Lusin-type approximation of Sobolev by Lipschitz functions, in Gaussian and RCD(K,∞)RCD(K,\infty) spaces

We establish new approximation results, in the sense of Lusin, of Sobolev functions by Lipschitz ones, in some classes of non-doubling metric measure structures. Our proof technique relies upon estimates for heat semigroups and applies to Gaussian and $RCD(K, \infty)$ spaces. As a consequence, we obtain quantitative stability for regular Lagrangian flows in Gaussian settings

Increased collagens in BLM-treated <i>Scgb3a2</i>-null lungs.

<p><b>(A)</b> Hydroxyproline content of lungs of wild-type (WT) and <i>Scgb3a2</i>-null (KO) mice intubated with BLM or PBS as control. The mean ± SD from N >6 in each group are shown. <b>(B)</b> qRT-PCR analysis of mRNAs for collagen 1a1 (<i>Col1a1</i>), collagen 3a1 (<i>Col3a1</i>), collagen 4a1 (<i>Col4a1</i>), and collagen 12a1 (<i>Col12a1</i>). Normalization control used was 18S. Relative expression levels with the mean ± SD from N>8 in each group are shown. *P<0.05, **P<0.01, and ***P<0.001 by one-way ANOVA. NS: not significant.</p

Increased cytokine levels in BLM-treated <i>Scgb3a2</i>-null lungs.

<p><b>(A)</b> qRT-PCR analysis of mRNAs encoding IL-4, IL-5, IL-13, IL-6, CCL7, CXCL13, MMP12, TNFα, ACTA2 (α-smooth muscle actin), TGFβ, and CTGF in lungs of wild-type (WT) and <i>Scgb3a2</i>-null (KO) mice intubated with BLM or PBS as control. Normalization control used was 18S. <b>(B)</b> IL-4, IL-5, and IL-13 protein levels in BALF of wild-type (WT) and <i>Scgb3a2</i>-null (KO) mice intubated with BLM or PBS as control. Relative expression levels with the mean ± SD from N>8 in each group are shown. *P<0.05, **P<0.01, and ***P<0.001 by one-way ANOVA. NS: not significant.</p

Analysis of mRNAs for surfactant proteins and SCGB proteins.

<p>qRT-PCR was carried out to determine levels of mRNAs encoding SPA (<i>Sftpa</i>), SP-B (S<i>ftpb</i>), SP-C (<i>Sftpc</i>), SP-D (<i>Sftpd</i>), <i>Scgb1a1</i> and <i>Scgb3a2</i> in the lungs of wild-type (WT) and <i>Scgb3a2</i>-null (KO) mice intubated with BLM or PBS as control. The normalization control was 18S. Relative expression levels with the mean ± SD from N>8 in each group are shown. **P<0.01 by one-way ANOVA. NS: not significant.</p

Increased inflammatory cells in BLM-treated <i>Scgb3a2</i>-null lungs.

<p>Total inflammatory cell numbers, macrophages, lymphocytes/monocytes, and neutrophils in BALF of wild-type (WT) and <i>Scgb3a2</i>-null (KO) mice intubated with BLM or PBS as control. The mean ± SD from N>5 in each group are shown. **P<0.01, and ***P<0.001 by one-way ANOVA. NS: not significant.</p

Additional file 1 of Disparities in treatment modalities and survival among older patients with high-grade serous ovarian cancer

Supplementary Material

Data_Sheet_1_Theorems and Methods of a Complete Q Matrix With Attribute Hierarchies Under Restricted Q-Matrix Design.DOCX

<p>The design of test Q matrix can directly influence the classification accuracy of a cognitive diagnostic assessment. In this paper, we focus on Q matrix design when attribute hierarchies are known prior to test development. A complete Q matrix design is proposed and theorems are presented to demonstrate that it is a necessary and sufficient condition to guarantee the identifiability of ideal response patterns. A simulation study is also conducted to detect the effects of the proposed design on a family of conjunctive diagnostic models. The results revealed that the proposed Q matrix design is the key condition for guaranteeing classification accuracy. When only one type of item pattern in R matrix is missing from the associated test Q matrix, the related attribute-wise agreement rate will decrease dramatically. When the entire R matrix is missing, both the pattern-wise and attribute-wise agreement rates will decrease sharply. This indicates that the proposed procedures for complete Q matrix design with attribute hierarchies can serve as guidelines for test blueprint development prior to item writing in a cognitive diagnostic assessment.</p

Data_Sheet_2_Theorems and Methods of a Complete Q Matrix With Attribute Hierarchies Under Restricted Q-Matrix Design.docx

<p>The design of test Q matrix can directly influence the classification accuracy of a cognitive diagnostic assessment. In this paper, we focus on Q matrix design when attribute hierarchies are known prior to test development. A complete Q matrix design is proposed and theorems are presented to demonstrate that it is a necessary and sufficient condition to guarantee the identifiability of ideal response patterns. A simulation study is also conducted to detect the effects of the proposed design on a family of conjunctive diagnostic models. The results revealed that the proposed Q matrix design is the key condition for guaranteeing classification accuracy. When only one type of item pattern in R matrix is missing from the associated test Q matrix, the related attribute-wise agreement rate will decrease dramatically. When the entire R matrix is missing, both the pattern-wise and attribute-wise agreement rates will decrease sharply. This indicates that the proposed procedures for complete Q matrix design with attribute hierarchies can serve as guidelines for test blueprint development prior to item writing in a cognitive diagnostic assessment.</p

Comparison of experimental and simulation results of pseudopalisade formation in GBM.

<p>The Histopathologic pictures of pseudopalisades in GBM (A, B and C) [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150296#pone.0150296.ref004" target="_blank">4</a>]. A, narrow pseudopalisades (<100 micron wide). B, medium-sized pseudopalisades (200–400 micron). C, large pseudopalisade (>500 micron). The simulation results of pseudopalisades with different sizes (A', B' and C'). Red dots represent the proliferating and migrating tumour cells gathered at the tumour periphery. Light red dots represent the quiescent cells. Arrows in C and C' show the outpouchings of pseudopalisades. Scale bar: 100 micron.</p

A zoom-in view of the vessel remodelling in the tumour region.

<p>Microvessel radius (R) is represented by different colour (unit:μm). Pink dots represent the approximate boundary of GBM invasion. White arrows indicate the vessel dilation (A, B, C). White arrowheads indicate the neo-vasculatures. D. 3D view of a cluster of capillaries before (top) and undergo (bottom) remodelling. Note the dilated vessels indicated by arrows.</p