We introduce the notion of \partial Occam algorithm". A partial Occam algorithm produces a succinct hypothesis that is partially consistent with given examples, where the proportion of consistent examples is a bit more than half. By using this new notion, we propose one approach for obtaining a PAC learning algorithm. First, as shown in this paper, a partial Occam algorithm is equivalent to a w...

For set functors preserving intersections, a new description of the final coalgebra and the initial algebra is presented: the former consists of all well-pointed coalgebras. These are the pointed coalgebras having no proper subobject and no proper quotient. And the initial algebra consists of all well-pointed coalgebras that are well-founded in the sense of Taylor [16]. Finally, the initial ite...

Esik and Maletti introduced the notion of a proper semiring and proved that some important (classes of) semirings – Noetherian semirings, natural numbers – are proper. Properness matters as the equivalence problem for weighted automata over a semiring which is proper and finitely and effectively presented is decidable. Milius generalised the notion of properness from a semiring to a functor. As...

An arc-colored digraph D is properly (properly-walk) connected if, for any ordered pair of vertices (u,v), the contains a directed path (a walk) from u to v such that arcs adjacent on (on have distinct colors. The proper connection number pc→(D) (the proper-walk wc→(D)) minimum colours make (properly-walk connected). We prove pc→(Cn(S))≤2 every circulant Cn(S) with S⊆{1,…,n−1},|S|≥2 and 1∈S. Fu...

We show that if a locally compact group G acts properly on a locally compact σ-compact space X, then there is a family of G-invariant proper continuous finite-valued pseudometrics which induces the topology of X. If X is, furthermore, metrizable, then G acts properly on X if and only if there exists a G-invariant proper compatible metric on X.

one of the important discussions in islamic fiqh and usul (jurisprudence), is the issue of going farther verified religious text (nass), as well as the ways of discovering the reason of a commandment. it seems that this subject has not yet reached its proper place in shi’i fiqh. while imami jurists use some methods to go farther the commandment of the nass, including one named “discovering the ...