Classification and enumeration of lattice polygons in a disc

In 1980, V. I. Arnold studied the classification problem for convex lattice polygons of given area. Since then, this problem and its analogues have been studied by many authors, including $\mathrm{B\acute{a}r\acute{a}ny}$, Lagarias, Pach, Santos, Ziegler and Zong. Recently, Zong proposed two computer programs to prove Hadwiger's covering conjecture and Borsuk's partition problem, respectively, based on enumeration of the convex lattice polytopes contained in certain balls. For this purpose, similar to $\mathrm{B\acute{a}r\acute{a}ny}$ and Pach's work on volume and Liu and Zong's work on cardinality, we obtain bounds on the number of non-equivalent convex lattice polygons in a given disc. Furthermore, we propose an algorithm to enumerate these convex lattice polygons.Comment: 19 pages, 3 figure

Earnings Management for Second-time IPOs: Evidence from China

In China’s IPO market, firms that fail in their first IPO application make considerable adjustments before making their second IPO application. Examining firms that applied for IPOs during 2004-2018, we find that failed IPO applicant firms “package” themselves to obtain approval of the China Securities Regulatory Commission (CSRC) by reducing accrual earnings management and increasing real earnings management. In addition, after a successful second IPO application, these firms relax their vigilance vis-à-vis the CSRC and increase both accrual and real earnings management. This pre-IPO “packaging” behavior deceives investors, leading to higher IPO prices and higher post-IPO returns

A Noise-Tolerant Zeroing Neural Network for Time-Dependent Complex Matrix Inversion Under Various Kinds of Noises

Complex-valued time-dependent matrix inversion (TDMI) is extensively exploited in practical industrial and engineering fields. Many current neural models are presented to find the inverse of a matrix in an ideal noise-free environment. However, the outer interferences are normally believed to be ubiquitous and avoidable in practice. If these neural models are applied to complex-valued TDMI in a noise environment, they need to take a lot of precious time to deal with outer noise disturbances in advance. Thus, a noise-suppression model is urgent to be proposed to address this problem. In this article, a complex-valued noise-tolerant zeroing neural network (CVNTZNN) on the basis of an integral-type design formula is established and investigated for finding complex-valued TDMI under a wide variety of noises. Furthermore, both convergence and robustness of the CVNTZNN model are carefully analyzed and rigorously proved. For comparison and verification purposes, the existing zeroing neural network (ZNN) and gradient neural network (GNN) have been presented to address the same problem under the same conditions. Numerical simulation consequences demonstrate the effectiveness and excellence of the proposed CVNTZNN model for complex-valued TDMI under various kinds of noises, by comparing the existing ZNN and GNN models

VLM-Eval: A General Evaluation on Video Large Language Models

Despite the rapid development of video Large Language Models (LLMs), a comprehensive evaluation is still absent. In this paper, we introduce a unified evaluation that encompasses multiple video tasks, including captioning, question and answering, retrieval, and action recognition. In addition to conventional metrics, we showcase how GPT-based evaluation can match human-like performance in assessing response quality across multiple aspects. We propose a simple baseline: Video-LLaVA, which uses a single linear projection and outperforms existing video LLMs. Finally, we evaluate video LLMs beyond academic datasets, which show encouraging recognition and reasoning capabilities in driving scenarios with only hundreds of video-instruction pairs for fine-tuning. We hope our work can serve as a unified evaluation for video LLMs, and help expand more practical scenarios. The evaluation code will be available soon

Impacts of Future Climate Change on Net Primary Productivity of Grassland in Inner Mongolia, China

Net Primary Productivity (NPP) of grassland is a key variable of terrestrial ecosystems and is an important parameter for characterizing carbon cycles in grassland ecosystems. In this research, the Inner Mongolia grassland NPP was calculated using the Miami Model and the impact of climate change on grassland NPP was subsequently analyzed under the Special Report on Emissions Scenarios (SRES) A2, B2, and A1B scenarios, which are inferred from Providing Regional Climates for Impacts Studies (PRECIS) climate model system. The results showed that: (1) the NPP associated with these three scenarios had a similar distribution in Inner Mongolia: the grassland NPP increased gradually from the western region, with less than 200 g/m2/yr, to the southeast region, with more than 800 g/m2/yr. Precipitation was the main factor determining the grassland NPP; (2) compared with the baseline (1961-1990), there would be an overall increase in grassland NPP during three time periods (2020s: 2011-2040, 2050s: 2041-2070, and 2080s: 2071-2100) under the A2 and B2 scenarios; (3) under the A1B scenario, there will be a decreasing trend at middle-west region during the 2020s and 2050s; while there will be a very significant decrease from the 2050s to 2080s for middle Inner Mongolia; and (4) grassland NPP under the A1B scenario would present the most significant increase among the three scenarios, and would have the least significant increase under the B2 scenario

A Regulatable Blockchain Transaction Model with Privacy Protection

Blockchain is a decentralized distributed ledger technology. The public chain represented by Bitcoin and Ethereum only realizes the limited anonymity of user identity, and the transaction amount is open to the whole network, resulting in user privacy leakage. Based on the existing anonymous technology, the concealment of the sender, receiver, amount of the transaction, and does not disclose any information, which makes the supervision difficult. Therefore, the design of blockchain scheme with privacy protection and supervision functions is of great significance. In this paper, a blockchain transaction model with both privacy and supervision function is proposed. It uses probability encryption to realize the hiding of the true identity of the blockchain transaction, and uses the commitment scheme and zero-knowledge proof technology to realize the privacy protection and guarantee legitimacy verification of the transaction. With the use of encryption technology, the regulators can supervise blockchain transactions without storing the users' information, which greatly reduces the pressure on storage, computing and key management. In addition, it does not rely on specific consensus mechanism and can be used as an independent module. The security performance analysis shows that the proposed scheme has great practicability and has potential application in many fields

Fossil data support a pre-Cretaceous origin of flowering plants

Data and scripts associated with the paper. Updated version of the code will be available here: https://github.com/dsilvestro/rootBB