Miracle-dz/UniFAR-FTUs huggingface dataset:
Equations of Rees algebras of ideals in two variables

Let I be an ideal of height two in R=k[x_0,x_1] generated by forms of the same degree, and let K be the ideal of defining equations of the Rees algebra of I. Suppose that the second largest column degree in the syzygy matrix of I is e. We give an algorithm for computing the minimal generators of K whose degree is at least e, as well as a simple formula for the bidegrees of these generators. In the case where I is an almost complete intersection, we give a generating set for each graded piece K_(i,*) with i>=e-1.
Determinants of the microbiome spatial variability in chronic rhinosinusitis

Background The sinus microbiome in patients with chronic rhinosinusitis (CRS) is considered homogenous across the sinonasal cavity. The middle nasal meatus is the recommended sampling site for 16S rRNA sequencing. However, individuals with unusually high between-site variability between the middle meatus and the sinuses were identified in previous studies. This study aimed to identify which factors determine increased microbial heterogeneity between sampling sites in the sinuses. Methodology In this cross-sectional study samples for 16S rRNA sequencing were obtained from the middle meatus, the maxillary and the frontal sinus in 50 patients with CRS. The microbiome diversity between sampling sites was analysed in relation to the size of the sinus ostia and clinical metadata. Results In approximately 15% of study participants, the differences between sampling sites within one patient were greater than between the patient and other individuals. Contrary to a popular hypothesis, obstruction of the sinus ostium resulted in decreased dissimilarity between the sinus and the middle meatus. The dissimilarity between the sampling sites was patient-specific: greater between-sinus differences were associated with greater meatus-sinus differences, regardless of the drainage pathway patency. Decreased spatial variability was observed in patients with nasal polyps and extensive mucosal changes in the sinuses. Conclusions Sampling from the middle meatus is not universally representative of the sinus microbiome. The differences between sites cannot be predicted from the patency of communication pathways between them.
On collapsing Calabi–Yau fibrations

We develop some techniques to study the adiabatic limiting behaviour of Calabi-Yau metrics on the total space of a fibration, and obtain strong control near the singular fibres by imposing restrictions on the singularity types. We prove a uniform lower bound on the metric up to the singular fibre, under fairly general hypotheses. Assuming a result in pluripotential theory, we prove a uniform fibre diameter bound for a Lefschetz K3 fibred Calabi-Yau 3-fold, which reduces the study of the collapsing metric to a locally non-collapsed situation, and we identify the Gromov-Hausdorff limit of the rescaled neighbourhood of the singular fibre.
S0950268822001601jra 1..6

Limited prospective severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) data in children regarding the impact of Omicron variant in seropositivity have been reported. We investigated SARS-CoV-2 seropositivity in children between 1 September 2021 and 30 April 2022, representing Delta and Omicron predominance periods. Serum samples from children admitted to the major tertiary Greek paediatric hospital for any cause, except for COVID-19, were randomly collected and tested for SARS-CoV-2 natural infection antibodies against nucleocapsid antigen (Elecsys® Anti-SARS-CoV-2 reagent). A total of 506/1312 (38.6%) seropositive children (0–16 years) were detected (males: 261/506(51.6%); median age (IQR): 95.2 months(24–144)). Seropositivity rates (%) increased from Delta to Omicron period from 29.7% to 48.5% (P-value<0.0001). Seropositivity increased for all age groups, except for the age group of 0–1 year (P-value:0.914). The highest seropositivity rate was detected in April 2022 (52.6%) and reached 73.9% specifically for the age group 12–16 years. No significant differences were detected in seropositivity with respect to gender, origin, or hospitalisation status. Median (IQR) antibody titres were higher in the Omicron vs. Delta period in all age groups, especially in 12–16 years [32.2 COI (7–77.1) vs. 11.4 COI(2.8–50.2), P-value:0.009). During Omicron variant period increased SARS-CoV-2 seropositivity was detected in paediatric population, especially in adolescents, implicating either increased transmissibility or reinfection rates.
Hamiltonian analysis of curvature-squared gravity with or without conformal invariance

Analyzujeme gravitacni teorie se cleny vyssich řadů v křivosti, kde specialnim připadem je Weylovska gravitace. Urcime lokalni podminky, ktere urcuji pocet fyzikalnich stupňů volnosti.
The classification of p-compact groups for p odd

