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Let V be an n-dimensional vector space over the finite field F q and let V k q denote the family of all k-dimensional subspaces of V. A family F ⊆ V k q is called intersecting if for all F, F ′ ∈ F , we have dim (F ∩ F ′) ≥ 1. A family F ⊆ V k q is called almost intersecting if for every F ∈ F there is at most one element F ′ ∈ F satisfying dim (F ∩ F ′) = 0. In this paper we investigate almost intersecting families in the vector space V. Firstly, for large n, we determine the maximum size of an almost intersecting family in V k q , which is the same as that of an intersecting family. Secondly, we characterize the structures of all maximum almost intersecting families under the condition that they are not intersecting. [ABSTRACT FROM AUTHOR]

A large set LOD(v) $\text{LOD}(v)$ is a partition of all ordered triples of a v $v$‐set into v−2 $v-2$ disjoint ordered designs of order v $v$. In this paper, we generalize the large set LOD(v) $\text{LOD}(v)$ with v=gt $v=gt$ to the notion of POT(gt) $\text{POT}({g}^{t})$, representing a partition of all ordered triples of a gt $gt$‐set into disjoint uniform holely ordered designs HOD(gt) $\text{HOD}({g}^{t})$s. We show that a POT(gt) $\text{POT}({g}^{t})$ exists if and only if g=1,2 $g=1,2$ and t≥3 $t\ge 3$, except for (g,t)=(1,6) $(g,t)=(1,6)$. Moreover, we study the existence of a POT(gt) $\text{POT}({g}^{t})$ with every member HOD(gt) $\text{HOD}({g}^{t})$ having a kind of resolution. We show that a resolvable POT(gt) $\text{POT}({g}^{t})$ exists if and only if g=1,2 $g=1,2$, t≥3 $t\ge 3$, (g,t)≠(1,6) $(g,t)\ne (1,6)$, with 27 possible exceptions. For almost resolvable POT(2t) $\text{POT}({2}^{t})$s, we prove the asymptotic existence and present a few infinite families. [ABSTRACT FROM AUTHOR]

A t-spontaneous emission error design, denoted by t-(v, k; m) SEED or t-SEED in short, is a system B of k-subsets of a v-set V with a partition B 1 , B 2 , … , B m of B satisfying | { B ∈ B i : E ⊆ B } | | B i | = μ E for any 1 ≤ i ≤ m and E ⊆ V , | E | ≤ t , where μ E is a constant depending only on E. A t-(v, k; m) SEED is an important combinatorial object with applications in quantum jump codes. The number m is called the dimension of the t-SEED and this corresponds to the number of orthogonal basis states in a quantum jump code. For given v, k and t, a t-(v, k; m) SEED is called optimal when m achieves the largest possible dimension. When k ∣ v , an optimal 1-(v, k; m) SEED has dimension v - 1 k - 1 and can be constructed by Baranyai’s Theorem. This note investigates optimal 1-(v, k; m) SEEDs with k ∤ v , in which a generalization of Baranyai’s Theorem plays a significant role. To be specific, we construct an optimal 1-(v, k; m) SEED for all positive integers v, k, s with v ≡ - s (mod k), k ≥ s + 1 and v ≥ max { 2 k , s (2 k - 1) } . [ABSTRACT FROM AUTHOR]

