Paul Pollack

Learn More
A clinical method for noninvasive measurement of regional cerebral blood flow (rCBF) and blood volume (rCBV) is described, based on Obrist's 10 minute, desaturation method after 1 minute inhalation of 133Xe. Sixteen collimated probes are placed over both hemispheres and brain stem-cerebellar regions. End-tidal 133Xe curves are used for correction of(More)
Fix an integer g = −1 that is not a perfect square. In 1927, Artin conjectured that there are infinitely many primes for which g is a primitive root. Forty years later, Hooley showed that Artin's conjecture follows from the Generalized Riemann Hypothesis (GRH). We inject Hooley's analysis into the Maynard–Tao work on bounded gaps between primes. This leads(More)
We consider the problem of counting the number of (not necessarily monic) 'twin prime pairs' P, P + M ∈ F q [T ] of degree n, where M is a polynomial of degree < n. We formulate an asymptotic prediction for the number of such pairs as q n → ∞ and then prove an explicit estimate confirming the conjecture in those cases where q is large compared with n 2.(More)
A 13-year, 6-month-old female was evaluated for subacute onset of left-sided hemichorea/hemiballismus, with an old, right parietal, cortical, and subcortical stroke as the presumed cause. Treatment with gabapentin was initiated, with good results at 6-month follow-up. Discussion of the differential diagnosis and evaluation of delayed-onset movement(More)
Suppose g ≥ 2. A natural number N is called a repdigit in base g if it has the shape a g n −1 g−1 for some 1 ≤ a < g, i.e., if all of its digits in its base g expansion are equal. The number N is called perfect if σ(N) = 2N , where σ(N) := d|N d is the usual sum of divisors function. We show that in each base g, there are at most finitely many repdigit(More)
Since ancient times, a natural number has been called perfect if it equals the sum of its proper divisors; e.g., 6 = 1+2+3 is a perfect number. In 1913, Dickson showed that for each fixed k, there are only finitely many odd perfect numbers with at most k distinct prime factors. We show how this result, and many like it, follow from embedding the natural(More)
For each positive-integer valued arithmetic function f , let V f ⊂ N denote the image of f , and put V f (x) := V f ∩ [1, x] and V f (x) := #V f (x). Recently Ford, Luca, and Pomerance showed that V φ ∩ V σ is infinite, where φ denotes Euler's totient function and σ is the usual sum-of-divisors function. Work of Ford shows that V φ (x) ≍ V σ (x) as x → ∞.(More)