A p-compact group, as defined by Dwyer and Wilkerson, is a purely homotopically defined p-local analog of a compact Lie group. It has long been the hope, and later the conjecture, that these objects should have a classification similar to the classification of compact Lie groups. In this paper we finish the proof of this conjecture, for p an odd prime, proving that there is a one-to-one correspondence between connected p-compact groups and finite reflection groups over the p-adic integers. We do this by providing the last, and rather intricate, piece, namely that the exceptional compact Lie groups are uniquely determined as p-compact groups by their Weyl groups seen as finite reflection groups over the p-adic integers. Our approach in fact gives a largely self-contained proof of the entire classification theorem for p odd.
Modes and geometry of crustal-scale detachment folding in hot orogens—Insights from physical modeling

Detachment folding can be defined as the displacement and buckling of a competent layer above a rheologically weak horizon during tectonic shortening, frequently addressed in the context of salt tectonics. More recent studies have focused on influence of detachments in large-scale lithospheric deformation where the detachment horizon is represented by partially molten lower crust. This study addresses the geometric, kinematic and dynamic behavior of crustal-scale detachment folds using heated paraffin wax as an analogue for partially molten lower crust. Various thermal and shortening rate scenarios were tested in order to characterize deformation patterns within hot orogens in general, and to find an appropriate range of temperature gradients and shortening rates for the detachment folding regime. Five different regimes of lower crustal deformation were identified: 1. Homogeneous thickening or bulging, 2. Short-wavelength folding, 3. Development of diapir-shape folds or ductile faults, 4. Detachment folding and 5. Formation of lower crustal finger-like protrusions. Models are compared to various natural prototypes worldwide, in particular a series of metamorphic domes in the Central Asian Orogenic Belt (CAOB). Detailed analysis of the kinematic-dynamic evolution of the detachment folding scenario revealed an asymmetrical evolution of the folds associated with rotation of the limbs, as well as flexural flow of the lower weak mushy crust around the molten core. Pressure gradients in the fold cores saturated by melt controlled the sequential injections and outflows of partially/molten material between folds’ cores and the melt source layer at the base of the system. This resulted in accumulation of melt in the foreland of the accretionary zone, with higher melt absorption potential for newly developed folds. These observations may have significant implications for the development of pseudo-symmetrical metamorphic domes in the CAOB.
Quaternary quadratic lattices over number fields

We relate proper isometry classes of maximal lattices in a totally definite quaternary quadratic space [Formula: see text] with trivial discriminant to certain equivalence classes of ideals in the quaternion algebra representing the Clifford invariant of [Formula: see text]. This yields a good algorithm to enumerate a system of representatives of proper isometry classes of lattices in genera of maximal lattices in [Formula: see text].
Deep-learning-based generation of synthetic 6-minute MRI from 2-minute MRI for use in head and neck cancer radiotherapy

Background Quick magnetic resonance imaging (MRI) scans with low contrast-to-noise ratio are typically acquired for daily MRI-guided radiotherapy setup. However, for patients with head and neck (HN) cancer, these images are often insufficient for discriminating target volumes and organs at risk (OARs). In this study, we investigated a deep learning (DL) approach to generate high-quality synthetic images from low-quality images. Methods We used 108 unique HN image sets of paired 2-minute T2-weighted scans (2mMRI) and 6-minute T2-weighted scans (6mMRI). 90 image sets (~20,000 slices) were used to train a 2-dimensional generative adversarial DL model that utilized 2mMRI as input and 6mMRI as output. Eighteen image sets were used to test model performance. Similarity metrics, including the mean squared error (MSE), structural similarity index (SSIM), and peak signal-to-noise ratio (PSNR) were calculated between normalized synthetic 6mMRI and ground-truth 6mMRI for all test cases. In addition, a previously trained OAR DL auto-segmentation model was used to segment the right parotid gland, left parotid gland, and mandible on all test case images. Dice similarity coefficients (DSC) were calculated between 2mMRI and either ground-truth 6mMRI or synthetic 6mMRI for each OAR; two one-sided t-tests were applied between the ground-truth and synthetic 6mMRI to determine equivalence. Finally, a visual Turing test using paired ground-truth and synthetic 6mMRI was performed using three clinician observers; the percentage of images that were correctly identified was compared to random chance using proportion equivalence tests. Results The median similarity metrics across the whole images were 0.19, 0.93, and 33.14 for MSE, SSIM, and PSNR, respectively. The median of DSCs comparing ground-truth vs. synthetic 6mMRI auto-segmented OARs were 0.86 vs. 0.85, 0.84 vs. 0.84, and 0.82 vs. 0.85 for the right parotid gland, left parotid gland, and mandible, respectively (equivalence p<0.05 for all OARs). The percent of images correctly identified was equivalent to chance (p<0.05 for all observers). Conclusions Using 2mMRI inputs, we demonstrate that DL-generated synthetic 6mMRI outputs have high similarity to ground-truth 6mMRI, but further improvements can be made. Our study facilitates the clinical incorporation of synthetic MRI in MRI-guided radiotherapy.
The Leydig cell biomarker INSL3 as a predictor of age-related morbidity: Findings from the EMAS cohort

