A generalization of the classical Krull dimension for modules

AbstractIn this article, we introduce and study a generalization of the classical Krull dimension for a module MR. This is defined to be the length of the longest strong chain of prime submodules of M (defined later) and, denoted by Cl.K.dim(M). This notion is analogous to that of the usual classical Krull dimension of a ring. This dimension, Cl.K.dim(M) exists if and only if M has virtual acc on prime submodules; see Section 2. If R is a ring for which Cl.K.dim(R) exists, then for any left R-module M, Cl.K.dim(M) exists and is no larger than Cl.K.dim(R). Over any ring, all homogeneous semisimple modules and over a PI-ring (or an FBN-ring), all semisimple modules as well as, all Artinian modules with a prime submodule lie in the class of modules with classical Krull dimension zero. For a multiplication module over a commutative ring, the notion of classical Krull dimension and the usual prime dimension coincide. This yields that for a multiplication module M, Cl.K.dim(M) exists if and only if M has acc on prime submodules. As an application, we obtain a nice generalization of Cohen's Theorem for multiplication modules. Also, PI-rings whose nonzero modules have zero classical Krull dimension are characterized

On the Diameter and Girth of an Annihilating-Ideal Graph

Let $R$ be a commutative ring with $1\neq 0$ and $\Bbb{A}(R)$ be the set of ideals with nonzero annihilators. The annihilating-ideal graph of $R$ is defined as the graph $\Bbb{AG}(R)$ with the vertex set $\Bbb{A}(R)^{*} = \Bbb{A}(R)\setminus \{(0)\}$ and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ = (0)$. In this paper, we first study the interplay between the diameter of annihilating-ideal graphs and zero-divisor graphs. Also, we characterize rings $R$ when ${\rm gr}(\Bbb{AG}(R))\geq 4$, and so we characterize rings whose annihilating-ideal graphs are bipartite. Finally, in the last section we discuss on a relation between the Smarandache vertices and diameter of $\Bbb {AG}(R)$.Comment: 11 pages, 1 figur

Paradox of Modern Pregnancy: A Phenomenological Study of Women's Lived Experiences from Assisted Pregnancy

The purpose of our study was describing the meaning of pregnancy through Assisted Reproductive Technologies (ARTs). A qualitative design with hermeneutic phenomenology approach was selected to carry out the research. Semistructured in-depth interviews were conducted with 12 women who experienced assisted pregnancy. Three themes emerged from women's experience including finding peace in life, paradoxical feelings, and struggling to realize a dream. We concluded that pregnancy is the beginning of a new and hard struggle for women with fertility problems. The findings of our study resulted in helpful implications for the health care professionals managing assisted pregnancies. Copyright © 2015 Fahimeh Ranjbar et al

Zero-divisor graphs of nilpotent-free semigroups

We find strong relationships between the zero-divisor graphs of apparently disparate kinds of nilpotent-free semigroups by introducing the notion of an \emph{Armendariz map} between such semigroups, which preserves many graph-theoretic invariants. We use it to give relationships between the zero-divisor graph of a ring, a polynomial ring, and the annihilating-ideal graph. Then we give relationships between the zero-divisor graphs of certain topological spaces (so-called pearled spaces), prime spectra, maximal spectra, tensor-product semigroups, and the semigroup of ideals under addition, obtaining surprisingly strong structure theorems relating ring-theoretic and topological properties to graph-theoretic invariants of the corresponding graphs.Comment: Expanded first paragraph in section 6. To appear in J. Algebraic Combin. 22 page

Transformer-Based Neural Surrogate for Link-Level Path Loss Prediction from Variable-Sized Maps

Estimating path loss for a transmitter-receiver location is key to many use-cases including network planning and handover. Machine learning has become a popular tool to predict wireless channel properties based on map data. In this work, we present a transformer-based neural network architecture that enables predicting link-level properties from maps of various dimensions and from sparse measurements. The map contains information about buildings and foliage. The transformer model attends to the regions that are relevant for path loss prediction and, therefore, scales efficiently to maps of different size. Further, our approach works with continuous transmitter and receiver coordinates without relying on discretization. In experiments, we show that the proposed model is able to efficiently learn dominant path losses from sparse training data and generalizes well when tested on novel maps.Comment: Accepted at IEEE GLOBECOM 2023, v2: Changed license on arxi

