Optimal plate design problem in steel production

In this paper, we address a new optimal plate design problem in steel production, in which slab selection is jointly considered. On the basis of the underlying features, the problem is formulated as a mixed integer nonlinear programming (MINLP) model with generalized disjunctive programming (GDP) constraints. A logic-based outer approximation (L-OA) algorithm is proposed to solve the problem. Specifically, a two-stage heuristic method is designed to initialize the L-OA algorithm. Numerical results are presented to demonstrate that the proposed L-OA algorithm and the heuristic method are effective and computationally efficient

The KEGG pathways enriched for predicted targets of differentially expressed miRNAs.

<p>The negative log of the <i>p</i> value (−log₁₀<i>P</i>) was plotted on the x-axis.</p

The differentially expressed miRNAs in porcine endometrium (gestational day 26 vs gestational day 15).

<p>logFC: log₂(fold-change).</p

Expression Patterns of MicroRNAs in Porcine Endometrium and Their Potential Roles in Embryo Implantation and Placentation

<div><p>Implantation and placentation are critical steps for successful pregnancy. The pig has a non-invasive placenta and the uterine luminal epithelium is intact throughout pregnancy. To better understand the regulation mechanisms in functions of endometrium at three certain gestational stages that are critical for embryo/fetal loss in pigs, we characterized microRNA (miRNA) expression profiles in the endometrium on days 15 (implantation period), 26 (placentation period) and 50 (mid-gestation period) of gestation. The differentially expressed miRNAs across gestational days were detected and of which, 65 miRNAs were grouped into 4 distinct categories according to the similarities in their temporal expression patterns: (1) categories A and B contain majority of miRNAs (51 miRNAs, such as the miR-181 family) that were down- or up-regulated between gestational days 15 and 26, respectively; (2) categories C and D (14 miRNAs) consist miRNAs that were down- or up-regulated between gestational days 26 and 50, respectively. The expression patterns represented by eleven miRNAs were validated by qPCR. The majority of miRNAs were in categories A and B, suggesting that these miRNAs were involved in regulation of embryo implantation and placentation. The pathway analysis revealed that the predicted targets were involved in several pathways, such as focal adhesion, cell proliferation and tissue remolding. Furthermore, we identified that genes well-known to affect embryo implantation in pigs, namely <i>SPP1</i>, <i>ITGB3</i> and <i>ESR1</i>, contain the miR-181a or miR-181c binding sites using the luciferase reporter system. The present study revealed distinctive miRNA expression patterns in the porcine endometrium during the implantation, placentation or mid-gestation periods. Additionally, our results suggested that miR-181a and miR-181c likely play important roles in the regulation of genes and pathways that are known to be involved in embryo implantation and placentation in pigs.</p></div

The hierarchical clustering based on differentially expressed miRNAs in porcine endometrium during pregnancy.

<p>Each row represents an individual miRNA and each column represents a sample. A color legend indicating the level of miRNA expression is at the top, with red indicating high expression level and green indicating low expression level. D15: gestational day 15; D26: gestational day 26; D50: gestational day 50.</p

The result of luciferase assay for <i>SPP1</i>, <i>ITGB3</i> and <i>ESR1</i> targeting by miR-181a and miR-181c.

<p>The error bars show the SEM. The significance of differences was calculated using two-tailed T-test. *, <i>p</i><0.05; **, <i>p</i><0.01.</p

Validation of differentially expressed miRNAs by qPCR.

<p>All samples were normalized to RNU6. The error bars show the SEM. The significance of differences for miRNA expression was calculated using two-tailed T-test. *, <i>p</i><0.05; **, <i>p</i><0.01. D15: gestational day 15; D26: gestational day 26; D50: gestational day 50.</p

The differentially expressed miRNAs in porcine endometrium (gestational day 50 vs gestational day 26).

<p>logFC: log₂(fold-change).</p

Principal Component Analysis (PCA) plot of microarray data in porcine endometrium.

<p>In each case, three replicates from each gestational day cluster together. Clustering of the samples according to gestational day is shown. The red, blue and green circles stand for three different gestational days. D15: gestational day 15; D26: gestational day 26; D50: gestational day 50.</p

The gene ontology biological process enriched for predicted targets of differentially expressed miRNAs.

<p>The negative log of the <i>p</i> value (−log₁₀<i>P</i>) was plotted on the x-axis.</p