Dynamics of Fractional Delayed Reaction-Diffusion Equations.

The long-term behavior of the weak solution of a fractional delayed reaction-diffusion equation with a generalized Caputo derivative is investigated. By using the classic Galerkin approximation method and comparison principal, the existence and uniqueness of the solution is proved in the sense of weak solution. In addition, the global attracting set of the considered system is obtained, with the help of the Sobolev embedding theorem and Halanay inequality.

Uncover the reasons for performance differences between measurement functions (Provably).

Recently, an exciting experimental conclusion in Li et al. (Knowl Inf Syst 62(2):611-637, 1) about measures of uncertainty for knowledge bases has attracted great research interest for many scholars. However, these efforts lack solid theoretical interpretations for the experimental conclusion. The main limitation of their research is that the final experimental conclusions are only derived from experiments on three datasets, which makes it still unknown whether the conclusion is universal. In our work, we first review the mathematical theories, definitions, and tools for measuring the uncertainty of knowledge bases. Then, we provide a series of rigorous theoretical proofs to reveal the reasons for the superiority of using the knowledge amount of knowledge structure to measure the uncertainty of the knowledge bases. Combining with experiment results, we verify that knowledge amount has much better performance for measuring uncertainty of knowledge bases. Hence, we prove an empirical conclusion established through experiments from a mathematical point of view. In addition, we find that for some knowledge bases that cannot be classified by entity attributes, such as ProBase (a probabilistic taxonomy), our conclusion is still applicable. Therefore, our conclusions have a certain degree of universality and interpretability and provide a theoretical basis for measuring the uncertainty of many different types of knowledge bases, and the findings of this study have a number of important implications for future practice.

Rethinking the framework constructed by counterfactual functional model.

The causal inference represented by counterfactual inference technology breathes new life into the current field of artificial intelligence. Although the fusion of causal inference and artificial intelligence has an excellent performance in many various applications, some theoretical justifications have not been well resolved. In this paper, we focus on two fundamental issues in causal inference: probabilistic evaluation of counterfactual queries and the assumptions used to evaluate causal effects. Both of these issues are closely related to counterfactual inference tasks. Among them, counterfactual queries focus on the outcome of the inference task, and the assumptions provide the preconditions for performing the inference task. Counterfactual queries are to consider the question of what kind of causality would arise if we artificially apply the conditions contrary to the facts. In general, to obtain a unique solution, the evaluation of counterfactual queries requires the assistance of a functional model. We analyze the limitations of the original functional model when evaluating a specific query and find that the model arrives at ambiguous conclusions when the unique probability solution is 0. In the task of estimating causal effects, the experiments are conducted under some strong assumptions, such as treatment-unit additivity. However, such assumptions are often insatiable in real-world tasks, and there is also a lack of scientific representation of the assumptions themselves. We propose a mild version of the treatment-unit additivity assumption coined as M-TUA based on the damped vibration equation in physics to alleviate this problem. M-TUA reduces the strength of the constraints in the original assumptions with reasonable formal expression.

Anatomical, Phytochemical, and Histochemical Study of Juniperus rigida Needles at Different Altitudes.

Needles of Juniperus rigida are used in Chinese traditional medicine for the treatment of brucellosis, dropsy, skin disease, and rheumatoid arthritis. This is the first study that reports anatomical structures of the J. rigida needles collected at different altitudes. The most common anatomical, phytochemical, and histochemical techniques and methods are used. The results show that anatomical structures and chemical composition change significantly at different altitudes. The main anatomical characters are significant xeromorphic structures (thick epidermis, hypodermis, and cuticle), a stomatal band, a developed vascular bundle, and a marginal resin duct. The xeromorphic structures become more pronounced with increasing altitude. The phytochemical and histochemical results demonstrate that the content of the main chemical compounds (phenols and terpenoids) basically increases at a higher elevation. Histochemical analysis localizes the phenols in epidermal cells, sponge tissue, endothelial layer cells, and stomatal bands, and the terpenoids in palisade tissue, sponge tissue, and the edge of the resin duct. This work reveals the relation between anatomy and chemistry in J. rigida needles, contributes to the quality control of its ethno-medicine, and provides the evidence to develop the commercial cultivation.