Basins of attraction for cascading maps

We study a finite uni-directional array of "cascading" or "threshold coupled" chaotic maps. Such systems have been proposed for use in nonlinear computing and have been applied to classification problems in bioinformatics. We describe some of the attractors for such systems and prove general results about their basins of attraction. In particular, we show that the basins of attraction have infinitely many path components. We show that these components always accumulate at the corners of the domain of the system. For all threshold parameters above a certain value, we show that they accumulate at a Cantor set in the interior of the domain. For certain ranges of the threshold, we prove that the system has many attractors.Comment: 15 pages, 9 figures. To appear in International Journal of Bifurcations and Chao

Examining the efficacy of six published time-lapse imaging embryo selection algorithms to predict implantation to demonstrate the need for the development of specific, in-house morphokinetic selection algorithms.

OBJECTIVE: To study the efficacy of six embryo-selection algorithms (ESAs) when applied to a large, exclusive set of known implantation embryos. DESIGN: Retrospective, observational analysis. SETTING: Fertility treatment center. PATIENT(S): Women undergoing a total of 884 in vitro fertilization (IVF) or intracytoplasmic sperm injection (ICSI) treatment cycles (977 embryos) between September 2014 and September 2015 with embryos cultured using G-TL (Vitrolife) at 5% O2, 89% N2, 6% CO2, at 37°C in EmbryoScope instruments. INTERVENTION(S): None. MAIN OUTCOME MEASURE(S): Efficacy of each ESA to predict implantation defined using specificity, sensitivity, positive predictive value (PPV), negative predictive value (NPV), area under the receiver operating characteristic curve (AUC), and likelihood ratio (LR), with differences in implantation rates (IR) in the categories outlined by each ESA statistically analyzed (Fisher's exact and Kruskal-Wallis tests). RESULT(S): When applied to an exclusive cohort of known implantation embryos, the PPVs of each ESA were 42.57%, 41.52%, 44.28%, 38.91%, 38.29%, and 40.45%. The NPVs were 62.12%, 68.26%, 71.35%, 76.19%, 61.10%, and 64.14%. The sensitivity was 16.70%, 75.33%, 72.94%, 98.67%, 51.19%, and 62.33% and the specificity was 85.83%, 33.33%, 42.33%, 2.67%, 48.17%, and 42.33%, The AUC were 0.584, 0.558, 0.573, 0.612, 0.543, and 0.629. Two of the ESAs resulted in statistically significant differences in the embryo classifications in terms of IR. CONCLUSION(S): These results highlight the need for the development of in-house ESAs that are specific to the patient, treatment, and environment. These data suggest that currently available ESAs may not be clinically applicable and lose their diagnostic value when externally applied

Preliminary investigation of the prevalence and implantation potential of abnormal embryonic phenotypes assessed using time-lapse imaging.

This retrospective, single site observational study aimed to delineate five abnormal embryonic developmental phenotypes, assessing their prevalence, development potential and suitability for inclusion in embryo selection models for IVF. In total, 15,819 embryos from 4559 treatment cycles cultured in EmbryoScope® incubators between January 2014 and January 2016 were included. Time-lapse images were assessed retrospectively for five abnormal embryo phenotypes: direct cleavage, reverse cleavage, absent cleavage, chaotic cleavage and cell lysis. The prevalence of each abnormal phenotype was assessed. Final embryo disposition, embryo quality and implantation rate were determined and compared with a control embryo cohort. The collective prevalence for the five abnormal phenotypes was 11.4%; chaotic cleavage and direct cleavage together constituted 9.7%. Implantation rates were 17.4%, 0%, 25%, 2.1% and 0% for direct, reverse, absent, chaotic cleavage and cell lysis, respectively. The overall implantation rate for all abnormal embryos with known implantation status was significantly lower compared with the control population (6.9% versus 38.7%, P < 0.0001). The proportion of good quality embryos in each category of abnormal cleavage remained below 25%. Embryos exhibiting an abnormal phenotype may have reduced developmental capability, manifested in both embryo quality and implantation potential, when compared with embryos of normal phenotype

A Geometric Approach to Stationary Defect Solutions in One Space Dimension

Analysis and Stochastic

Lin's method for heteroclinic chains involving periodic orbits

We present an extension of the theory known as Lin's method to heteroclinic chains that connect hyperbolic equilibria and hyperbolic periodic orbits. Based on the construction of a so-called Lin orbit, that is, a sequence of continuous partial orbits that only have jumps in a certain prescribed linear subspace, estimates for these jumps are derived. We use the jump estimates to discuss bifurcation equations for homoclinic orbits near heteroclinic cycles between an equilibrium and a periodic orbit (EtoP cycles)

