Fici, Restivo, Silva, and Zamboni define a $k$-antipower to be word composed of $k$ pairwise distinct, concatenated words equal length. Berger Defant conjecture that for any sufficiently well-behaved aperiodic morphic $w$, there exists constant $c$ such index $i$, with block length at most $ck$ starts the $i$th position $w$. They prove their in case binary words, we extend result alphabets arbi...

Let b ≥ 2 be an integer. We prove that the b-ary expansion of every irrational algebraic number cannot have low complexity. Furthermore, we establish that irrational morphic numbers are transcendental, for a wide class of morphisms. In particular, irrational automatic numbers are transcendental. Our main tool is a new, combinatorial transcendence criterion.

The graph isomorphism problem is to determine whether two given graphs are iso-morphic or not. In this paper, we present a new graph invariant, called the probability propagation matrix. By means of this graph invariant, we present a heuristic algorithm for the problem. The algorithm is easy to implement and highly parallelizable.

Quantum theory of self-organization based on the idea that quantum jump serves as the basic step of self-organization, is represented. The notion of self and the identification of self as the fundamental statistical ensemble gives totally new meaning for the concept of selforganization as a generation of hierarchies of selves. Zero modes of the configuration space geometry, whose existence deri...

We show that every binary pattern of length greater than 14 is abelian-2-avoidable. The best known upper bound on the length of abelian-2-unavoidable binary pattern was 118, and the best known lower bound is 7. We designed an algorithm to decide, under some reasonable assumptions, if a morphic word avoids a pattern in the abelian sense. This algorithm is then used to show that some binary patte...