Background Insulin-like peptide 3 (INSL3) is a constitutive hormone secreted in men by the mature Leydig cells of the testes. It is an accurate biomarker for Leydig cell functional capacity, reflecting their total cell number and differentiation status. Objectives To determine the ability of INSL3 to predict hypogonadism and age-related morbidity using the EMAS cohort of older community-dwelling men. Materials & methods Circulating INSL3 was assessed in the EMAS cohort and its cross-sectional and longitudinal relationships to hypogonadism, here defined by testosterone (T) <10.5nmol/l, and a range of age-related morbidities determined by correlation and regression analysis. Results & discussion While INSL3 is an accurate measure of primary hypogonadism, secondary and compensated hypogonadism also indicate reduced levels of INSL3, implying that testicular hypogonadism does not improve even when LH levels are increased, and that ageing-related hypogonadism may combine both primary and secondary features. Unadjusted, serum INSL3, like calculated free testosterone (cFT), LH, or the T/LH ratio reflects hypogonadal status and is associated with reduced sexual function, bone mineral density, and physical activity, as well as increased occurrence of hypertension, cardiovascular disease, cancer, and diabetes. Using multiple regression analysis to adjust for a range of hormonal, anthropometric, and lifestyle factors, this relationship is lost for all morbidities, except for reduced bone mineral density, implying that INSL3 and/or its specific receptor, RXFP2, may be causally involved in promoting healthy bone metabolism. Elevated INSL3 also associates with hypertension and cardiovascular disease. When unadjusted, INSL3 in phase 1 of the EMAS study was assessed for its association with morbidity in phase 2 (mean 4.3 years later); INSL3 significantly predicts 7 out of 9 morbidity categories, behaving as well as cFT in this regard. In contrast, total T was predictive in only 3 of the 9 categories. Conclusion Together with its low within-individual variance, these findings suggest that assessing INSL3 in men could offer important insight into the later development of disease in the elderly.
Partial orders on metric measure spaces

A partial order on the set of metric measure spaces is defined; it generalizes the Lipschitz order of Gromov. We show that our partial order is closed when metric measure spaces are equipped with the Gromov-weak topology and give a new characterization for the Lipschitz order. We will then consider some probabilistic applications. The main importance is given to the study of Fleming-Viot processes with different resampling rates. Besides that application we also consider tree-valued branching processes and two semigroups on metric measure spaces.
Evaluation of the presence of SARS-CoV-2 in vaginal and anal swabs of women with omicron variants of SARS-CoV-2 infection

