The Lower Bounds for Eigenvalues of Elliptic Operators --By Nonconforming Finite Element Methods

The aim of the paper is to introduce a new systematic method that can produce lower bounds for eigenvalues. The main idea is to use nonconforming finite element methods. The general conclusion herein is that if local approximation properties of nonconforming finite element spaces $V_h$ are better than global continuity properties of $V_h$, corresponding methods will produce lower bounds for eigenvalues. More precisely, under three conditions on continuity and approximation properties of nonconforming finite element spaces we first show abstract error estimates of approximate eigenvalues and eigenfunctions. Subsequently, we propose one more condition and prove that it is sufficient to guarantee nonconforming finite element methods to produce lower bounds for eigenvalues of symmetric elliptic operators. As one application, we show that this condition hold for most nonconforming elements in literature. As another important application, this condition provides a guidance to modify known nonconforming elements in literature and to propose new nonconforming elements. In fact, we enrich locally the Crouzeix-Raviart element such that the new element satisfies the condition; we propose a new nonconforming element for second order elliptic operators and prove that it will yield lower bounds for eigenvalues. Finally, we prove the saturation condition for most nonconforming elements.Comment: 24 page

Recovery type a posteriori error estimation of an adaptive finite element method for Cahn--Hilliard equation

In this paper, we derive a novel recovery type a posteriori error estimation of the Crank-Nicolson finite element method for the Cahn--Hilliard equation. To achieve this, we employ both the elliptic reconstruction technique and a time reconstruction technique based on three time-level approximations, resulting in an optimal a posteriori error estimator. We propose a time-space adaptive algorithm that utilizes the derived a posteriori error estimator as error indicators. Numerical experiments are presented to validate the theoretical findings, including comparing with an adaptive finite element method based on a residual type a posteriori error estimator.Comment: 36 pages, 7 figure

Comparative analysis of 17 complete chloroplast genomes reveals intraspecific variation and relationships among Pseudostellaria heterophylla (Miq.) Pax populations

Pseudostellaria heterophylla (Miq.) Pax is a well-known medicinal and ecologically important plant. Effectively distinguishing its different genetic resources is essential for its breeding. Plant chloroplast genomes can provide much more information than traditional molecular markers and provide higher-resolution genetic analyses to distinguish closely related planting materials. Here, seventeen P. heterophylla samples from Anhui, Fujian, Guizhou, Hebei, Hunan, Jiangsu, and Shandong provinces were collected, and a genome skimming strategy was employed to obtain their chloroplast genomes. The P. heterophylla chloroplast genomes ranged from 149,356 bp to 149,592 bp in length, and a total of 111 unique genes were annotated, including 77 protein-coding genes, 30 tRNA genes, and four rRNA genes. Codon usage analysis showed that leucine had the highest frequency, while UUU (encoding phenylalanine) and UGC (encoding cysteine) were identified as the most and least frequently used codons, respectively. A total of 75–84 SSRs, 16–21 short tandem repeats, and 27–32 long repeat structures were identified in these chloroplast genomes. Then, four primer pairs were revealed for identifying SSR polymorphisms. Palindromes are the dominant type, accounting for an average of 47.86% of all long repeat sequences. Gene orders were highly collinear, and IR regions were highly conserved. Genome alignment indicated that there were four intergenic regions (psaI-ycf4, ycf3-trnS, ndhC-trnV, and ndhI-ndhG) and three coding genes (ndhJ, ycf1, and rpl20) that were highly variable among different P. heterophylla samples. Moreover, 10 SNP/MNP sites with high polymorphism were selected for further study. Phylogenetic analysis showed that populations of Chinese were clustered into a monophyletic group, in which the non-flowering variety formed a separate subclade with high statistical support. In this study, the comparative analysis of complete chloroplast genomes revealed intraspecific variations in P. heterophylla and further supported the idea that chloroplast genomes could elucidate relatedness among closely related cultivation materials

