Sobolev spaces on locally finite graphs

In this paper, we develop the theory of Sobolev spaces on locally finite graphs, including completeness, reflexivity, separability, and Sobolev inequalities. Since there is no exact concept of dimension on graphs, classical methods that work on Euclidean spaces or Riemannian manifolds can not be directly applied to graphs. To overcome this obstacle, we introduce a new linear space composed of vector-valued functions with variable dimensions, which is highly applicable for this issue on graphs and is uncommon when we consider to apply the standard proofs on Euclidean spaces to Sobolev spaces on graphs. The gradients of functions on graphs happen to fit into such a space and we can get the desired properties of various Sobolev spaces along this line. Moreover, we also derive several Sobolev inequalities under certain assumptions on measures or weights of graphs. As fundamental analytical tools, all these results would be extremely useful for partial differential equations on locally finite graphs.Comment: 19 page

Finding disease-specific coordinated functions by multi-function genes: Insight into the coordination mechanisms in diseases

AbstractWe developed an approach using multi-function disease genes to find function pairs whose co-deregulation might induce a disease. Analyzing cancer genes, we found many cancer-specific coordinated function pairs co-deregulated by dysfunction of multi-function genes and other molecular changes in cancer. Studying two subtypes of cardiomyopathy, we found they show certain consistency at the functional coordination level. Our approach can also provide important information for finding novel disease genes as well as their mechanisms in diseases

Dosimetric comparison of intensity modulated radiotherapy and three-dimensional conformal radiotherapy in patients with gynecologic malignancies: a systematic review and meta-analysis

BACKGROUND: To quantitatively evaluate the safety and related-toxicities of intensity modulated radiotherapy (IMRT) dose–volume histograms (DVHs), as compared to the conventional three-dimensional conformal radiotherapy (3D-CRT), in gynecologic malignancy patients by systematic review of the related publications and meta-analysis. METHODS: Relevant articles were retrieved from the PubMed, Embase, and Cochrane Library databases up to August 2011. Two independent reviewers assessed the included studies and extracted data. Pooled average percent irradiated volumes of adjacent non-cancerous tissues were calculated and compared between IMRT and 3D-CRT for a range of common radiation doses (5-45Gy). RESULTS: In total, 13 articles comprised of 222 IMRT-treated and 233 3D-CRT-treated patients were included. For rectum receiving doses ≥30 Gy, the IMRT pooled average irradiated volumes were less than those from 3D-CRT by 26.40% (30 Gy, p = 0.004), 27.00% (35 Gy, p = 0.040), 37.30% (40 Gy, p = 0.006), and 39.50% (45 Gy, p = 0.002). Reduction in irradiated small bowel was also observed for IMRT-delivered 40 Gy and 45 Gy (by 17.80% (p = 0.043) and 17.30% (p = 0.012), respectively), as compared with 3D-CRT. However, there were no significant differences in the IMRT and 3D-CRT pooled average percent volumes of irradiated small bowel or rectum from lower doses, or in the bladder or bone marrow from any of the doses. IMRT-treated patients did not experience more severe acute or chronic toxicities than 3D-CRT-treated patients. CONCLUSIONS: IMRT-delivered high radiation dose produced significantly less average percent volumes of irradiated rectum and small bowel than 3D-CRT, but did not differentially affect the average percent volumes in the bladder and bone marrow

Physiological and transcriptome analyses to infer regulatory networks in flowering transition of Rosa rugosa

Rosa rugosa is a famous Chinese traditional flowering species with high economic value. Flowering transition is an important process in plant growth and development. Although characterization of the flowering transition process has made great progress in some plants such as model plants, the process in R. rugosa has not been rigorously characterized to establish a mechanism. In this study, the changes of buds during flowering transition in R. rugosa ‘Duoji Huangmei’ were analyzed through transcriptomic sequencing combined with morphological and physiological index determinations. Results showed that with the morphology changes of buds, both sugar and starch content showed a similar up-down pattern while phytohormones content displayed various trends, which implied that sugar, starch and phytohormones might play diverse roles during flowering transition in R. rugosa. Moreover, a total of 4363 differentially expressed genes (DEGs) were identified at three developmental stages. Among them, 74 DEGs were involved in metabolism, transport, and signal transduction of sugar, starch, and phytohormones, as well as photoperiod and vernalization response. We proposed that these DEGs were not regulated independently but interacted with each other to construct a gene-gene network to regulate flowering transition of R. rugosa, and the regulatory network from vegetative growth stage (S1) to flowering transition stage (S2) was more complicated. These results further enriched the study of flowering transition in Rosa and lay an important foundation for breeding new varieties with desired floral traits

Transcriptomic and metabolomic analyses reveal the mechanism of uniconazole inducing hypocotyl dwarfing by suppressing BrbZIP39–BrPAL4 module mediating lignin biosynthesis in flowering Chinese cabbage