Clomifene citrate or low-dose FSH for the first-line treatment of infertile women with anovulation associated with polycystic ovary syndrome : a prospective randomized multinational study

BACKGROUND: Clomifene citrate (CC) is accepted as the first-line method for ovulation induction (OI) in patients with polycystic ovary syndrome (PCOS) associated with infertility owing to anovulation. Low-dose FSH has been reserved for women failing to conceive with CC. In this RCT, we tested the hypothesis that pregnancy rate (PR) and live birth rates (LBR) are higher after OI with low-dose FSH than with CC as first-line treatment. METHODS: Infertile women (<40 years old) with PCOS-related anovulation, without prior OI treatment, attending 10 centres in Europe/South America were randomized to OI with either CC (50-150 mg/day for 5 days) or FSH (starting dose 50 IU) for up to three treatment cycles. The primary outcome was clinical PR. RESULTS: Patients (n = 302) were randomized to OI with FSH (n = 132 women; 288 cycles) or CC (n = 123; 310 cycles). Per protocol analysis revealed that reproductive outcome was superior after OI with FSH than with CC with respect to PR per first cycle [30 versus 14.6%, respectively, 95 confidence interval (CI) 5.3-25.8, P = 0.003], PR per woman, (58 versus 44% of women, 95% CI 1.5-25.8, P = 0.03), LBR per woman (52 versus 39%, 95% CI 0.4-24.6, P = 0.04), cumulative PR (52.1 versus 41.2%, P = 0.021) and cumulative LBR (47.4 versus 36.9%, P = 0.031), within three cycles of OI. CONCLUSIONS: Pregnancies and live births are achieved more effectively and faster after OI with low-dose FSH than with CC. This result has to be balanced by convenience and cost in favour of CC. FSH may be an appropriate first-line treatment for some women with PCOS and anovulatory infertility, particularly older patients.peer-reviewe

Retrospective observational RT-PCR analyses on 688 babies born to 843 SARS-CoV-2 positive mothers, placental analyses and diagnostic analyses limitations suggest vertical transmission is possible

Research question: Is there vertical transmission (from mother to baby antenatally or intrapartum) after SARS-CoV-2 (COVID-19) infected pregnancy? Study design: A systematic search related to SARS-CoV-2 (COVID-19), pregnancy, neonatal complications, viral and vertical transmission. The duration was from December 2019 to May 2020. Results: A total of 84 studies with 862 COVID positive women were included. Two studies had ongoing pregnancies while 82 studies included 705 babies, 1 miscarriage and 1 medical termination of pregnancy (MTOP). Most publications (50/84, 59.5%), reported small numbers (&lt;5) of positive babies. From 75 studies, 18 babies were COVID-19 positive. The first reverse transcription polymerase chain reaction (RT-PCR) diagnostic test was done in 449 babies and 2 losses, 2nd RT-PCR was done in 82 babies, IgM tests were done in 28 babies, and IgG tests were done in 28 babies. On the first RT-PCR, 47 studies reported time of testing while 28 studies did not. Positive results in the first RT-PCR were seen in 14 babies. Earliest tested at birth and the average time of the result was 22 hours. Three babies with negative first RT-PCR became positive on the second RT-PCR at day 6, day 7 and at 24 hours which continued to be positive at 1 week. Four studies with a total of 4 placental swabs were positive demonstrating SARS-CoV-2 localised in the placenta. In 2 studies, 10 tests for amniotic fluid were positive for SARS-CoV-2. These 2 babies were found to be positive on RT-PCR on serial testing. Conclusion: Diagnostic testing combined with incubation period and placental pathology indicate a strong likelihood that intrapartum vertical transmission of SARS-CoV-2 (COVID-19) from mother to baby is possible

Binding Energy of Charged Excitons in ZnSe-based Quantum Wells

Excitons and charged excitons (trions) are investigated in ZnSe-based quantum well structures with (Zn,Be,Mg)Se and (Zn,Mg)(S,Se) barriers by means of magneto-optical spectroscopy. Binding energies of negatively () and positively (X+) charged excitons are measured as functions of quantum well width, free carrier density and in external magnetic fields up to 47 T. The binding energy of shows a strong increase from 1.4 to 8.9 meV with decreasing quantum well width from 190 to 29 A. The binding energies of X+ are about 25% smaller than the binding energy in the same structures. The magnetic field behavior of and X+ binding energies differ qualitatively. With growing magnetic field strength, increases its binding energy by 35-150%, while for X+ it decreases by 25%. Zeeman spin splittings and oscillator strengths of excitons and trions are measured and discussed