“Mental illness is not reducible to brain illness, even when mental phenomena have their basis in the brain” (Schramme, 2013, p. 8) and “ . . .because of the normative nature of psychiatry, mental disorder cannot be completely reduced to neuronal or molecular processes. [. . . ] A mental state as such may well be reducible to the brain, but determining whether this very state is (part of) a dis...

We show that a topological space is hereditarily irresolvable if and only if it is Hausdorff-reducible. We construct a compact irreducible T1-space and a connected Hausdorff space, each of which is strongly irresolvable. Furthermore, we show that the three notions of scattered, Hausdorff-reducible, and hereditarily irresolvable coincide for a large class of spaces, including metric, locally com...

We propose an algorithm for deciding whether a given braid is pseudo-Anosov, reducible, or periodic. The algorithm is based on Garside's weighted decomposition and is polynomial-time in the word-length of an input braid. Moreover, a reduction system of circles can be found completely if the input is a certain type of reducible braids. 1. Preliminaries and introduction As a homeomorphism of a 2-...

Considering the network structure is one of the new approaches in studying stochastic PERT networks (SPN). In this paper, planar networks are studied as a special class of networks. Two structural reducible mechanisms titled arc contraction and deletion are developed to convert any planar network to a series-parallel network structure.&#10In series-parallel SPN, the completion time distribution...

Considering the network structure is one of the new approaches in studying stochastic PERT networks (SPN). In this paper, planar networks are studied as a special class of networks. Two structural reducible mechanisms titled arc contraction and deletion are developed to convert any planar network to a series-parallel network structure. In series-parallel SPN, the completion time distribution f...