Carsten Thomassen in 1989 conjectured that if a graph has minimum degree much more than the number of atoms in the universe (δ(G)≥101010), then it contains a pillar, which is a graph that consists of ...two vertex-disjoint cycles of the same length, s say, along with s vertex-disjoint paths of the same length3 which connect matching vertices in order around the cycles. Despite the simplicity of the structure of pillars and various developments of powerful embedding methods for paths and cycles in the past three decades, this innocent looking conjecture has seen no progress to date. In this paper, we give a proof of this conjecture by building a pillar (algorithmically) in sublinear expanders.
Disjoint isomorphic balanced clique subdivisions Fernández, Irene Gil; Hyde, Joseph; Liu, Hong ...
Journal of combinatorial theory. Series B,
July 2023, 2023-07-00, Volume:
161
Journal Article
Peer reviewed
Open access
A classical result, due to Bollobás and Thomason, and independently Komlós and Szemerédi, states that there is a constant C such that every graph with average degree at least Ck2 has a subdivision of ...Kk, the complete graph on k vertices. We study two directions extending this result.•Verstraëte conjectured that a quadratic bound guarantees in fact two vertex-disjoint isomorphic copies of a Kk-subdivision.•Thomassen conjectured that for each k∈N there is some d=d(k) such that every graph with average degree at least d contains a balanced subdivision of Kk. Recently, Liu and Montgomery confirmed Thomassen's conjecture, but the optimal bound on d(k) remains open. In this paper, we show that a quadratic lower bound on average degree suffices to force a balanced Kk-subdivision. This gives the right order of magnitude of the optimal d(k) needed in Thomassen's conjecture. Since a balanced Kmk-subdivision trivially contains m vertex-disjoint isomorphic Kk-subdivisions, this also confirms Verstraëte's conjecture in a strong sense.
Nested cycles with no geometric crossings Irene Gil Fernández; Jaehoon Kim; Younjin Kim ...
Proceedings of the American Mathematical Society. Series B,
2/2022, Volume:
9, Issue:
3
Journal Article
Peer reviewed
Open access
In 1975, Erdős asked the following question: what is the smallest function f(n) for which all graphs with n vertices and f(n) edges contain two edge-disjoint cycles C_1 and C_2, such that the vertex ...set of C_2 is a subset of the vertex set of C_1 and their cyclic orderings of the vertices respect each other? We prove the optimal linear bound f(n)=O(n) using sublinear expanders.
Synopsis
The seroprevalence of severe acute respiratory syndrome coronavirus 2 among first‐trimester pregnant women January 1 to May 15, 2020, was 8.2%. There were no significant differences in ...complications in seropositive women.
Objective
To evaluate the level of agreement between ultrasound measurements to evaluate fetal head position and progress of labor by attending midwives and obstetricians after appropriate training.
...Methods
In this prospective study, women in the first stage of labor giving birth to a single baby in cephalic presentation at our Obstetric Unit between March 2018 and December 2019 were invited to participate; 109 women agreed. Transperineal and transabdominal ultrasound was independently performed by a trained midwife and an obstetrician. Two paired measurements were available for comparisons in 107 cases for the angle of progression (AoP), in 106 cases for the head‐to‐perineum distance (HPD), in 97 cases for the cervical dilatation (CD), and in 79 cases for the fetal head position.
Results
We found a good correlation between the AoP measured by obstetricians and midwives (intra‐class correlation coefficient ICC = 0.85; 95% confidence interval CI 0.80–0.89). There was a moderate correlation between the HPD (ICC = 0.75; 95% CI 0.68–0.82). There was a very good correlation between the CD measured (ICC = 0.94; 95% CI 0.91–0.96). There was a very good level of agreement in the classification of the fetal head position (Cohen's κ = 0.89; 95% CI 0.80–0.98).
Conclusions
Ultrasound assessment of fetal head position and progress of labor can effectively be performed by attending midwives without previous experience in ultrasound.
Synopsis
Ultrasound assessment of fetal head position and progress of labor can effectively be performed by attending midwives without previous experience on ultrasound.
While the presence of SARS-CoV-2 in human breast milk is contentious, anti-SARS-CoV-2 antibodies have been consistently detected in human breast milk. However, it is uncertain when and how long the ...antibodies are present.
This was a prospective cohort study including all consecutive pregnant women with confirmed SARS-CoV-2 infection during pregnancy, recruited at six maternity units in Spain and Hong Kong from March 2020 to March 2021. Colostrum (day of birth until day 4 postpartum) and mature milk (day 7 postpartum until 6 weeks postpartum) were prospectively collected, and paired maternal blood samples were also collected. Colostrum samples were tested with rRT-PCR-SARS-CoV-2, and skimmed acellular milk and maternal sera were tested against SARS-CoV-2 specific immunoglobulin M, A, and G reactive to receptor binding domain of SARS-CoV-2 spike protein 1 to determine the presence of immunoglobulins. Then, we examined how each immunoglobulin type in the colostrum was related to the time of infection by logistic regression analysis, the concordance between these immunoglobulins in the colostrum, maternal serum, and mature milk by Cohen's kappa statistic, and the relationship between immunoglobulin levels in mature milk and colostrum with McNemar.
One hundred eighty-seven pregnant women with confirmed SARS-CoV-2 infection during pregnancy or childbirth were recruited and donated the milk and blood samples. No SARS-CoV-2 was found in the human breast milk. Immunoglobulin A, G, and M were present in 129/162 (79·6%), 5/163 (3·1%), and 15/76 (19·7%) colostrum samples and in 17/62 (27·42%), 2/62 (3·23%) and 2/62 (3·23%) mature milk samples, respectively. Immunoglobulin A was the predominant immunoglobulin found in breast milk, and its levels were significantly higher in the colostrum than in the mature milk (p-value < 0.001). We did not find that the presence of immunoglobulins in the colostrum was associated with their presence in maternal, the severity of the disease, or the time when the infection had occurred.