The effects of vitamin D supplementation on indices of glycemic control in Iranian diabetics: A systematic review and meta-analysis

Background and purpose: This systematic review and meta-analysis aimed to assess the effects of vitamin D supplements on indices of glycemic control [homeostatic model assessment-insulin resistance (HOMA-IR), hemoglobin A1C (HbA1C), fasting blood glucose (FBG), and quantitative insulin-sensitivity check index (QUICKI) and lipid profile in diabetic patients. Methods: Eight databases were searched, for randomized controlled trials (RCTs) or cross-sectional and cohort studies that have been published up to December 2017. We used the comprehensive meta-analysis (CMA) software for all statistical analysis and used the I2 index for assessing heterogeneity. A p value of <0.05 was considered as statistically significant. Results: We found 621 articles, and after the exclusion of ineligible publications, 82 studies remained to be assessed of which 37 were used for meta-analysis. Vitamin D supplementation was associated with a significant improvement in FBG (p = 0.001 and 95% CI: −0.526 to −0.136) and HbA1C (p = 0.003 and 95% CI: 1.719 to −0.361) in individuals with type 2 diabetes mellitus (T2DM); while in women with gestational diabetes mellitus (GDM) the reduction in FBG (p = 0.071 and 95% CI: −0.873 to −0.035) and HbA1C (p = 0.199 and 95% CI: 3.270 to 0.681) failed to reach statistical significance. Treatment with vitamin D supplements was associated with an improvement in HOMA-IR in pregnant diabetic women (p = 0.028 and 95% CI: 0.924 to −0.053) and for individuals with diabetes mellitus (p = 0.005 and 95% CI: 1.772 to −0.319). The pooled result of the cross-sectional meta-analysis indicated that serum vitamin D concentrations were significantly lower in diabetic patients than in healthy controls (p = 0.018 and 95% CI: 0.587 to −0.054). Conclusion: This meta-analysis suggests that vitamin D supplementation improves indices of glycemic control (FBG, HOMA-IR, and HbA1C) in patients with diabetes mellitus. Hence, vitamin D supplements may be of potential therapeutic value in diabetic patients, as an adjuvant therapy along with other treatment

Chemical vapor deposited polymer layer for efficient passivation of planar perovskite solar cells

Reducing non-radiative recombination losses by advanced passivation strategies is pivotal to maximize the power conversion efficiency (PCE) of perovskite solar cells (PSCs). Previously, polymers such as poly(methyl methacrylate), poly(ethylene oxide), and polystyrene were successfully applied in solution-processed passivation layers. However, controlling the thickness and homogeneity of these ultra-thin passivation layers on top of polycrystalline perovskite thin films is a major challenge. In response to this challenge, this work reports on chemical vapor deposition (CVD) polymerization of poly(p-xylylene) (PPX) layers at controlled substrate temperatures (14–16 °C) for efficient surface passivation of perovskite thin films. Prototype double-cation PSCs using a ∼1 nm PPX passivation layer exhibit an increase in open-circuit voltage (V$_{OC}$) of ∼40 mV along with an enhanced fill factor (FF) compared to a non-passivated PSC. These improvements result in a substantially enhanced PCE of 20.4% compared to 19.4% for the non-passivated PSC. Moreover, the power output measurements over 30 days under ambient atmosphere (relative humidity ∼40–50%) confirm that the passivated PSCs are more resilient towards humidity-induced degradation. Considering the urge to develop reliable, scalable and homogeneous deposition techniques for future large-area perovskite solar modules, this work establishes CVD polymerization as a novel approach for the passivation of perovskite thin films