[Display omitted] • Serum FGF23 levels increased with gestational age in normal pregnant women. • Preeclampsia group had lower FGF23 levels than control group in the third trimester. • FGF23 promoted cell migration, invasion and tube formation abilities in vitro. • FGF23 stimulated placental VEGF-A expression via ERK1/2-EGR-1 pathway. • This study provides a potential mechanism involved in progression of preeclampsia. This study aimed to investigate the expression of fibroblast growth factor 23 (FGF23) in pregnant women with preeclampsia and elucidate its role in promoting placental angiogenesis through the ERK1/2-EGR-1 signaling pathway. Serum FGF23 levels were measured by ELISA in healthy pregnant women and patients with preeclampsia during the first, second, and third trimesters of pregnancy. Wound healing, Transwell, and tube formation assays were performed to investigate the effects of FGF23 on cell migration, invasion and tube formation. The expression of vascular endothelial growth factor A (VEGF-A) and its upstream signaling molecules, p-ERK, and EGR-1, in placental tissues was detected by RT-qPCR and western blotting. Additionally, the effect of FGF23 on VEGF-A, p-ERK, and EGR-1 expression was further explored in vitro. Serum FGF23 levels increased with gestational age. During the third trimester, the control group exhibited a more pronounced increase in FGF23 levels than the preeclampsia group. Administering exogenous FGF23 promoted trophoblast cell migration, invasion and enhanced tube formation in vascular endothelial cells. The expression levels of VEGF-A, p-ERK, and EGR-1 in the placental tissues were significantly lower in the preeclampsia group than in the control group. In vitro experiments confirmed that FGF23 up-regulated VEGF-A expression through the p-ERK/EGR-1 signaling pathway. The serum level of FGF23 decreased in pregnant women with preeclampsia, inhibiting the ERK1/2-EGR-1 pathway and resulting in decreased expression of VEGF-A, thereby inhibiting placental angiogenesis. This could be a potential mechanism involved in the progression of preeclampsia. [ABSTRACT FROM AUTHOR]

Experimental investigations and density functional theory (DFT) calculations were carried out to study the comprehensive effect of different 3,5-heptanedioldibenzoate (HDDB) optical isomers as the internal electron donor on the catalytic performance of Ziegler−Natta catalysts. The experimental catalytic activity of HDDB has a positive correlation with the relative content of the mesomer incorporated during catalyst preparation, while the hydrogen response of HDDB displayed a negative correlation with the relative content of the mesomer. In order to apply the DFT calculation results to the macroscopic activity of the catalyst, the content of the active centers of the catalyst was analyzed. Assuming that the content of the active centers is proportional to the internal electron donor content of the catalyst, binary linear regression was carried out, which showed a good linear correlation between experimental activity data and internal electron donor content. Furthermore, the fitted activity of the single active centers aligned well with the calculated activation energies. These results revealed that the catalytic activity of polypropylene (PP) catalysts is dependent on both the active center content and the catalytic activity of an individual active center. Additionally, the lower hydrogen response of HDDB leads to a higher molecular weight of polypropylene obtained from the RS-containing catalyst compared to the SS-containing catalyst. Further study reveals that the hydrogen transfer reactions of 2,4-pentanediol dibenzoate (PDDB)/HDDB are influenced by the orientation of the methyl/ethyl groups in different isomers, which affect the activation energy differences between the hydrogen transfer reaction and the propylene insertion reaction, and finally influence the molecular weight of PP. [ABSTRACT FROM AUTHOR]

This Mendelian randomization (MR) study aimed to investigate the relationships between type 1 diabetes (T1D), type 2 diabetes (T2D), and glycemic traits, including fasting insulin, fasting glucose, and HbA1c, with cardiovascular diseases (CVDs). We selected genetic instruments for predisposition to T1D, T2D, fasting insulin, fasting glucose, and HbA1c based on published genome-wide association studies. Using a 2-Sample MR approach, we assessed associations with 12 common CVDs sourced from the FinnGen and UK Biobank studies, along with stroke subtypes obtained from the GIGASTROKE and MEGASTROKE Consortium. T1D was associated with SVS. T2D showed associations with AIS, LAA, CES, SVS, coronary heart disease, myocardial infarction, pulmonary embolism, DVT of lower extremities, peripheral vascular diseases. Genetically predicted higher HbA1c levels were associated with eight CVDs. The results of MVMR aligned with the primary findings for T1D and T2D. T1D and T2D exhibit different genetic predisposition to CVDs. BMI, LDL, and HDL play intermediary roles in connecting TID and T2D to specific types of CVDs, providing insights into the potential underlying pathways and mechanisms involved in these relationships. Strategies aimed at achieving sustained reductions in HbA1c levels may offer potential for reducing the risk of various CVDs. [ABSTRACT FROM AUTHOR]