomized design, half of the participants were informed of the response's origin while the other half remained unaware. Our findings indicate that, overall, participants tend to prefer AI-generated responses. However, when the AI origin is revealed, this preference diminishes significantly, suggesting that evaluative judgments are influenced by the disclosure of the response's provenance rather than solely by its quality. These results underscore a bias against AI-generated content, highlighting the societal challenge of improving the perception of AI work in contexts where quality assessments should be paramount.

This paper introduces a simple JavaScript-based web application designed to assist educators in detecting AI-generated content in student essays and written assignments. Unlike existing AI detection tools that rely on obfuscated machine learning models, AIDetection.info employs a heuristic-based approach to identify common syntactic traces left by generative AI models, such as ChatGPT, Claude, Grok, DeepSeek, Gemini, Llama/Meta, Microsoft Copilot, Grammarly AI, and other text-generating models and wrapper applications. The tool scans documents in bulk for potential AI artifacts, as well as AI citations and acknowledgments, and provides a visual summary with downloadable Excel and CSV reports. This article details its methodology, functionalities, limitations, and applications within educational settings.

This research addresses the growing need to measure and understand AI literacy in the context of generative AI technologies. Through three sequential studies involving a total of 517 participants, we establish AI literacy as a coherent, measurable construct with significant implications for education, workforce development, and social equity. Study 1 (N=85) revealed a dominant latent factor - termed the "A-factor" - that accounts for 44.16% of variance across diverse AI interaction tasks. Study 2 (N=286) refined the measurement tool by examining four key dimensions of AI literacy: communication effectiveness, creative idea generation, content evaluation, and step-by-step collaboration, resulting in an 18-item assessment battery. Study 3 (N=146) validated this instrument in a controlled laboratory setting, demonstrating its predictive validity for real-world task performance. Results indicate that AI literacy significantly predicts performance on complex, language-based creative tasks but shows domain specificity in its predictive power. Additionally, regression analyses identified several significant predictors of AI literacy, including cognitive abilities (IQ), educational background, prior AI experience, and training history. The multidimensional nature of AI literacy and its distinct factor structure provide evidence that effective human-AI collaboration requires a combination of general and specialized abilities. These findings contribute to theoretical frameworks of human-AI collaboration while offering practical guidance for developing targeted educational interventions to promote equitable access to the benefits of generative AI technologies.

We identify various classes of neural networks that are able to approximate continuous functions locally uniformly subject to fixed global linear growth constraints. For such neural networks the associated neural stochastic differential equations can approximate general stochastic differential equations, both of It\^o diffusion type, arbitrarily well. Moreover, quantitative error estimates are derived for stochastic differential equations with sufficiently regular coefficients.