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  1. Abstract

    This paper presents a normalized standard error-based statistical data binning method, termed “bin size index” (BSI), which yields an optimized, objective bin size for constructing a rational histogram to facilitate subsequent deconvolution of multimodal datasets from materials characterization and hence the determination of the underlying probability density functions. Totally ten datasets, including four normally-distributed synthetic ones, three normally-distributed ones on the elasticity of rocks obtained by statistical nanoindentation, and three lognormally-distributed ones on the particle size distributions of flocculated clay suspensions, were used to illustrate the BSI’s concepts and algorithms. While results from the synthetic datasets prove the method’s accuracy and effectiveness, analyses of other real datasets from materials characterization and measurement further demonstrate its rationale, performance, and applicability to practical problems. The BSI method also enables determination of the number of modes via the comparative evaluation of the errors returned from different trial bin sizes. The accuracy and performance of the BSI method are further compared with other widely used binning methods, and the former yields the highest BSI and smallest normalized standard errors. This new method particularly penalizes the overfitting that tends to yield too many pseudo-modes via normalizing the errors by the number of modes hidden in the datasets, and also eliminates the difficulty in specifying criteria for acceptable values of the fitting errors. The advantages and disadvantages of the new method are also discussed.

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  2. Abstract Background Nuclear endosperm development is a common mechanism among Angiosperms, including Arabidopsis. During nuclear development, the endosperm nuclei divide rapidly after fertilization without cytokinesis to enter the syncytial phase, which is then followed by the cellularized phase. The endosperm can be divided into three spatial domains with distinct functions: the micropylar, peripheral, and chalazal domains. Previously, we identified two putative small invertase inhibitors, InvINH1 and InvINH2, that are specifically expressed in the micropylar region of the syncytial endosperm. In addition, ectopically expressing InvINH1 in the cellularized endosperm led to a reduction in embryo growth rate. However, it is not clear what are the upstream regulators responsible for the specific expression of InvINHs in the syncytial endosperm. Results Using protoplast transient expression system, we discovered that a group of type I MADS box transcription factors can form dimers to activate InvINH1 promoter. Promoter deletion assays carried out in the protoplast system revealed the presence of an enhancer region in InvINH1 promoter, which contains several consensus cis-elements for the MADS box proteins. Using promoter deletion assay in planta , we further demonstrated that this enhancer region is required for InvINH1 expression in the syncytial endosperm. One of the MADS box genes, AGL62, is a key transcription factor required for syncytial endosperm development. Using promoter-GFP reporter assay, we demonstrated that InvINH1 and InvINH2 are not expressed in agl62 mutant seeds. Collectively, our data supports the role of AGL62 and other type I MADS box genes as the upstream activators of InvINHs expression in the syncytial endosperm. Conclusions Our findings revealed several type I MADS box genes that are responsible for activating InvINH1 in the syncytial endosperm, which in turn regulates embryo growth rate during early stage of seed development. 
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  3. null (Ed.)