摘要：
Watermelon is a crop susceptible to diseases. Rapid and effective detection of watermelon diseases is of great significance to ensure the yield of watermelon. Aiming at the interference of the environment and obstacles in the natural environment, resulting in low target detection accuracy and poor robustness, this paper takes watermelon leaves as the research object, considering anthracnose, leaf blight, leaf spot and normal leaves as examples. A disease recognition method based on deep learning is proposed. This paper has improved the pre-selected box setting formula of the SSD model and tested it in multiple SSD models. Experiments show that the average accuracy of the final SSD768 model is 92.4%, and the average accuracy of the IOU is 88.9%. It shows that this method can be used to detect watermelon diseases in natural environment.
期刊：
COMMUNICATIONS IN MATHEMATICAL SCIENCES,2020年18(7):2059-2074 ISSN：1539-6746
通讯作者：
Wang, Yong;Xu, Jiankai
作者机构：
[Tan, Zhong] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China.;[Wang, Yong] South China Normal Univ, South China Res Ctr Appl Math & Interdisciplinary, Guangzhou 510631, Guangdong, Peoples R China.;[Xu, Jiankai] Hunan Agr Univ, Coll Informat Sci & Technol, Changsha 410128, Hunan, Peoples R China.
通讯机构：
[Wang, Yong] S;[Xu, Jiankai] H;South China Normal Univ, South China Res Ctr Appl Math & Interdisciplinary, Guangzhou 510631, Guangdong, Peoples R China.;Hunan Agr Univ, Coll Informat Sci & Technol, Changsha 410128, Hunan, Peoples R China.
关键词：
Axis-symmetric kernel;Integral equation;Non-existence of radial solutions;Regularity lifting lemma
期刊：
Frontiers in Genetics,2020年10:488214 ISSN：1664-8021
通讯作者：
Chen, Yuan
作者机构：
[Zhang, Haojian; Jiang, Heling; Yuan, Zheming; Chen, Yuan; Wang, Qifei; Liang, Yuqing] Hunan Agr Univ, Hunan Engn & Technol Res Ctr Agr Big Data Anal &, Changsha, Peoples R China.;[Tan, Siqiao] Hunan Agr Univ, Sch Informat Sci & Technol, Changsha, Peoples R China.;[Luo, Feng] Clemson Univ, Sch Comp, Clemson, SC USA.
通讯机构：
[Chen, Yuan] H;Hunan Agr Univ, Hunan Engn & Technol Res Ctr Agr Big Data Anal &, Changsha, Peoples R China.
关键词：
RNA sequencing;Maximal information coefficient;Differential expressed gene;Gene selection;normalized differential correlation
摘要：
For precision medicine, there is a need to identify genes that accurately distinguish the physiological state or response to a particular therapy, but this can be challenging. Many methods of analyzing differential expression have been established and applied to this problem, such as t-test, edgeR, and DEseq2. A common feature of these methods is their focus on a linear relationship (differential expression) between gene expression and phenotype. However, they may overlook nonlinear relationships due to various factors, such as the degree of disease progression, sex, age, ethnicity, and environmental factors. Maximal information coefficient (MIC) was proposed to capture a wide range of associations of two variables in both linear and nonlinear relationships. However, with MIC it is difficult to highlight genes with nonlinear expression patterns as the genes giving the most strongly supported hits are linearly expressed, especially for noisy data. It is thus important to also efficiently identify nonlinearly expressed genes in order to unravel the molecular basis of disease and to reveal new therapeutic targets. We propose a novel nonlinearity measure called normalized differential correlation (NDC) to efficiently highlight nonlinearly expressed genes in transcriptome datasets. Validation using six real-world cancer datasets revealed that the NDC method could highlight nonlinearly expressed genes that could not be highlighted by t-test, MIC, edgeR, and DEseq2, although MIC could capture nonlinear correlations. The classification accuracy indicated that analysis of these genes could adequately distinguish cancer and paracarcinoma tissue samples. Furthermore, the results of biological interpretation of the identified genes suggested that some of them were involved in key functional pathways associated with cancer progression and metastasis. All of this evidence suggests that these nonlinearly expressed genes may play a central role in regulating cancer progression.
通讯机构：
[Xu, Jian] H;Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China.
摘要：
In the one-dimensional Diophantine approximation, by using the continued fractions, Khintchine's theorem and Jarnik's theorem are concerned with the growth of the large partial quotients, while the improvability of Dirichlet's theorem is concerned with the growth of the product of consecutive partial quotients. This paper aims to establish a complete characterization on the metric properties of the product of the partial quotients, including the Lebesgue measure-theoretic result and the Hausdorff dimensional result. More precisely, for anyx is an element of [0, 1), letx=[a(1),a(2), horizontal ellipsis ] beits continued fraction expansion. The size of the following set, in the sense of Lebesgue measure and Hausdorff dimension,E-m(phi):= {x is an element of [0, 1):a(n)(x) MIDLINE HORIZONTAL ELLIPSISa(n+m-1)(x) >=phi(n) for infinitely manyn is an element of N}, are given completely, wherem >= 1 is an integer and phi: N -> Double-struck capital R(+)is a positive function.
关键词：
roth展式;“0-1”律;重对数律α-Lu摘要：
Abstract: For the α-Lüroth expansion, some metric properties, such as “0-1” law, iterated logarithm law of the digits are studied in this paper. As the extension of alternating-Lüroth expansion, the conclusions in this paper include those of alternating-Lüroth case.#@#@#摘要: 对于α-Lüroth展式，在此篇文章我们研究了α-Lüroth展式的一些度量性质，获得了该展式数字“0-1”律，基于该结果，得到了相应的重对数律，进一步完善了该展式的度量性质。作为交错Lüroth展式的推广，该论文的结论包括了交错Lüroth的相应的结果。
