A Fast Algorithm for Determining the Existence and Value of Integer Roots of N

We show that all perfect odd integer squares not divisible by 3, can be usefully written as sqrt(N) = a + 18p, where the constant a is determined by the basic properties of N. The equation can be solved deterministically by an efficient four step algorithm that is solely based on integer arithmetic. There is no required multiplication or division by multiple digit integers, nor does the algorithm need a seed value. It finds the integer p when N is a perfect square, and certifies N as a non-square when the algorithm terminates without a solution. The number of iterations scales approximately as log(sqrt(N)/2) for square roots. The paper also outlines how one of the methods discussed for squares can be extended to finding an arbitrary root of N. Finally, we present a rule that distinguishes products of twin primes from squares.Comment: 12 pages, 8 figure

Fault Tolerant, Radiation Hard, High Performance Digital Signal Processor

An architecture has been developed for a high performance VLSI digital signal processor that is highly reliable, fault tolerant and radiation hard. The signal processor, part of a spacecraft receiver designed to support uplink radio science experiments at the outer planets, organizes the connections between redundant arithmetic resources, register files and memory through a shuffle exchange communication network. The configuration of the network and the state of the processor resources are all under microprogram control which both maps the resources according to algorithmic needs and reconfigures the processing should a failure occur. In addition, the microprogram is reloadable through the uplink to accommodate changes in the science objectives throughout the course of the mission. The processor will be implemented with silicon compiler tools and its design will be verified through silicon compilation simulation at all levels from the resources to full functionality. By blending reconf..

Oxygen targets and 6-month outcome after out of hospital cardiac arrest: a pre-planned sub-analysis of the targeted hypothermia versus targeted normothermia after Out-of-Hospital Cardiac Arrest (TTM2) trial

International audienceAbstract Background Optimal oxygen targets in patients resuscitated after cardiac arrest are uncertain. The primary aim of this study was to describe the values of partial pressure of oxygen values (PaO 2 ) and the episodes of hypoxemia and hyperoxemia occurring within the first 72 h of mechanical ventilation in out of hospital cardiac arrest (OHCA) patients. The secondary aim was to evaluate the association of PaO 2 with patients’ outcome. Methods Preplanned secondary analysis of the targeted hypothermia versus targeted normothermia after OHCA (TTM2) trial. Arterial blood gases values were collected from randomization every 4 h for the first 32 h, and then, every 8 h until day 3. Hypoxemia was defined as PaO 2  300 mmHg. Mortality and poor neurological outcome (defined according to modified Rankin scale) were collected at 6 months. Results 1418 patients were included in the analysis. The mean age was 64 ± 14 years, and 292 patients (20.6%) were female. 24.9% of patients had at least one episode of hypoxemia, and 7.6% of patients had at least one episode of severe hyperoxemia. Both hypoxemia and hyperoxemia were independently associated with 6-month mortality, but not with poor neurological outcome. The best cutoff point associated with 6-month mortality for hypoxemia was 69 mmHg (Risk Ratio, RR = 1.009, 95% CI 0.93–1.09), and for hyperoxemia was 195 mmHg (RR = 1.006, 95% CI 0.95–1.06). The time exposure, i.e., the area under the curve (PaO 2 -AUC), for hyperoxemia was significantly associated with mortality ( p = 0.003). Conclusions In OHCA patients, both hypoxemia and hyperoxemia are associated with 6-months mortality, with an effect mediated by the timing exposure to high values of oxygen. Precise titration of oxygen levels should be considered in this group of patients. Trial registration : clinicaltrials.gov NCT02908308 , Registered September 20, 2016

Ventilatory settings in the initial 72 h and their association with outcome in out-of-hospital cardiac arrest patients: a preplanned secondary analysis of the targeted hypothermia versus targeted normothermia after out-of-hospital cardiac arrest (TTM2) trial

International audienc