Algorithmic construction of Lyapunov functions for continuous vector fields via convex semi-infinite programs

This article presents a novel numerically tractable technique for synthesizing Lyapunov functions for equilibria of nonlinear vector fields. In broad strokes, corresponding to an isolated equilibrium point of a given vector field, a selection is made of a compact neighborhood of the equilibrium and a dictionary of functions in which a Lyapunov function is expected to lie. Then an algorithmic procedure based on the recent work [DACC22] is deployed on the preceding neighborhood-dictionary pair and charged with the task of finding a function satisfying a compact family of inequalities that defines the behavior of a Lyapunov function on the selected neighborhood. The technique applies to continuous nonlinear vector fields without special algebraic structures and does not even require their analytical expressions to proceed. Several numerical examples are presented to illustrate our results.Comment: 26 pages. Submitte

SARS-CoV-2 specific antibody and neutralization assays reveal the wide range of the humoral immune response to virus.

Development of antibody protection during SARS-CoV-2 infection is a pressing question for public health and for vaccine development. We developed highly sensitive SARS-CoV-2-specific antibody and neutralization assays. SARS-CoV-2 Spike protein or Nucleocapsid protein specific IgG antibodies at titers more than 1:100,000 were detectable in all PCR+ subjects (n = 115) and were absent in the negative controls. Other isotype antibodies (IgA, IgG1-4) were also detected. SARS-CoV-2 neutralization was determined in COVID-19 and convalescent plasma at up to 10,000-fold dilution, using Spike protein pseudotyped lentiviruses, which were also blocked by neutralizing antibodies (NAbs). Hospitalized patients had up to 3000-fold higher antibody and neutralization titers compared to outpatients or convalescent plasma donors. Interestingly, some COVID-19 patients also possessed NAbs against SARS-CoV Spike protein pseudovirus. Together these results demonstrate the high specificity and sensitivity of our assays, which may impact understanding the quality or duration of the antibody response during COVID-19 and in determining the effectiveness of potential vaccines

Luteoma of pregnancy associated with nearly complete virilization of genetically female twins

Objective: To describe a pregnancy that was complicated by the virilization of the mother and two 46XX infants.Methods: We outline the clinical presentation and diagnosis of the virilization of a mother and her twins, reviewing pertinent literature.Results: We report the case of a 40-year-old Caucasian female who conceived a trichorionic triplet pregnancy through in vitro fertilization (IVF) but underwent cytoreduction at 13 weeks of gestation, leaving a diamniotic dichorionic twin pregnancy. At 16 weeks of gestation the mother experienced increasing acne, facial hair, and deepening of her voice. Due to preeclampsia, the twins were delivered via caesarean section at 33 weeks of gestation. The infants had male-appearing external genitalia (Prader score IV-V) but no palpable gonads. Congenital adrenal hyperplasia was ruled out for both twins and they were both found to have a uterus and a 46XX karyotype. Maternal testosterone level was elevated at birth (1,981 ng/dL), but the infants had normal levels. Maternal testosterone levels returned to normal after delivery, consistent with a luteoma of pregnancy, although imaging was negative for a mass.Conclusion: This is the second reported case of complete virilization associated with a luteoma of pregnancy. Whether or not IVF and related procedures increase the risk for a luteoma and whether or not fetal reduction procedures disrupt placental aromatases and increase the risk of virilization in the face of elevated androgen levels are questions that require further research

Colon Necrosis Due to Sodium Polystyrene Sulfonate with and without Sorbitol: An Experimental Study in Rats

<div><p>Introduction</p><p>Based on a single rat study by Lillemoe et al, the consensus has been formed to implicate sorbitol rather than sodium polystyrene sulfonate (SPS) as the culprit for colon necrosis in humans treated with SPS and sorbitol. We tested the hypothesis that colon necrosis by sorbitol in the experiment was due to the high osmolality and volume of sorbitol rather than its chemical nature.</p><p>Methods</p><p>26 rats underwent 5/6 nephrectomy. They were divided into 6 groups and given enema solutions under anesthesia (normal saline, 33% sorbitol, 33% mannitol, SPS in 33% sorbitol, SPS in normal saline, and SPS in distilled water). They were sacrificed after 48 hours of enema administration or earlier if they were very sick. The gross appearance of the colon was visually inspected, and then sliced colon tissues were examined under light microscopy.</p><p>Results</p><p>1 rat from the sorbitol and 1 from the mannitol group had foci of ischemic colonic changes. The rats receiving SPS enema, in sorbitol, normal saline, distilled water, had crystal deposition with colonic necrosis and mucosal erosion. All the rats not given SPS survived until sacrificed at 48 h whereas 11 of 13 rats that received SPS in sorbitol, normal saline or distilled water died or were clearly dying and sacrificed sooner. There was no difference between sorbitol and mannitol when given without SPS.</p><p>Conclusions</p><p>In a surgical uremic rat model, SPS enema given alone or with sorbitol or mannitol seemed to cause colon necrosis and high mortality rate, whereas 33% sorbitol without SPS did not.</p></div