• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.547-562
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• 2011

We establish a new formalism of the non-periodic autocorrelation function (NPAF) of two sequences, which is suitable for the computation of the NPAF of any two sequences. It is shown, that this encoding of NPAF is efficient for sequences of small weight. In particular, the check for two sequences of length n having weight w to have zero NPAF can be decided in $O(n+w^2{\log}w)$. For n > w^2{\log}w$, the complexity is O(n) thus we cannot expect asymptotically faster algorithms.

• Maxillofacial Plastic and Reconstructive Surgery
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• v.20 no.3
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• pp.250-255
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• 1998

The purpose of this study was to evaluate the histologic change of the inferior alveolar nerve according to distraction amount following mandibular lengthening. Seven rabbits weighing about 2 kg were used. Corticotomy was performed on the mandibular body anterior to the right first premolar region and unilateral external fixation device was placed. Every effort was made to preserve the inferior alveolar nerve during the corticotomy. The rabbits were then allowed to heal for 7 days without distraction of the device. The mandible was lengthened 0.36 mm/day, 0.76 mm/day, or 1.0 mm/day. Corticotomy and lengthening of mandible were not performed in control group. After the completion of the lengthening process, a 14-day-consolidation period was allowed. After consolidation, rabbits were sacrificed, and histologic examination of the inferior alveolar nerve was performed. The results obtained were as follows : 1. In the control group, normal trifascicular pattern of inferior alveolar nerve was observed. Epineurium, perineurium, endoneurium, and axon with myelin sheath were observed in normal appearance. 2. In 0.36 mm/day distraction group, the trifascicular pattern was normally shown, and there was no destruction in epineurium, perineurium, and endoneurium. The mild changes including myelin attenuation, axoplasmic swelling and darkening were observed. 3. In 0.72 mm/day distraction group, it was possible to differentiate the epineurium from the perineurium. Two normal fascicles and one injuried fascicle were observed with a partially destructed perineurium. Most of the axons had axoplasmic swelling and darkening. 4. In 1 mm/day distraction group, it was difficult to differentiate the nerve structures such as fascicles, epineurium, perineurium, and endoneurium. The axons were severely destroyed, except few which showed decreases in size and changes in shape. Some collagen matrices were observed around the axons. These results suggest that the higher the distraction amount, the more severe the injury to the inferior alveolar nerve, fascicles, axons. Although distraction osteogenesis may be useful, the amount of distraction should be carefully selected.