Finite-width Gaussian sum rules for 0−+0^{-+} pseudoscalar glueball based on correction from instanton-gluon interference to correlation function

Based on correction from instanton-gluon interference to correlation function, the properties of the $0^{-+}$ pseudoscalar glueball is investigated in a family of finite-width Gaussian sum rules. In the framework of semiclassical expansion for quantum chromodynamics $(\textrm{QCD})$ in the instanton liquid background, the contribution arising from the the interference between instantons and the quantum gluon fields is calculated, and included in the correlation function together with pure-classical contribution from instantons and the perturbative one. The interference contribution is turned to be gauge-invariant, free of infrared divergence, and has a great role to restore the positivity of the spectra of the full correlation function. The negligible contribution from vacuum condensates is excluded in our correlation function to avoid the double counting. Instead of the usual zero-width approximation for the resonances, the usual Breit-Wigner form with a suitable threshold behavior for the spectral function of the finite-width resonances is adopted. A consistency between the subtracted and unsubtracted sum rules is very well justified. The values of the mass, decay width and coupling constants for the $0^{-+}$ resonance in which the glueball fraction is dominant are obtained, and agree with the phenomenological analysis.Comment: 18 pages, 10 figure

Capacity sharing strategy with sustainable revenue-sharing contracts

This paper develops a duopoly model to analyse capacity sharing strategy and the optimal revenue-sharing contract under a two-part tariff and examines the effects of capacity sharing, cost, and sharing charges in three scenarios. The paper uses the two-part tariff method and adds a more realistic assumption of incremental marginal costs to improve the research on capacity sharing strategies. The results show that capacity constraints affect the sustainable development of firms. A sustainable revenue-sharing contract can create a win-win situation for both firms and promote capacity sharing. Capacity sharing, cost, and the revenue-sharing rate have different impacts in different scenarios; the optimal revenue-sharing rate and fixed fee can be determined to maximise the profits of firms that share capacity. However, capacity sharing may not improve social welfare. First published online 28 December 202

Extending LLMs' Context Window with 100 Samples

Large Language Models (LLMs) are known to have limited extrapolation ability beyond their pre-trained context window, constraining their application in downstream tasks with lengthy inputs. Recent studies have sought to extend LLMs' context window by modifying rotary position embedding (RoPE), a popular position encoding method adopted by well-known LLMs such as LLaMA, PaLM, and GPT-NeoX. However, prior works like Position Interpolation (PI) and YaRN are resource-intensive and lack comparative experiments to assess their applicability. In this work, we identify the inherent need for LLMs' attention entropy (i.e. the information entropy of attention scores) to maintain stability and introduce a novel extension to RoPE which combines adjusting RoPE's base frequency and scaling the attention logits to help LLMs efficiently adapt to a larger context window. We validate the superiority of our method in both fine-tuning performance and robustness across different context window sizes on various context-demanding tasks. Notably, our method extends the context window of LLaMA-2-7B-Chat to 16,384 with only 100 samples and 6 training steps, showcasing extraordinary efficiency. Finally, we also explore how data compositions and training curricula affect context window extension for specific downstream tasks, suggesting fine-tuning LLMs with lengthy conversations as a good starting point. We release our code and SFT data at https://github.com/GAIR-NLP/Entropy-ABF

Privatisation policy with different oligopolistic competition in the public utilities market

This study constructs an oligopoly model in public utilities sector to explore the optimal privatisation policy and the factors affecting equilibrium outcomes and explores the optimal proportion of state-owned shares. We also offer empirical evidence of China’s public utilities from 1985 to 2019 to prove the applicability of model results. The results show that, depending on product differentiation, cost variance, technical level, nationalisation, partial or full privatisation can be optimal. Improving capital efficiency increases social welfare in Model PP, but not in Model PS. Product differentiation improves social welfare at the expense of profits in SS model. In Model PM, technical improvements boost private enterprise profits but induce a decrement in social welfare. A high proportion of state-owned shares fail to improve social welfare in Model SM. In a word, the value range of parameters and competition modes in public utilities sector affect market players’ welfare distribution, which identifies with the empirical analysis of China’s public utilities development

