`HP's 2008 memristor paper in Nature used M(q)=ROFF(1-mvRON/D^2 q) where ROFF, RON are the off and on resistances, mv is the ionic mobility of oxygen vacancies, D is the film thickness and q is charge.   Regarding the more general idea beyond magnetic flux this is usually associated with Chua and Kang's 1976 paper on memristive systems which used a dynamic systems definition rather then the ``fourth fundamental circuit element`` memristor definition. In reality most real materials exhibiting memristive effects obey the 1976 dynamic system definition but have nothing to do with the 1971 magnetic flux definition. My opinion is that HP has used the 1971 definition more for marketing purposes then for any real technical merit.   Regarding negative memristance, one of the proven mathematical properties of memristive systems is that they are passive and do not produce energy. Thus if there are devices having some properties similar to a memristor but which produce (or amplify) energy it would not be formally describable as a memristor or a memristive system. This is one reason why it is unlikely for memristors to replace transistors since they are incapable of performing signal amplification on their own.    `