Since anti-SARS-CoV-2 antibodies are found in the colostrum irrespective of the time of infection during pregnancy, but the virus itself is not detected in human breast milk, our study found no indications to withhold breastfeeding, taking contact precautions when there is active disease.
Background and Objectives: Over the last few years, great interest has arisen in the role of the cerebroplacental ratio (CPR) to identify low-risk pregnancies at higher risk of adverse pregnancy ...outcomes. This study aimed to assess the predictive capacity of the CPR for adverse perinatal outcomes in all uncomplicated singleton pregnancies attending an appointment at 40–42 weeks. Materials and Methods: This is a retrospective cohort study including all consecutive singleton pregnancies undergoing a routine prenatal care appointment after 40 weeks in three maternity units in Spain and the United Kingdom from January 2017 to December 2019. The primary outcome was adverse perinatal outcomes defined as stillbirth or neonatal death, cesarean section or instrumental delivery due to fetal distress during labor, umbilical arterial cord blood pH < 7.0, umbilical venous cord blood pH < 7.1, Apgar score at 5 min < 7, and admission to the neonatal unit. Logistic mixed models and ROC curve analyses were used to analyze the data. Results: A total of 3143 pregnancies were analyzed, including 537 (17.1%) with an adverse perinatal outcome. Maternal age (odds ratio (OR) 1.03, 95% confidence interval (CI) 1.01 to 1.04), body mass index (OR 1.04, 95% CI 1.03 to 1.06), racial origin (OR 2.80, 95% CI 1.90 to 4.12), parity (OR 0.36, 95% CI 0.29 to 0.45), and labor induction (OR 1.79, 95% CI 1.36 to 2.35) were significant predictors of adverse perinatal outcomes with an area under the ROC curve of 0.743 (95% CI 0.720 to 0.766). The addition of the CPR to the previous model did not improve performance. Additionally, the CPR alone achieved a detection rate of only 11.9% (95% CI 9.3 to 15) when using the 10th centile as the screen-positive cutoff. Conclusions: Our data on late-term unselected pregnancies suggest that the CPR is a poor predictor of adverse perinatal outcomes.
Objective
To evaluate the clinical implementation of a preventive COVID-19 protocol regarding re-organization of appointments and documented infections among health workers in an obstetric outpatient ...service.
Methods
Descriptive analysis of the antenatal care at our obstetric outpatient service and infection rates among health care providers from March 19th to May 22nd, 2020. Appointments were divided into telephone calls or face-to-face examinations. A pre-consultation triage was implemented to identify suspected SARS-CoV2 infected women to reschedule them 14 days later or, if the consultation was non-delayable, to use complete Personal Protective Equipment (PPE). Firstly, the number of face-to-face appointments, telephone appointments, and COVID-19 diagnoses in pregnant women were analyzed. Secondly, the number of obstetricians and nurses diagnosed with SARS-CoV2 infection and their serologic status during universal screening in May 2020 were recorded.
Results
One thousand eight hundred forty-two obstetric appointments were scheduled during this period, including 432 (23.5%) telephone appointments (96.53% according to clinical protocol, 1.62% symptomatic patients advised to stay at home, and 1.85% COVID-19 confirmed cases), and 1,410 (76.5%) face-to-face appointments (9.7% did not attend due to fear of getting the infection, 3.1% were lost-to-follow-up, 0.5% were rescheduled due to COVID-19 symptoms and 86.7% who did attend). Of the 1,223 women attending their hospital appointment, 3.6% screened positive at the triage (72.7% rescheduled and 27.3% seen with PPE). 43 rRT-PCR-SARS-CoV2 tests were performed, and two tested positive. No COVID-19 symptoms were reported among health workers at the outpatient obstetric service, and only one nurse presented immunoglobulin (Ig)G anti-SARS-CoV2.
Conclusion
A prompt implementation of a preventive protocol in a hospital obstetric outpatient service, including triage, hygienic and preventive measurements, and rescheduling pregnancy appointments, reduces the percentage of health workers affected by SARS-CoV2.
Pregnant women are especially vulnerable to respiratory diseases. We aimed to study seroconversion rates during pregnancy in a cohort of consecutive pregnancies tested in the first and third ...trimesters and to compare the maternal and obstetric complications in the women who seroconverted in the first trimester and those who did so in the third. This was an observational cohort study carried out at the Hospital Universitario de Torrejón, in Madrid, Spain, during the first peak of the COVID-19 pandemic. All consecutive singleton pregnancies with a viable fetus attending their 11-13-week scan between 1 January and 15 May 2020 were included and seropositive women for SARS-CoV2 were monthly follow up until delivery. Antibodies against SARS-CoV-2 (IgA and IgG) were analyzed on stored serum samples obtained from first- and third-trimester routine antenatal bloods in 470 pregnant women. Antibodies against SARS-CoV-2 were detected in 31 (6.6%) women in the first trimester and in 66 (14.0%) in the third trimester, including 48 (10.2%) that were negative in the first trimester (seroconversion during pregnancy). Although the rate of infection was significantly higher in the third versus the first trimester (
= 0.003), no significant differences in maternal or obstetric complications were observed in women testing positive in the first versus the third trimester.
We present a new lower bound on the Bowen-Radin maximal density of radius-R ball packings in the m-dimensional hyperbolic space, improving on the basic covering bound by factor \Omega(m(R+\ln m)) as ...m tends to infinity. This is done by applying the recent theorem of Campos, Jenssen, Michelen and Sahasrabudhe on independent sets in graphs with sparse neighbourhoods.
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