From Euler's play with infinite series to the anomalous magnetic moment

During a first St. Petersburg period Leonhard Euler, in his early twenties, became interested in the Basel problem: summing the series of inverse squares (posed by Pietro Mengoli in mid 17th century). In the words of Andre Weil (1989) "as with most questions that ever attracted his attention, he never abandoned it". Euler introduced on the way the alternating "phi-series", the better converging companion of the zeta function, the first example of a polylogarithm at a root of unity. He realized - empirically! - that odd zeta values appear to be new (transcendental?) numbers. It is amazing to see how, a quarter of a millennium later, the numbers Euler played with, "however repugnant" this game might have seemed to his contemporary lovers of the "higher kind of calculus", reappeared in the analytic calculation of the anomalous magnetic moment of the electron, the most precisely calculated and measured physical quantity. Mathematicians, inspired by ideas of Grothendieck, are reviving the dream of Galois of uncovering a group structure in the ring of periods (that includes the multiple zeta values) - applied to the study of Feynman amplitudes.Comment: v.2: minor corrections, references adde

Impaired everyday memory associated with encephalopathy of severe malaria: the role of seizures and hippocampal damage.

BACKGROUND: Seizures are common in children admitted with severe falciparum malaria and are associated with neuro-cognitive impairments. Prolonged febrile seizures are associated with hippocampal damage and impaired memory. It was hypothesized that severe malaria causes impaired everyday memory which may be associated with hippocampal damage. METHODS: An everyday memory battery was administered on 152 children with cerebral malaria (CM) (mean age, 7 y 4 months [SD 13 months]; 77 males) 156 children (mean age, 7 y 4 months [SD, 14 months]; 72 males) with malaria plus complex seizures (MS) and 179 children (mean age, 7 y 6 months [SD, 13 months]; 93 males) unexposed to either condition. RESULTS: CM was associated with poorer everyday memory [95% CI, -2.46 to -0.36, p = 0.004] but not MS [95% CI, -0.91 to 1.16, p = 1.00] compared to unexposed children. Children with exposure to CM performed more poorly in recall [95% CI, -0.79 to -0.04, p = 0.024] and recognition subtests [95% CI, -0.90 to -0.17, p = 0.001] but not in prospective memory tests compared to controls. The health factors that predicted impaired everyday memory outcome in children with exposure to CM was profound coma [95% CI, 0.02 to 0.88, p = 0.037] and multiple episodes of hypoglycaemia [95% CI, 0.05 to 0.78, p = 0.020], but not seizures. DISCUSSION: The findings show that exposure to CM was associated with a specific impairment of everyday memory. Seizures commonly observed in severe malaria may not have a causal relationship with poor outcome, but rather be associated with profound coma and repeated metabolic insults (multi-hypoglycaemia) that are strongly associated with impaired everyday memory

Isoelectric Electroencephalography in Infants and Toddlers during Anesthesia for Surgery: An International Observational Study

Background: Intraoperative isoelectric electroencephalography (EEG) has been associated with hypotension and postoperative delirium in adults. This international prospective observational study sought to determine the prevalence of isoelectric EEG in young children during anesthesia. The authors hypothesized that the prevalence of isoelectric events would be common worldwide and associated with certain anesthetic practices and intraoperative hypotension. Methods: Fifteen hospitals enrolled patients age 36 months or younger for surgery using sevoflurane or propofol anesthetic. Frontal four-channel EEG was recorded for isoelectric events. Demographics, anesthetic, emergence behavior, and Pediatric Quality of Life variables were analyzed for association with isoelectric events. Results: Isoelectric events occurred in 32% (206 of 648) of patients, varied significantly among sites (9 to 88%), and were most prevalent during pre-incision (117 of 628; 19%) and surgical maintenance (117 of 643; 18%). Isoelectric events were more likely with infants younger than 3 months (odds ratio, 4.4; 95% CI, 2.57 to 7.4; P < 0.001), endotracheal tube use (odds ratio, 1.78; 95% CI, 1.16 to 2.73; P = 0.008), and propofol bolus for airway placement after sevoflurane induction (odds ratio, 2.92; 95% CI, 1.78 to 4.8; P < 0.001), and less likely with use of muscle relaxant for intubation (odds ratio, 0.67; 95% CI, 0.46 to 0.99; P = 0.046]. Expired sevoflurane was higher in patients with isoelectric events during preincision (mean difference, 0.2%; 95% CI, 0.1 to 0.4; P = 0.005) and surgical maintenance (mean difference, 0.2%; 95% CI, 0.1 to 0.3; P = 0.002). Isoelectric events were associated with moderate (8 of 12, 67%) and severe hypotension (11 of 18, 61%) during preincision (odds ratio, 4.6; 95% CI, 1.30 to 16.1; P = 0.018) (odds ratio, 3.54; 95% CI, 1.27 to 9.9; P = 0.015) and surgical maintenance (odds ratio, 3.64; 95% CI, 1.71 to 7.8; P = 0.001) (odds ratio, 7.1; 95% CI, 1.78 to 28.1; P = 0.005), and lower Pediatric Quality of Life scores at baseline in patients 0 to 12 months (median of differences, -3.5; 95% CI, -6.2 to -0.7; P = 0.008) and 25 to 36 months (median of differences, -6.3; 95% CI, -10.4 to -2.1; P = 0.003) and 30-day follow-up in 0 to 12 months (median of differences, -2.8; 95% CI, -4.9 to 0; P = 0.036). Isoelectric events were not associated with emergence behavior or anesthetic (sevoflurane vs. propofol). Conclusions: Isoelectric events were common worldwide in young children during anesthesia and associated with age, specific anesthetic practices, and intraoperative hypotension

Difficult or impossible facemask ventilation in children with difficult tracheal intubation: a retrospective analysis of the PeDI registry

BackgroundDifficult facemask ventilation is perilous in children whose tracheas are difficult to intubate. We hypothesised that certain physical characteristics and anaesthetic factors are associated with difficult mask ventilation in paediatric patients who also had difficult tracheal intubation.MethodsWe queried a multicentre registry for children who experienced "difficult" or "impossible" facemask ventilation. Patient and case factors known before mask ventilation attempt were included for consideration in this regularised multivariable regression analysis. Incidence of complications, and frequency and efficacy of rescue placement of a supraglottic airway device were also tabulated. Changes in quality of mask ventilation after injection of a neuromuscular blocking agent were assessed.ResultsThe incidence of difficult mask ventilation was 9% (483 of 5453 patients). Infants and patients having increased weight, being less than 5th percentile in weight for age, or having Treacher-Collins syndrome, glossoptosis, or limited mouth opening were more likely to have difficult mask ventilation. Anaesthetic induction using facemask and opioids was associated with decreased risk of difficult mask ventilation. The incidence of complications was significantly higher in patients with "difficult" mask ventilation than in patients without. Rescue placement of a supraglottic airway improved ventilation in 71% (96 of 135) of cases. Administration of neuromuscular blocking agents was more frequently associated with improvement or no change in quality of ventilation than with worsening.ConclusionsCertain abnormalities on physical examination should increase suspicion of possible difficult facemask ventilation. Rescue use of a supraglottic airway device in children with difficult or impossible mask ventilation should be strongly considered