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We provide a comprehensive presentation of algorithms, data structures, and implementation techniques for high-performance sparse multivariate polynomial arithmetic over the integers and rational numbers as implemented in the freely available Basic Polynomial Algebra Subprograms (BPAS) library. We report on an algorithm for sparse pseudo-division, based on the algorithms for division with remainder, multiplication, and addition, which are also examined herein. The pseudo-division and division with remainder operations are extended to multi-divisor pseudo-division and normal form algorithms, respectively, where the divisor set is assumed to form a triangular set. Our operations make use of two data structures for sparse distributed polynomials and sparse recursively viewed polynomials, with a keen focus on locality and memory usage for optimized performance on modern memory hierarchies. Experimentation shows that these new implementations compare favorably against competing implementations, performing between a factor of 3 better (for multiplication over the integers) to more than 4 orders of magnitude better (for pseudo-division with respect to a triangular set).

Objectives: The aim of this study was to evaluate whether intraoperative ciprofloxacin-soaked gelfoam is safe in tympanoplasty or not.Method: In this randomized, double-blind controlled clinical study, we included 100 patients between 18 and 60 years old, having perforation ≥50% of the tympanic membrane and dry ear for at least 2 months who were a candidate for underlay tympanoplasty via postauricular approach. We used ciprofloxacin soaked gelfoam in the case group and betamethasone soaked gelfoam in the control group for packing the middle ear cavity and external auditory canal during their operation. The graft success rate and tympanogram after 6 months follow-up period was considered as the primary outcome. Also, we evaluated the postoperative hearing results 6 months after the surgery as the secondary outcomes.Results: Postoperative microscopic otoscopy showed a graft success rate of 100% (44/44) and 97.7% (42/43) in the case and control groups, respectively. The level of improvement between the two groups was not significant for air-bone gap (ciprofloxacin: 9.01 ± 7.89 dB, betamethasone 5.31 ± 10.53 dB, P = .160), and speech reception thresholds (SRT; ciprofloxacin: 10.23 ± 8.62 dB, betamethasone 7.33 ± 12.60 dB, P = .260). 93.2% of all the ears in the case group and 81.4% of those in the control group achieved postoperative air-bone gap within 20 dB, but the difference between them was not significant (P = .118). Conclusions:We found that the application of ciprofloxacin impregnated gelfoam in the middle ear, and the external auditory canal had no adverse effect on the graft success rate in tympanoplasty. Levels of evidence: 1b.

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