What are biominerals and how are they formed? It is usually assumed: (i) that the prototype for most apatitic biominerals is hydroxyapatite (OHAp), Ca5(PO4)3OH; and (ii) that the OHAp structure has been modified by the presence of impurity ions and vacancy defects in specific OHAp lattice sites. The usual answer, at least implicitly, to the second question is that the apatitic mineral is formed...

The resource-bounded measures of complexity classes are shown to be robust with respect to certain changes in the underlying probability measure. Speci cally, for any real number > 0, any uniformly polynomial-time computable sequence ~ = ( 0; 1; 2; : : : ) of real numbers (biases) i 2 [ ; 1 ], and any complexity class C (such as P, NP, BPP, P/Poly, PH, PSPACE, etc.) that is closed under positiv...