Objectives The study aimed to determine whether SARS-CoV-2 Omicron variant could be detected in the vaginal fluid and anal swabs of reproductive-aged and postmenopausal women infected with SARS-CoV-2 Omicron variant. Methods Included in this study were 63 women who were laboratory confirmed as having SARS-CoV-2 Omicron variant infection and admitted to the responsible ward of Daping Hospital of at the National Exhibition and Convention Center(Shanghai) Makeshift Hospital from May 1–24, 2022.From them, vaginal and anal swabs were obtained with informed consent. The demographic and baseline clinical characteristics and the swab test results were analyzed. Results The 63 included patients ranged in age from 18 to 72 years with a median of 47.71 ± 15.21 years. Of them, 38 women (60.3%) were in their reproductive years. Most of the participants (77.8%) were healthy without significant underlying diseases. Fourteen patients (22.2%) had asymptomatic infection and the remaining 49 (77.8%) had mild infection. The upper respiratory tract symptoms including cough (40/63.5%) and sore throat (18/28.6%)were the most common clinical manifestations of these mildly infected patients. Only 5 patients (7.8%) had gastrointestinal (GI) symptoms, including simple diarrhea in 4 patients, and diarrhea with vomiting in one patient. Pharyngeal,vaginal and anal swabs were collected simultaneously from all 63 patients 8–16 (mean 11.25 ± 2.23) days after SARS-Cov-2 Omicron variant infection. The vaginal swabs were negative for SARS-CoV-2 in all 63 patients, and the anal swabs were positive in 4 patients (6.5%). The overall median hospitalization duration was 16.73 ± 3.16 days. Conclusion The results of the present study suggest that there is a low possibility of SARS-Cov-2 Omicron variant transmission via the digestive tract and vaginal fluid. The correlation between the GI symptoms and the presence of viral RNA in anal swabs is uncertain.
One-loop nonbirefringent effects on the electromagnetic vertex in the Standard Model Extension

Lorentz violation emerged from a fundamental description of nature may impact, at low energies, the Maxwell sector, so that contributions from such new physics to the electromagnetic vertex would be induced. Particularly, nonbirefringent CPT-even effects from the electromagnetic sector modified by the Lorentz- and CPT-violating Standard Model Extension alter the structure of the free photon propagator. We calculate Lorentz-violating contributions to the electromagnetic vertex, at the one-loop level, by using a modified photon propagator carrying this sort of effects. We take the photon off shell, and find an expression that involves both isotropic and anisotropic effects of nonbirefringent violation of Lorentz invariance. Our analysis of the one-loop vertex function includes gauge invariance, transformation properties under C, P and T, and tree-level contributions from Lorentz-violating nonrenormalizable interactions. These elements add to previous studies of the one-loop contributions to the electromagnetic vertex in the context of Lorentz violation in the photon sector. Finally, we restrict our analysis to the isotropic case and derive a finite contribution from isotropic Lorentz violation to the anomalous magnetic moment of fermions that coincides with the result already reported in the literature.
THE CARNEGIE SUPERNOVA PROJECT: SECOND PHOTOMETRY DATA RELEASE OF LOW-REDSHIFT TYPE Ia SUPERNOVAE

The Carnegie Supernova Project (CSP) was a five-year observational survey conducted at Las Campanas Observatory that obtained, among other things, high-quality light curves of ∼100 low-redshift Type Ia supernovae (SNe Ia). Presented here is the second data release of nearby SN Ia photometry consisting of 50 objects, with a subset of 45 having near-infrared follow-up observations. Thirty-three objects have optical pre-maximum coverage with a subset of 15 beginning at least five days before maximum light. In the near-infrared, 27 objects have coverage beginning before the epoch of B-band maximum, with a subset of 13 beginning at least five days before maximum. In addition, we present results of a photometric calibration program to measure the CSP optical (uBgVri) bandpasses with an accuracy of ∼1%. Finally, we report the discovery of a second SN Ia, SN 2006ot, similar in its characteristics to the peculiar SN 2006bt.
Knockdown of NtCPS2 promotes plant growth and reduces drought tolerance in Nicotiana tabacum

Drought stress is one of the primary environmental stress factors that gravely threaten crop growth, development, and yields. After drought stress, plants can regulate the content and proportion of various hormones to adjust their growth and development, and in some cases to minimize the adverse effects of drought stress. In our previous study, the tobacco cis-abienol synthesis gene (NtCPS2) was found to affect hormone synthesis in tobacco plants. Unfortunately, the role of NtCPS2 genes in the response to abiotic stress has not yet been investigated. Here, we present data supporting the role of NtCPS2 genes in drought stress and the possible underlying molecular mechanisms. NtCPS2 gene expression was induced by polyethylene glycol, high-temperature, and virus treatments. The results of subcellular localization showed that NtCPS2 was localized in the cell membrane. The NtCPS2-knockdown plants exhibited higher levels of gibberellin (GA) content and synthesis pathway genes expression but lower abscisic acid (ABA) content and synthesis pathway genes expression in response to drought stress. In addition, the transgenic tobacco lines showed higher leaf water loss and electrolyte loss, lower soluble protein and reactive oxygen species content (ROS), and lower antioxidant enzyme activity after drought treatment compared to wild type plants (WT). In summary, NtCPS2 positively regulates drought stress tolerance possibly by modulating the ratio of GA to ABA, which was confirmed by evidence of related phenotypic and physiological indicators. This study may provide evidence for the feedback regulation of hormone to abiotic and biotic stresses.
A Lightcone Embedding of the Twin Building of a Hyperbolic Kac-Moody Group

