The current treatments of inverse functions suffer from two deficiencies. The first is simply confusion of notation, with different standard reference works using different, and contradictory, conventions. The second deficiency is the way in which the multivalued nature of the functions is handled. A new approach is offered here which addresses both problems. A new notation is proposed that mak...

The canalizing properties of biological functions have been mainly studied in the context Boolean modelling gene regulatory networks. An important mathematical consequence canalization is a low average sensitivity, which ensures particular expected robustness to noise. In certain situations, description too crude, and it may be necessary consider involving more than two levels expression. We in...

In the present paper‎, ‎we introduce the concept of generalized multivalued $F$ -‎contraction mappings and give a fixed point result‎, ‎which is a proper‎ ‎generalization of some multivalued fixed point theorems including Nadler's‎.

This work introduces collected size semantics of strict functional programs over lists. The collected size semantics of a function definition is a multivalued size function that collects the dependencies between every possible output size and the corresponding input sizes. Such functions annotate standard types and are defined by conditional rewriting rules generated during type inference. We f...