Keith Flint, 1969–2019

Keith Simmons

Computer scientists use formal verification to attempt to provide guarentees to the users of software about the run time characteristics of a given program. Verification techniques today often require a TCB or Trusted Code Base which due to time or effort constraints, the authors were not able to prove correct. When bugs occure in these pieces, they break down the strong guarentees of formal ve...

Glomerulonephritis Keith

Early diagnosis of glomerulonephritis (GN) in the adolescent is important in initiating appropriate treatment and controlling chronic glomerular injury that may eventually lead to end-stage renal disease (ESRD). The spectrum of GN in adolescents is more similar to that seen in young and middle-aged adults than to that observed in prepubertal children. In this article, the authors discuss the cl...

Joseph Marshall Flint

NTL vs FLINT

All tests were carried out on a very lightly loaded machine with a 64-bit Intel “Haswell” CPU (Intel Xeon CPU E5-2698 v3 at 2.30GHz) with plenty of memory (over 250GB). The operating system was Cent OS. The compiler was gcc v4.8.5. We compared NTL v9.9.1 with FLINT v2.5.2. These were both built using GMP v6.1.0. All of these were the most recent releases of these packages at the time we carried...

Counting Keith numbers

A Keith number is a positive integer N with the decimal representation a1a2 . . . an such that n ≥ 2 and N appears in the sequence (Km)m≥1 given by the recurrence K1 = a1, . . . ,Kn = an and Km = Km−1 + Km−2 + · · · + Km−n for m > n. We prove that there are only finitely many Keith numbers using only one decimal digit (i.e., a1 = a2 = · · · = an), and that the set of Keith numbers is of asympto...