Let A be a symmetrizable hyperbolic generalized Cartan matrix with Kac-Moody algebra g = g(A) and (adjoint) Kac-Moody group G = G(A)=$\langle\exp(ad(t e_i)), \exp(ad(t f_i)) \,|\, t\in C\rangle$ where $e_i$ and $f_i$ are the simple root vectors. Let $(B^+, B^-, N)$ be the twin BN-pair naturally associated to G and let $(\mathcal B^+,\mathcal B^-)$ be the corresponding twin building with Weyl group W and natural G-action, which respects the usual W-valued distance and codistance functions. This work connects the twin building of G and the Kac-Moody algebra g in a new geometrical way. The Cartan-Chevalley involution, $\omega$, of g has fixed point real subalgebra, k, the 'compact' (unitary) real form of g, and k contains the compact Cartan t = k $\cap$ h. We show that a real bilinear form $(\cdot,\cdot)$ is Lorentzian with signatures $(1, \infty)$ on k, and $(1, n -1)$ on t. We define $\{x\in {\rm k} \,|\, (x, x) \leq 0\}$ to be the lightcone of k, and similarly for t. Let K be the compact (unitary) real form of G, that is, the fixed point subgroup of the lifting of $\omega$ to G. We construct a K-equivariant embedding of the twin building of G into the lightcone of the compact real form k of g. Our embedding gives a geometric model of part of the twin building, where each half consists of infinitely many copies of a W-tessellated hyperbolic space glued together along hyperplanes of the faces. Locally, at each such face, we find an $SU(2)$-orbit of chambers stabilized by $U(1)$ which is thus parametrized by a Riemann sphere $SU(2)/U(1)\cong S^2$. For n = 2 the twin building is a twin tree. In this case, we construct our embedding explicitly and we describe the action of the real root groups on the fundamental twin apartment. We also construct a spherical twin building at infinity, and construct an embedding of it into the set of rays on the boundary of the lightcone.
Age-specific transmission dynamic of mumps: A long-term large-scale modeling study in Jilin Province, China

Objectives Despite the adoption of a new childhood immunization program in China, the incidence of mumps remains high. This study aimed to describe the epidemiological characteristics of mumps in Jilin Province from 2005 to 2019 and to assess the transmissibility of mumps virus among the whole population and different subgroups by regions and age groups. Methods The Non-age-specific and age-specific Susceptible–Exposed–Pre-symptomatic–Infectious–Asymptomatic–Recovered (SEPIAR) models were fitted to actual mumps incidence data. The time-varying reproduction number (Rt) was used to evaluate and compare the transmissibility. Results From 2005 to 2019, a total of 57,424 cases of mumps were reported in Jilin Province. The incidence of mumps was the highest in people aged 5 to 9 years (77.37 per 100,000). The two SEPIAR models fitted the reported data well (P < 0.01). The median transmissibility (Rt) calculated by the two SEPIAR models were 1.096 (range: 1.911 × 10−5–2.192) and 1.074 (range: 0.033–2.114) respectively. The age-specific SEPIAR model was more representative of the actual epidemic of mumps in Jilin Province from 2005–2019. Conclusions For mumps control, it is recommended that mumps-containing vaccines (MuCV) coverage be increased nationwide in the 5–9 years age group, either by a mumps vaccine alone or by a combination of vaccines such as measles-mumps-rubella (MMR) vaccine. The coverage of vaccines in Jilin Province should be continuously expanded to establish solid immunity in the population. China needs to redefine the optimal time interval for MuCV immunization.