Comparative maturation of cynomolgus monkey oocytes in vivo and in vitro

BACKGROUND: In vitro maturation (IVM) of oocytes followed by fertilization in vitro (IVF) and embryo transfer offers an alternative to conventional IVF treatment that minimises drug administration and avoids ovarian hyperstimulation. However, the technique is less efficient than maturation in vivo. In the present study, a non-human primate model was used to address the hypothesis that the number of oocytes is increased and their nuclear and cytoplasmic maturity after IVM are improved when maturation is initiated in vivo by priming with hCG. METHODS: Young, adult cynomolgus monkeys were given recombinant human (rh) gonadotropins to stimulate the development of multiple follicles, and oocytes were aspirated 0, 12, 24, or 36 h after injection of an ovulatory dose of rhCG. The nuclear status of oocytes was determined at the time of recovery and after culture for a total elapsed time of 40–44 hours after hCG. RESULTS: Priming with hCG significantly increased the number of oocytes harvested, especially after delaying aspiration for 24 h or longer. Nuclear maturation after the full period in culture was also enhanced by priming: 71.5, 83.6, and 94.6% of oocytes collected at 0, 12, and 24 h hCG had progressed to MII by the end of the culture period, compared to 87.8% of oocytes that were retrieved at 36 h. A large proportion of oocytes reaching the MII stage had either or both abnormal spindles (>40%) and misaligned chromosomes (>60%), judging by immunofluorescence microscopy, but these abnormalities were independent of culture time. The mitochondria were evenly distributed throughout the cytoplasm at all stages of maturation. Importantly, there was no microscopic evidence that the duration of culture had any injurious effects on the cells. CONCLUSION: In conclusion, the evidence supports this non-human primate as a model for human IVM and the practice of priming with hCG to promote developmental potential

Testing the priority-of-access model in a seasonally breeding primate species

In mammals, when females are clumped in space, male access to receptive females is usually determined by a dominance hierarchy based on fighting ability. In polygynandrous primates, as opposed to most mammalian species, the strength of the relationship between male social status and reproductive success varies greatly. It has been proposed that the degree to which paternity is determined by male rank decreases with increasing female reproductive synchrony. The priority-of-access model (PoA) predicts male reproductive success based on female synchrony and male dominance rank. To date, most tests of the PoA using paternity data involved nonseasonally breeding species. Here, we examine whether the PoA explains the relatively low reproductive skew in relation to dominance rank reported in the rhesus macaque, a strictly seasonal species. We collected behavioral, genetic, and hormonal data on one group of the free-ranging population on Cayo Santiago (Puerto Rico) for 2 years. The PoA correctly predicted the steepness of male reproductive skew, but not its relationship to male dominance: the most successful sire, fathering one third of the infants, was high but not top ranking. In contrast, mating success was not significantly skewed, suggesting that other mechanisms than social status contributed to male reproductive success. Dominance may be less important for paternity in rhesus macaques than in other primate species because it is reached through queuing rather than contest, leading to alpha males not necessarily being the strongest or most attractive male. More work is needed to fully elucidate the mechanisms determining paternity in rhesus macaques

Cytokine Gene Expression in the Maternal-Fetal Interface in Somatic Cell Nuclear Transfer Pregnancies in Small Ruminants

The present retrospective study investigates pregnancy rates, incidence of pregnancy losses and large offspring syndrome (LOS), and immune-related gene expression of sheep and goat somatic cell nuclear transfer (SCNT) pregnancies. We hypothesized that significantly higher pregnancy losses observed in sheep SCNT pregnancies compared to goats are due to the increased amounts of T-helper 1 cytokines and pro-inflammatory mediators at the maternal-fetal interface. Sheep and goat SCNT pregnancies were generated using the same procedure. Control pregnancies were established by natural breeding. Although SCNT pregnancy rates at 45 days were similar in both species, pregnancy losses between 45 and 60 days and incidence of LOS were significantly increased in sheep compared with goats. At term, the expression of pro-inflammatory genes in sheep SCNT placentas was increased while the one of goat SCNT was similar to the control animals. Among the genes that had altered expression in sheep SCNT placentas are CTLA4, IL2RA, CD28, IFNG, IL6, IL10, TGFB1, TNF, IL1A and CXCL8. MHC-I protein expression was greater in sheep and goat SCNT placentas at term compared with control pregnancies. An unfavorable immune environment is present at the maternal-fetal interface in sheep SCNT pregnancies