L-q (L-p)-theory of stochastic differential equations

Xia P, Xie L, Zhang X, Zhao G. L-q (L-p)-theory of stochastic differential equations. STOCHASTIC PROCESSES AND THEIR APPLICATIONS. 2020;130(8):5188-5211.In this paper we show the weak differentiability of the unique strong solution with respect to the starting point x as well as Bismut-Elworthy-Li's derivative formula for the following stochastic differential equation in R-d : dX(t) = b(t, X-t)dt + sigma(t, X-t)dW(t), X-0 =x, where sigma is bounded, uniformly continuous and nondegenerate, b is an element of (L) over tilde (p1)(q1) and del sigma is an element of (L) over tilde (p2)(q2) for some Pi, qi is an element of [2, infinity) with d/pi + 2/qi (pi)(qi) (,) i = 1, 2 are some localized spaces of L-qi (R+; L-pi (R-d)). Moreover, in the endpoint case b is an element of (L) over tilde (d;uni)(infinity) subset of (L) over tilde (d)(infinity), we also show the weak well-posedness. (C) 2020 Elsevier B.V. All rights reserved

The identification, adaptive evolutionary analyses and mRNA expression levels of homeobox (hox) genes in the Chinese mitten crab Eriocheir sinensis

Abstract Background Arthropods are the largest group in the animal kingdom and are morphologically characterized by heterorhythmic segments. Brachyuran decapod crustaceans undergo brachyurization metamorphosis in the early developmental process, characterized by a reduced abdomen that is folded beneath the cephalothorax and inserted between the pereiopods or in a special cavity. As the main cause of major alterations in the evolution of animal body plans, Hox genes encode transcription factors and are involved in bilaterian anterior-posterior axis patterning. Results We found eight Hox genes (labial, proboscipedia, Deformed, zerknüllt, Sex combs reduced, Antennapedia, Ultrabithorax, fushi tarazu, abdominal-A and Abdominal-B) in Eriocheir sinensis. The phylogenetic topology of 13 arthropod Hox genes was closely related to traditional taxonomic groupings. Genome collinearity analysis was performed using genomic data and chromosomal location data of E. sinensis and Portunus trituratus. We found that their chromosomes were highly collinear, and there was a corresponding collinear relationship between the three Hox genes (lab, ftz and Abd-B). The mRNA expression levels of Scr and Antp fluctuated significantly in different developmental stages of E. sinensis, especially in the brachyurization stages. Evolutionary analysis indicated the presence of positively selected sites in Ubx. Conclusions In this study, we used genome-wide analysis to identify and analyze all members of the Hox genes in E. sinensis. Our data will contribute to a better understanding of Hox genes in E. sinensis and provide useful molecular evolutionary information for further investigation on their roles in the brachyurization of crabs

Comparing the diagnostic efficacy of [18F]FDG PET/CT and [18F]FDG PET/MRI for detecting bone metastases in breast cancer: a meta-analysis

This meta-analysis aimed to evaluate the comparative diagnostic efficacy of [18F]FDG PET/CT and [18F] FDG PET/MRI in detecting bone metastases in breast cancer patients

Phylogenetic Analysis and Genetic Structure of Schlegel’s Japanese Gecko (<i>Gekko japonicus</i>) from China Based on Mitochondrial DNA Sequences

Gekko japonicus, i.e., Schlegel’s Japanese Gecko, is an important species which is widely distributed in East Asia. However, the information about population genetics of this species from China remains unclear. To address this issue, we used sequences from a fragment of the mitochondrial protein-coding gene cytochrome c oxidase I to estimate genetic diversity, genetic structure, and historical demography of G. japonicus populations from China. Phylogenetic analysis indicated that G. japonicus had a close relationship with Gekko wenxianensis. A total of 14 haplotypes were obtained, of which haplotype 1 was the most common and widely distributed. The genetic diversity of G. japonicus was comparatively low across different geographic populations. The populations of G. japonicus were divided into four groups which exhibited low levels of genetic differentiation, and expressed an unclear pattern of population structuring. In addition, potential population expansion of G. japonicus has occurred as well. Overall, these results demonstrate that the populations of G. japonicus reveal low genetic diversity in China, which is attributed to the founder and bottleneck events among populations. Our results will provide meaningful information on the population genetics of G. japonicus and will provide some insights into the study of origin of populations