Uniconazole, a triazole plant growth regulator, is widely used to regulate plant height and prevent the overgrowth of seedlings. However, the underlying molecular mechanism of uniconazole in inhibiting the hypocotyl elongation of seedlings is still largely unclear, and there has been little research on the integration of transcriptomic and metabolomic data to investigate the mechanisms of hypocotyl elonga-tion. Herein we observed that the hypocotyl elongation of flowering Chinese cabbage seedings was significantly inhibited by uniconazole. Interestingly, based on combined transcriptome and metabolome analyses, we found that the “phenylpropanoid biosynthesis” pathway was significantly affected by uniconazole. In this pathway, only one member of the portal enzyme gene family, named BrPAL4, was remarkably downregulated, which was related to lignin biosynthesis. Furthermore, the yeast one-hybrid and dual-luciferase assays showed that BrbZIP39 could directly bind to the promoter region of BrPAL4 and activate its transcript. The virus-induced gene silencing system further demonstrated that BrbZIP39 could positively regulate hypocotyl elongation and the lignin biosynthesis of hypocotyl. Our findings provide a novel insight into the molecular regulatory mechanism of uniconazole inhibiting hypocotyl elongation in flowering Chinese cabbage and confirm, for the first time, that uniconazole decreases lignin content through repressing the BrbZIP39–BrPAL4 module-mediated phenylpropanoid biosynthesis, which leads to the hypocotyl dwarfing of flowering Chinese cabbage seedlings

Surface Dynamics Transition of Vacuum Vapor Deposited CH 3

The growth dynamics of CH3NH3PbI3 perovskite thin films on ITO covered glass substrate were investigated. The evolution of the film could be divided into two stages. A mound-like surface was obvious at the first stage. Stable dynamic scaling was observed for thicker films at the second stage. Through analyzing the scaling exponent, growth exponent β, and 2D fast Fourier transform, it is concluded that, at the second stage, the growth mechanism of mound formation does not play a major role, and the film growth mechanism can be described by Mullins diffusion equation

Light-responsive nanogated ensemble based on polymer grafted mesoporous silica hybrid nanoparticles

Mesoporous silica nanoparticles grafted with light-responsive polymer on the outer surface were developed as novel nanogated ensembles, which allow encapsulation and release of drug and biological molecules under light irradiation.National Natural Science Foundation of China [20875079, 20835005]; Planned Science and Technology Project of Xiamen, China [3502z20080011]; Specialized Research Fund for the Doctoral Program of Higher Education of China [200803840007

Integrating single-cell and bulk transcriptomic analyses to develop a cancer-associated fibroblast-derived biomarker for predicting prognosis and therapeutic response in breast cancer

BackgroundCancer-associated fibroblasts (CAFs) contribute to the progression and treatment of breast cancer (BRCA); however, risk signatures and molecular targets based on CAFs are limited. This study aims to identify novel CAF-related biomarkers to develop a risk signature for predicting the prognosis and therapeutic response of patients with BRCA.MethodsCAF-related genes (CAFRGs) and a risk signature based on these genes were comprehensively analyzed using publicly available bulk and single-cell transcriptomic datasets. Modular genes identified from bulk sequencing data were intersected with CAF marker genes identified from single-cell analysis to obtain reliable CAFRGs. Signature CAFRGs were screened via Cox regression and least absolute shrinkage and selection operator (LASSO) analyses. Multiple patient cohorts were used to validate the prognosis and therapeutic responsiveness of high-risk patients stratified based on the CAFRG-based signature. In addition, the relationship between the CAFRG-based signature and clinicopathological factors, tumor immune landscape, functional pathways, chemotherapy sensitivity and immunotherapy sensitivity was examined. External datasets were used and sample experiments were performed to examine the expression pattern of MFAP4, a key CAFRG, in BRCA.ResultsIntegrated analyses of single-cell and bulk transcriptomic data as well as prognostic screening revealed a total of 43 prognostic CAFRGs; of which, 14 genes (TLN2, SGCE, SDC1, SAV1, RUNX1, PDLIM4, OSMR, NT5E, MFAP4, IGFBP6, CTSO, COL12A1, CCDC8 and C1S) were identified as signature CAFRGs. The CAFRG-based risk signature exhibited favorable efficiency and accuracy in predicting survival outcomes and clinicopathological progression in multiple BRCA cohorts. Functional enrichment analysis suggested the involvement of the immune system, and the immune infiltration landscape significantly differed between the risk groups. Patients with high CAF-related risk scores (CAFRSs) exhibited tumor immunosuppression, enhanced cancer hallmarks and hyposensitivity to chemotherapy and immunotherapy. Five compounds were identified as promising therapeutic agents for high-CAFRS BRCA. External datasets and sample experiments validated the downregulation of MFAP4 and its strong correlation with CAFs in BRCA.ConclusionsA novel CAF-derived gene signature with favorable predictive performance was developed in this study. This signature may be used to assess prognosis and guide individualized treatment for patients with BRCA