Bakry-Émery Ricci Curvature Bounds for Doubly Warped Products of Weighted Spaces.

We introduce a notion of doubly warped product of weighted graphs that is consistent with the doubly warped product in the Riemannian setting. We establish various discrete Bakry-Émery Ricci curvature-dimension bounds for such warped products in terms of the curvature of the constituent graphs. This requires deliberate analysis of the quadratic forms involved, prompting the introduction of some crucial notions such as curvature saturation at a vertex. In the spirit of being thorough and to provide a frame of reference, we also introduce the R 1 , R 2 -doubly warped products of smooth measure spaces and establish N -Bakry-Émery Ricci curvature (lower) bounds thereof in terms of those of the factors. At the end of these notes, we present examples and demonstrate applications of warped products with some toy models.

Comparing four laboratory three-parent techniques to construct human aged non-surrounded nucleolus germinal vesicle oocytes: A case-control study.

BACKGROUND: The three-parent assisted reproductive technique may increase oocyte competence. OBJECTIVE: In this case-control study, the suitability of germinal vesicle transfer (GVT), synchronous ooplasmic transfer (sOT), asynchronous ooplasmic transfer using cryopreserved MII oocyte (caOT), and asynchronous ooplasmic transfer using waste MII oocyte (waOT) for maturation of the human-aged non-surrounded nucleolus germinal vesicle-stage (NSN-GV) oocyte were investigated. MATERIALS AND METHODS: NSN-GV oocytes were subjected to four methods: group A (GVT), B (sOT), C (caOT) D (waOT), and E (Control). The fusion rates, MI, MII, ICSI observations and cleavage at 2-cell, 4-cell, and 8-cell stages were compared in the groups. RESULTS: In GVT, none of the oocytes fused. In sOT, all oocytes fused, 20 achieved the MI, 14 progressed to MII, 8 fertilized, 6 cleaved and 5, 4, and 3 achieved the 2-cells, 4-cells and 8-cells, respectively. In caOT, all oocytes fused and achieved the MI, 8 progressed to MII and fertilized, 6 cleaved and 6, 5, and 5 achieved the 2-cells, 4-cells, and 8-cells respectively. In waOT, all oocytes fused, 5 and 3 progressed to MI and MII, respectively, but only one fertilized, cleaved and reached a 4-cells stage. In group E, 6 and 2 oocytes progressed to MI and MII, respectively, and only one fertilized but arrested at the zygote stage. caOT had the highest survival rate when compared to sOT (p = 0.04), waOT (p = 0.002), and control (p = 0.001). CONCLUSION: The caOT method was beneficial over sOT, waOT, and GVT in supplementing the developmental capacity of human-aged NSN-GV oocytes.

Assessing the potential of HSPA2 and ADAM2 as two biomarkers for human sperm selection.

Selection of the best sperm, with the least defects, is a critical factor in the success of ART especially in male factor infertility. This study assessed the potential Heat shock protein (HSPA2) and metallopeptidase domain2 (ADAM2) biomarkers for sperm selection. Sperm were obtained from 72 asthenoteratozoospermic and 42 normospermic ejaculates. The semen characteristic, DNA fragmentation (DFI), chromatin maturation index (CMI), ADAM2 and HSPA2 levels on sperm, and their correlation with embryo quality were assessed in both groups. Results showed the significant reduction in HSPA2 and ADAM2 in asthenoteratozoospermic compared to normazoospermic ejaculates regarding the cut-off value of 14 and 13% for these two biomarkers. The specificity of HSPA2 and ADAM2 separately, and the combination of these two biomarkers, were 95.2, 90.5 and 93.5%, respectively, for sperm from normozoospermic ejaculates. However, they were 48.6, 50.0 and 54.5% for asthenoteratozoospermic ones. A significant correlation was observed with HSPA2, ADAM2 and a combination of these two biomarkers with CMI, DFI and embryo quality. Although a combination of these two biomarkers have the potential to be a good choice for selecting sperm with the lowest level of chromatin damage, it seems that selection according to HSPA2 has priority over ADAM2 or a combination of the two.

Flow Cytometry: A Novel Approach for Indirect Assessment of Protamine Deficiency by CMA3 Staining, Taking into Account the Presence of M540 or Apoptotic Bodies.

BACKGROUND: Chromomycin A3 (CMA3) staining, either by the slide method or fluorescence microscopy, is widely used for indirect assessment of protamine deficiency in a semen sample. Flow cytometry is the most suitable tool to improve assessment accuracy, both in terms of statistical analysis and for prevention of observer variation. This study provides a simple procedure to account for merocyanine 540 (M540) or apoptotic bodies, which result in underestimation of the percentage of CMA3 positivity, by using propidium iodide (PI) staining. Therefore, this study aims to evaluate the percentage of CMA3 by PI staining to exclude M540 bodies that prevent underestimation of CMA3 staining. MATERIALS AND METHODS: This study is an experimental study. Semen samples collected from 104 infertile men who referred to the Andrology Unit of the Isfahan Fertility and Infertility Center were initially assessed according to World Health Organization (WHO) criteria. Samples were washed twice with Ham's. Each sample was divided into two portions, a control and the other processed for density gradient centrifugation (DGC). Each portion was assessed for CMA3 staining by both the slide and flow cytometry methods. Coefficients of correlation and student t-test were carried out using the Statistical Package for the Social Studies (SPSS 11.5). RESULTS: Detection of CMA3 staining was more appropriate with fluorescence detector 3 (FL-3) rather than fluorescence detector 2 (FL-2) in the evaluation of protamine deficiency to exclude M540 bodies. CONCLUSION: This study, for the first time, provides the basis for assessment of CMA3 staining for flow cytometry. However, since the maximum excitation for CMA3 is not covered by the 488 nm laser, we recommend further experimentation using a flow cytometer with optimal excitation.