Increased R2* in the Caudate Nucleus of Asymptomatic Welders

Welding has been associated with neurobehavioral disorders. Welding fumes contain several metals including copper (Cu), manganese (Mn), and iron (Fe) that may interact to influence welding-related neurotoxicity. Although welding-related airborne Fe levels are about 10-fold higher than Mn, previous studies have focused on Mn and its accumulation in the basal ganglia. This study examined differences in the apparent transverse relaxation rates [R2* (1/T2*), estimate of Fe accumulation] in the basal ganglia (caudate nucleus, putamen, and globus pallidus) between welders and controls, and the dose–response relationship between estimated Fe exposure and R2* values. Occupational questionnaires estimated recent and lifetime Fe exposure, and blood Fe levels and brain magnetic resonance imaging (MRI) were obtained. Complete exposure and MRI R2* and R1 (1/T1: measure to estimate Mn accumulation) data from 42 subjects with welding exposure and 29 controls were analyzed. Welders had significantly greater exposure metrics and higher whole-blood Fe levels compared with controls. R2* in the caudate nucleus was significantly higher in welders after controlling for age, body mass index, respirator use, caudate R1, and blood metals of Cu and Mn, whereas there was no difference in R1 values in the basal ganglia between groups. The R2* in the caudate nucleus was positively correlated with whole-blood Fe concentration. This study provides the first evidence of higher R2* in the caudate nucleus of welders, which is suggestive of increased Fe accumulation in this area. Further studies are needed to replicate the findings and determine the neurobehavioral relevance

Crosstalk between Spinal Astrocytes and Neurons in Nerve Injury-Induced Neuropathic Pain

Emerging research implicates the participation of spinal dorsal horn (SDH) neurons and astrocytes in nerve injury-induced neuropathic pain. However, the crosstalk between spinal astrocytes and neurons in neuropathic pain is not clear. Using a lumbar 5 (L5) spinal nerve ligation (SNL) pain model, we testified our hypothesis that SDH neurons and astrocytes reciprocally regulate each other to maintain the persistent neuropathic pain states. Glial fibrillary acidic protein (GFAP) was used as the astrocytic specific marker and Fos, protein of the protooncogene c-fos, was used as a marker for activated neurons. SNL induced a significant mechanical allodynia as well as activated SDH neurons indicated by the Fos expression at the early phase and activated astrocytes with the increased expression of GFAP during the late phase of pain, respectively. Intrathecal administration of c-fos antisense oligodeoxynucleotides (ASO) or astroglial toxin L-α-aminoadipate (L-AA) reversed the mechanical allodynia, respectively. Immunofluorescent histochemistry revealed that intrathecal administration of c-fos ASO significantly suppressed activation of not only neurons but also astrocytes induced by SNL. Meanwhile, L-AA shortened the duration of neuronal activation by SNL. Our data offers evidence that neuronal and astrocytic activations are closely related with the maintenance of neuropathic pain through a reciprocal “crosstalk”. The current study suggests that neuronal and non-neuronal elements should be taken integrally into consideration for nociceptive transmission, and that the intervention of such interaction may offer some novel pain therapeutic strategies

Genetic Variation of Promoter Sequence Modulates XBP1 Expression and Genetic Risk for Vitiligo

Our previous genome-wide linkage analysis identified a susceptibility locus for generalized vitiligo on 22q12. To search for susceptibility genes within the locus, we investigated a biological candidate gene, X-box binding protein 1(XBP1). First, we sequenced all the exons, exon-intron boundaries as well as some 5′ and 3′ flanking sequences of XBP1 in 319 cases and 294 controls of Chinese Hans. Of the 8 common variants identified, the significant association was observed at rs2269577 (p_trend = 0.007, OR = 1.36, 95% CI = 1.09–1.71), a putative regulatory polymorphism within the promoter region of XBP1. We then sequenced the variant in an additional 365 cases and 404 controls and found supporting evidence for the association (p_trend = 0.008, OR = 1.31, 95% CI = 1.07–1.59). To further validate the association, we genotyped the variant in another independent sample of 1,402 cases and 1,288 controls, including 94 parent-child trios, and confirmed the association by both case-control analysis (p_trend = 0.003, OR = 1.18, 95% CI = 1.06–1.32) and the family-based transmission disequilibrium test (TDT, p = 0.005, OR = 1.93, 95% CI = 1.21–3.07). The analysis of the combined 2,086 cases and 1,986 controls provided highly significant evidence for the association (p_trend = 2.94×10−6, OR = 1.23, 95% CI = 1.13–1.35). Furthermore, we also found suggestive epistatic effect between rs2269577 and HLA-DRB1*07 allele on the development of vitiligo (p = 0.033). Our subsequent functional study showed that the risk-associated C allele of rs2269577 had a stronger promoter activity than the non-risk G allele, and there was an elevated expression of XBP1 in the lesional skins of patients carrying the risk-associated C allele. Therefore, our study has demonstrated that the transcriptional modulation of XBP1 expression by a germ-line regulatory polymorphism has an impact on the development of vitiligo