Paul Pollack

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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)
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)
  • Abel Castillo, Chris Hall, Robert J Lemke, Oliver, Paul Pollack, Lola Thompson
  • 2014
The Hardy–Littlewood prime k-tuples conjecture has long been thought to be completely unapproachable with current methods. While this sadly remains true, startling breakthroughs of Zhang, Maynard, and Tao have nevertheless made significant progress toward this problem. In this work, we extend the Maynard-Tao method to both number fields and the function(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)
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)
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)