Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry

A new method to obtain trigonometry for the real spaces of constant curvature and metric of any (even degenerate) signature is presented. The method encapsulates trigonometry for all these spaces into a single basic trigonometric group equation. This brings to its logical end the idea of an absolute trigonometry, and provides equations which hold true for the nine two-dimensional spaces of constant curvature and any signature. This family of spaces includes both relativistic and non-relativistic homogeneous spacetimes; therefore a complete discussion of trigonometry in the six de Sitter, minkowskian, Newton--Hooke and galilean spacetimes follow as particular instances of the general approach. Any equation previously known for the three classical riemannian spaces also has a version for the remaining six spacetimes; in most cases these equations are new. Distinctive traits of the method are universality and self-duality: every equation is meaningful for the nine spaces at once, and displays explicitly invariance under a duality transformation relating the nine spaces. The derivation of the single basic trigonometric equation at group level, its translation to a set of equations (cosine, sine and dual cosine laws) and the natural apparition of angular and lateral excesses, area and coarea are explicitly discussed in detail. The exposition also aims to introduce the main ideas of this direct group theoretical way to trigonometry, and may well provide a path to systematically study trigonometry for any homogeneous symmetric space.Comment: 51 pages, LaTe

Association of maternal body composition and diet on breast milk hormones and neonatal growth during the first month of lactation

Introduction: Preterm birth is associated with altered growth patterns and an increased risk of cardiometabolic diseases, with breast milk (BM) being a counteracting factor. Preterm infants also show alterations in adipokines and gut hormones influencing appetite and metabolism. Since these hormones are present in BM, it is possible that their levels may equilibrate deficiencies improving infant growth. We aimed to assess 1) the BM levels of ghrelin, resistin, leptin, insulin, peptide YY, and the gastrointestinal peptide in women with preterm and term labor; 2) the relationship between BM hormones and neonatal growth; and 3) the influence of maternal body composition and diet on these BM hormones. Methods: BM from 48 women (30 term and 18 preterm labor) was collected at days 7, 14, and 28 of lactation. Maternal body composition was evaluated by bioimpedance, and neonate anthropometric parameters were collected from medical records. The maternal dietary pattern was assessed by a 72-h dietary recall at days 7 and 28 of lactation. BM hormones were analyzed by the U-Plex Ultra-sensitive method. Data were analyzed using linear regression models. BM from women with preterm labor had lower ghrelin levels, with the other hormones being significantly higher compared to women with term delivery. Results: In premature infants, growth was positively associated with BM ghrelin, while, in term infants, it was positively associated with insulin and negatively with peptide YY. In the first week of lactation, women with preterm labor had higher body fat compared to women with term labor. In this group, ghrelin levels were positively associated with maternal body fat and with fiber and protein intake. In women with term labor, no associations between anthropometric parameters and BM hormones were found, and fiber intake was negatively associated with peptide YY. Discussion: Preterm labor is a factor influencing the levels of BM adipokines and gut hormones, with BM ghrelin being a relevant hormone for premature infant growth. Since ghrelin is lower in BM from women with preterm labor and the levels are associated with maternal fat storage and some dietary components, our data support the importance to monitor diet and body composition in women who gave birth prematurely to improve the BM hormonal statusThis research was funded by Promotion of Knowledge Transfer program (PTC-2020) from Universidad Autónoma de Madrid in collaboration with Alter Farmacia, SA, Spanish Ministry of Science, and Innovation (RTI2018-097504-B-I00

Association of maternal body composition and diet on breast milk hormones and neonatal growth during the first month of lactation

Preterm birth is associated with altered growth patterns and an increased risk of cardiometabolic diseases, with breast milk (BM) being a counteracting factor. Preterm infants also show alterations in adipokines and gut hormones influencing appetite and metabolism. Since these hormones are present in BM, it is possible that their levels may equilibrate deficiencies improving infant growth. We aimed to assess 1) the BM levels of ghrelin, resistin, leptin, insulin, peptide YY, and the gastrointestinal peptide in women with preterm and term labor; 2) the relationship between BM hormones and neonatal growth; and 3) the influence of maternal body composition and diet on these BM hormone

Maternal and neonatal factors modulating breast milk cytokines in the first month of lactation

