a b s t r a c tWe give an algorithm for the interpolation of a polynomial A given by a straight-line program. Its complexity is polynomial in τ , log(d), L, n, where τ is an input bound on the number of terms in A, d is a bound on its partial degree in all variables, L is the length of the given straight-line program and n is the number of variables.

The “Dolomite Problem” has been a controversy for over a century, owing to massive assemblages of low-temperature dolomite in ancient rocks with little dolomite forming today despite favorable geochemical conditions. Experiments show that microbes and their exopolymeric substances (EPS) nucleate dolomite. However, factors controlling ancient abundances of dolomite can still not be explained. To decode the enigma of ancient dolomite, we examined a modern dolomite forming environment, and found that a cyclic shift in microbial community between cyanobacteria and anoxygenic phototrophs creates EPS suited to dolomite precipitation. Specifically, EPS show an increased concentration of carboxylic functional groups as microbial composition cycles from cyanobacterial to anoxygenic phototroph driven communities at low-and high- salinity, respectively. Comparing these results to other low-T forming environments suggests that large turnover of organic material under anoxic conditions is an important driver of the process. Consequently, the shift in atmospheric oxygen throughout Earth’s history may explain important aspects of “The Dolomite Problem”. Our results provide new context for the interpretation of dolomite throughout Earth’s history.

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EdentulousComplete denture a b s t r a c t Clinical implication: The purpose of this study is to record the vertical distance between anterior attachment of lingual frenum and incisal edge of mandibular central incisors in dentulous subjects and then determine the mean vertical distance and to suggest guidelines for positioning of mandibular central incisors in complete dentures. Method: In this study, 150 dentulous subjects (75 males and 75 females) were chosen based on predecided inclusion criteria. A mandibular cast was obtained from irreversible hydrocolloid impression in modified stock trays for each subject. All subjects were instructed to elevate the tongue while the impressions were made. The vertical distance between the anterior attachment of the lingual frenum and incisal edges of mandibular central incisors was measured on the casts and then the values were statistically analyzed. Result: The distance between anterior attachment of lingual frenum (AALF) mesioincisal edge of mandibular central incisor (CI) in male, female and total (male þ female) subjects was measured. In males it ranged from 7.3 to 8.9 mm with mean (±SD) 8.29 ± 0.36 mm while in females it ranged from 7.1 to 9.0 mm with mean (±SD) 8.21 ± 0.38 mm. Conclusion: It is believed that the application of this anatomic relation can provide a reliable point for arranging and checking the position of the mandibular central incisors for complete dentures in patients with class I ridge relationship.