  In this paper we study structural properties of LV-degrees of the algebra of
collections of sequences that are non-negligible in the sense that they can be
computed by a probabilistic algorithm with positive probability. We construct
atoms and infinitely divisible elements of this algebra generated by sequences,
which cannot be Martin-L\"of random and, moreover, these sequences cannot be
Turing equivalent to random sequences. The constructions are based on the
corresponding templates which can be used for defining the special LV-degrees.
In particular, we present the template for defining atoms of the algebra of
LV-degrees and obtain the decomposition of the maximal LV-degree into a
countable sequence of atoms and their non-zero complement -- infinitely
divisible LV-degree. We apply the templates to establish new facts about
specific LV-degrees, such as the LV-degree of the collection of sequences of
hyperimmune degree. We construct atoms defined by collections of hyperimmune
sequences, moreover, a representation of LV-degree of the collection of all
hyperimmune sequences will be obtained in the form of a union of an infinite
sequence of atoms and an infinitely divisible element.
