Infinite Monochromatic Sumsets for Colourings of the Reals.

N. Hindman, I. Leader and D. Strauss proved that it is consistent that there is a finite colouring of R so that no infinite sumset X + X is monochromatic. Our aim in this paper is to prove a consistency result in the opposite direction: we show that, under certain set-theoretic assumptions, for any finite colouring c of R there is an infinite X ⊆ R so that c ↾ X + X is constant

Time and Out-of-Pocket Costs Associated with Respiratory Syncytial Virus Hospitalization of Infants

AbstractObjectiveThe objective of this study was to quantify time spent plus out-of-pocket costs associated with confirmed respiratory syncytial virus (RSV) hospitalization of infants not prophylaxed against RSV.MethodsA prospective survey was carried out at multiple tertiary care hospitals in the United States.PatientsThe patients consisted of a consecutive sample of infants <12 months, born between 33 and 35 weeks of gestation. One site also enrolled full-term infants hospitalized with confirmed RSV. Daily patient census identified eligible patients. Consenting caregivers of eligible subjects (n=84, 1 refusal) were interviewed on discharge day and by telephone ∼30 days following discharge regarding time and out-of-pocket costs due to RSV.ResultsTotal average out of pocket expenses were $643.69 (range$21–$16,867; SD$2,403) for premature and $214.42 (range$6–$827; SD$218) (P=.0158) for full-term subjects. Total average economic burden per admission was $4517.07 for premature and$2135.30 for full-term infants, including the value of lost productivity but excluding inpatient hospital and physician bills and lost income. Premature infants (n=48) had longer hospital stays (mean 6.9 days; SD 7.5 vs. 3.4 days; SD 2.6 days) (P=.001) with an associated mean total time spent by up to 5 adults of 281.7 hours (range 25–2819.7 hours; SD 465.8 hours) versus a mean of 139.7 hours (range 31.8–561.3 hours; SD 118.1 hours) for term infants (P=.109). Time and out-of-pocket costs continued after discharge.ConclusionsRSV hospitalization of infants is associated with substantial, previously unmeasured time and monetary losses. These losses continued following discharge. The economic burden on families and society appears heavier for infants born at 33 to 35 weeks of gestation than for full-term infants