Government regulation of emergency supplies under the epidemic crisis

This paper constructs a multi-oligopoly model of emergency supplies and analyses the market equilibrium results under normal conditions and epidemic conditions. The impacts of the degree of change in market demand, externalities, the material cost of emergency supplies and government regulation on the equilibrium results, especially on the prices of emergency supplies, are discussed. The results show that an increase in material cost will lead to low output and social welfare and a high price, under either normal conditions or epidemic conditions. Moreover, under epidemic conditions, the degree of change in market demand, externalities, material cost and the presence and mode of government regulation all have multiple and complex influences on the equilibrium results. Under epidemic conditions, both government output and price regulation can increase the supply of emergency supplies. In addition, when market demand changes drastically, consumer surplus and social welfare can be enhanced by the implementation of regulations. Particularly, price regulation is more effective when there is a high material cost

Further Development of the Improved QMD Model and its Applications to Fusion Reaction near Barrier

The Improved Quantum Molecular Dynamics model is further developed by introducing new parameters in interaction potential energy functional based on Skyrme interaction of SkM$^{*}$ and SLy series. The properties of ground states of selected nuclei can be reproduced very well. The Coulomb barriers for a series of reaction systems are studied and compared with the results of the proximity potential. The fusion excitation functions for a series of fusion reactions are calculated and the results are in good agreement with experimental data.Comment: 17 pages, 10 figures, PRC accepte

Feature Fusion and Detection in Alzheimer’s Disease Using a Novel Genetic Multi-Kernel SVM Based on MRI Imaging and Gene Data

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).Voxel-based morphometry provides an opportunity to study Alzheimer’s disease (AD) at a subtle level. Therefore, identifying the important brain voxels that can classify AD, early mild cognitive impairment (EMCI) and healthy control (HC) and studying the role of these voxels in AD will be crucial to improve our understanding of the neurobiological mechanism of AD. Combining magnetic resonance imaging (MRI) imaging and gene information, we proposed a novel feature construction method and a novel genetic multi-kernel support vector machine (SVM) method to mine important features for AD detection. Specifically, to amplify the differences among AD, EMCI and HC groups, we used the eigenvalues of the top 24 Single Nucleotide Polymorphisms (SNPs) in a p-value matrix of 24 genes associated with AD for feature construction. Furthermore, a genetic multi-kernel SVM was established with the resulting features. The genetic algorithm was used to detect the optimal weights of 3 kernels and the multi-kernel SVM was used after training to explore the significant features. By analyzing the significance of the features, we identified some brain regions affected by AD, such as the right superior frontal gyrus, right inferior temporal gyrus and right superior temporal gyrus. The findings proved the good performance and generalization of the proposed model. Particularly, significant susceptibility genes associated with AD were identified, such as CSMD1, RBFOX1, PTPRD, CDH13 and WWOX. Some significant pathways were further explored, such as the calcium signaling pathway (corrected p-value = 1.35 × 10−6) and cell adhesion molecules (corrected p-value = 5.44 × 10−4). The findings offer new candidate abnormal brain features and demonstrate the contribution of these features to AD.Peer reviewedFinal Published versio

Self-Learning Symmetric Multi-view Probabilistic Clustering

Multi-view Clustering (MVC) has achieved significant progress, with many efforts dedicated to learn knowledge from multiple views. However, most existing methods are either not applicable or require additional steps for incomplete MVC. Such a limitation results in poor-quality clustering performance and poor missing view adaptation. Besides, noise or outliers might significantly degrade the overall clustering performance, which are not handled well by most existing methods. In this paper, we propose a novel unified framework for incomplete and complete MVC named self-learning symmetric multi-view probabilistic clustering (SLS-MPC). SLS-MPC proposes a novel symmetric multi-view probability estimation and equivalently transforms multi-view pairwise posterior matching probability into composition of each view's individual distribution, which tolerates data missing and might extend to any number of views. Then, SLS-MPC proposes a novel self-learning probability function without any prior knowledge and hyper-parameters to learn each view's individual distribution. Next, graph-context-aware refinement with path propagation and co-neighbor propagation is used to refine pairwise probability, which alleviates the impact of noise and outliers. Finally, SLS-MPC proposes a probabilistic clustering algorithm to adjust clustering assignments by maximizing the joint probability iteratively without category information. Extensive experiments on multiple benchmarks show that SLS-MPC outperforms previous state-of-the-art methods