Limit cycles in uniform isochronous centers of discontinuous differential systems with four zones

We apply the averaging theory of first order for discontinuous differential systems to study the bifurcation of limit cycles from the periodic orbits of the uniform isochronous center of the differential systems ẋ = -y+x, y = x + xy, and ẋ = -y + xy, y = x + xy, when they are perturbed inside the class of all discontinuous quadratic and cubic polynomials differential systems with four zones separately by the axes of coordinates, respectively. Using averaging theory of first order the maximum number of limit cycles that we can obtain is twice the maximum number of limit cycles obtained in a previous work for discontinuous quadratic differential systems perturbing the same uniform isochronous quadratic center at origin perturbed with two zones separately by a straight line, and 5 more limit cycles than those achieved in a prior result for discontinuous cubic differential systems with the same uniform isochronous cubic center at the origin perturbed with two zones separately by a straight line. Comparing our results with those obtained perturbing the mentioned centers by the continuous quadratic and cubic differential systems we obtain 8 and 9 more limit cycles respectively

Parental experiences of ultrarapid genomic testing for their critically unwell infants and children

Published online : 28 July 2020PURPOSE:To explore parental experiences of ultrarapid genomic testing for their critically unwell infants and children. METHODS:Parents of critically unwell children who participated in a national ultrarapid genomic diagnosis program were surveyed >12 weeks after genomic results return. Surveys consisted of custom questions and validated scales, including the Decision Regret Scale and Genomics Outcome Scale. RESULTS:With 96 survey invitations sent, the response rate was 57% (n = 55). Most parents reported receiving enough information during pretest (n = 50, 94%) and post-test (n = 44, 83%) counseling. Perceptions varied regarding benefits of testing, however most parents reported no or mild decision regret (n = 45, 82%). The majority of parents (31/52, 60%) were extremely concerned about the condition recurring in future children, regardless of actual or perceived recurrence risk. Parents whose child received a diagnostic result reported higher empowerment. CONCLUSION:This study provides valuable insight into parental experiences of ultrarapid genomic testing in critically unwell children, including decision regret, empowerment, and post-test reproductive planning, to inform design and delivery of rapid diagnosis programs. The findings suggest considerations for pre- and post-test counseling that may influence parental experiences during the testing process and beyond, such as the importance of realistically conveying the likelihood for clinical and/or personal utility.Gemma R. Brett, Melissa Martyn, Fiona Lynch, Michelle G. de Silva, Samantha Ayres, Lyndon Gallacher ... et al