Three Iranian native strains and three Japanese commercial lines of the silkworm Bombyx mori were analyzed using amplified fragment length polymorphism (AFLP) markers. A set of ten PstI/TaqI primer combinations amplified a total of 322 bands out of which 251 (%78) were polymorphic. Estimates of Nei’s gene diversity for all loci in individual strains and commercial lines indicated a higher degre...

In this paper, we suggest to exploit the framework of rough set for detecting outliers — individuals who behave in an unexpected way or feature abnormal properties. The ability to locate outliers can help to maintain knowledge base integrity and to single out irregular individuals. First, we formally define the notions of exceptional set and minimal exceptional set. We then analyze some special...

In three case studies on notions of fuzzy logic and fuzzy set theory (Dubois–Prade’s gradual elements, the entropy of a fuzzy set, and aggregation operators), the paper exemplifies methodological differences between traditional and deductive fuzzy logic. While traditional fuzzy logic admits various interpretations of membership degrees, deductive fuzzy logic always interprets them as degrees of...

We show that for any computably enumerable (c.e.) degree a and any low n–c.e. degree l (n ≥ 1), if l < a, then there are n–c.e. degrees a0,a1 such that l < a0,a1 < a and a0 ∨ a1 = a. In particular, there is no low maximal d.c.e. degree.

We show that there is a strong minimal pair in the computably enumerable Turing degrees, i.e., a pair of nonzero c.e. degrees a and b such that a ∩ b = 0 and for any nonzero c.e. degree x ≤ a, b ∪ x ≥ a.

Let G3−out denote the random graph on vertex set [n] in which each vertex chooses 3 neighbors uniformly at random. Note that G3−out has minimum degree 3 and average degree 6. We prove that the probability that G3−out is Hamiltonian goes to 1 as n tends to infinity.

Let G3−out denote the random graph on vertex set [n] in which each vertex chooses 3 neighbors uniformly at random. Note that G3−out has minimum degree 3 and average degree 6. We prove that the probability that G3−out is Hamiltonian goes to 1 as n tends to infinity.