Breast milk (BM) cytokines support and modulate infant immunity, being particularly relevant in premature neonates with adverse outcomes (NAO). This study aimed to examine, in a cohort of Spanish breastfeeding women, changes in BM cytokines in the first month of lactation, their modulation by neonatal factors (sex, gestational age, and NAO), maternal factors (obstetric complications, C-section, and diet), and their relationship with oxidative status. Sixty-three mother-neonate dyads were studied at days 7 and 28 of lactation. Dietary habits were assessed by a 72-h dietary recall, and the maternal dietary inflammatory index (mDII) was calculated. BM cytokines (IL-10, IL-13, IL-8, MCP-1, and TNFα) were assessed by ultra-sensitive chemiluminescence. Total antioxidant capacity was assessed by the ABTS method and lipid peroxidation by the MDA+HNE kit. From days 7 to 28 of lactation, the levels of IL-10 and TNFα remained stable, while IL-13 increased (β = 0.85 ± 0.12, p < 0.001) and IL-8 and MCP-1 levels decreased (β = −0.64 ± 0.27, p = 0.019; β = −0.98 ± 0.22, p < 0.001; respectively). Antioxidant capacity and lipid peroxidation also decrease during lactation. Neonatal sex did not influence any of the cytokines, but BM from mothers with male infants had a higher antioxidant capacity. Gestational age was associated with male sex and NAO, being inversely correlated with the BM proinflammatory cytokines IL-8, MCP-1, and TNFα. From days 7 to 28 of lactation, BM from women with NAO infants increased MCP-1 levels and had a larger drop in antioxidant capacity, with the opposite trend in lipid peroxidation. MCP-1 was also significantly higher in women undergoing C-section; this cytokine declined in women who decreased mDII during lactation, while IL-10 increased. Linear mixed regression models evidenced that the most important factors modulating BM cytokines were lactation period and gestational age. In conclusion, during the first month of lactation, BM cytokines shift towards an anti-inflammatory profile, influenced mainly by prematurity. BM MCP-1 is associated with maternal and neonatal inflammatory processe

Influence of chronic ocular hypertension on emmetropia: Refractive, structural and functional study in two rat models

Chronic ocular hypertension (OHT) influences on refraction in youth and causes glaucoma in adulthood. However, the origin of the responsible mechanism is unclear. This study analyzes the effect of mild-moderate chronic OHT on refraction and neuroretina (structure and function) in young-adult Long-Evans rats using optical coherence tomography and electroretinography over 24 weeks. Data from 260 eyes were retrospectively analyzed in two cohorts: an ocular normotension (ONT) cohort (20 mmHg), in which OHT was induced either by sclerosing the episcleral veins (ES group) or by injecting microspheres into the anterior chamber. A trend toward emmetropia was found in both cohorts over time, though it was more pronounced in the OHT cohort (p < 0.001), especially in the ES group (p = 0.001) and males. IOP and refraction were negatively correlated at week 24 (p = 0.010). The OHT cohort showed early thickening in outer retinal sectors (p < 0.050) and the retinal nerve fiber layer, which later thinned. Electroretinography demonstrated early supranormal amplitudes and faster latencies that later declined. Chronic OHT accelerates emmetropia in Long–Evans rat eyes towards slowly progressive myopia, with an initial increase in structure and function that reversed over time. © 2021 by the authors. Licensee MDPI, Basel, Switzerland

Direct observation of multivalent states and charge transfer in Ce-doped yttrium iron garnet thin films

Due to their large magneto-optic responses, rare-earth-doped yttrium iron garnets, Y3Fe5O12 (YIG), are highly regarded for their potential in photonics and magnonics. Here, we consider the case of Ce-doped YIG (Ce-YIG) thin films, in which substitutional Ce3+ ions are magnetic because of their 4f1 ground state. In order to elucidate the impact of Ce substitution on the magnetization of YIG, we have carried out soft x-ray spectroscopy measurements on Ce-YIG films. In particular, we have used the element specificity of x-ray magnetic circular dichroism to extract the individual magnetization curves linked to Ce and Fe ions. Our results show that Ce doping triggers a selective charge transfer from Ce to the Fe tetrahedral sites in the YIG structure. This, in turn, causes a disruption of the electronic and magnetic properties of the parent compound, reducing the exchange coupling between the Ce and Fe magnetic moments and causing atypical magnetic behavior. Our work is relevant for understanding magnetism in rare-earth-doped YIG and, eventually, may enable a quantitative evaluation of the magneto-optical properties of rare-earth incorporation into YIG

Novel use of plga microspheres to create an animal model of glaucoma with progressive neuroretinal degeneration

Progressive degeneration of neuroretinal tissue with maintained elevated intraocular pressure (IOP) to simulate chronic glaucoma was produced by intracameral injections of poly (lactic-co-glycolic) acid (PLGA) microspheres (Ms) in rat eyes. The right eye of 39 rats received different sizes of PLGA-Ms (2 µL suspension; 10% w/v): 14 with 38–20 µm Ms (Ms38/20 model) and 25 with 20–10 µm particles (Ms20/10 model). This novel glaucoma animal model was compared to the episcleral vein sclerosis (EPI) model (25 eyes). Injections were performed at baseline, two, four and six weeks. Clinical signs, IOP, retina and optic nerve thicknesses (using in vivo optical coherence tomography; OCT), and histological studies were performed. An IOP increment was observed in all three groups, however, the values obtained from the PLGA-Ms injection resulted lower with a better preservation of the ocular surface. In fact, the injection of Ms20/10 created a gentler, more progressive, and more sustained increase in IOP. This IOP alteration was correlated with a significant decrease in most OCT parameters and in histological ganglion-cell count for the three conditions throughout the eight-week follow-up. In all cases, progressive degeneration of the retina, retinal ganglion cells and optic nerve, simulating chronic glaucoma, was detected by OCT and corroborated by histological study. Results showed an alternative glaucoma model to the well-known episcleral vein model, which was simpler to perform, more reproducible and easier to monitor in vivo