The subword complexity of an infinite word counts the number of subwords of a given length, while the abelian complexity counts this number up to letter permutation. Although a lot of research has been done on the subword complexity of morphic words, i.e., words obtained as fixed points of iterated morphisms, little is known on their abelian complexity. In this paper, we undertake the classific...

A thermo-morphic transition of a silicon nanowire (Si-NW) is investigated in vacuum and air ambients, and notable differences are found under each ambient. In the vacuum ambient, permanent electrical breakdown occurs as a result of the Joule self-heating arising from the applied voltage across both ends of the Si-NW. The resulting current abruptly declines from a maximum value at the breakdown ...

The height of an algebraic number in the sense of Diophantine geometry is known to be related to the entropy of an automorphism of a solenoid associated to the number. An el-liptic analogue is considered, which necessitates introducing a notion of entropy for sequences of transformations. A sequence of transformations are defined for which there is a canonical arithmetically defined quotient wh...

Abstract Automatic sequences are not suitable for cryptographic applications since both their subword complexity and expansion small, correlation measure of order 2 is large. These highly predictable despite having a large maximum complexity. However, recent results show that polynomial subsequences automatic sequences, such as the Thue–Morse sequence, better candidates pseudorandom sequences. ...

4 threshold corrections in IIB string theory and (p,q) string instantons. ABSTRACT We obtain the full non-perturbative thresholds of R 4 terms in IIB string theory compactified to eight and seven dimensions. They are given by the perturbative results plus a sum over D-instantons and (p,q) string instantons. The thresholds are shown to be U-duality invariant. They are given by a weight-3/2 non h...

A graph H is called an interpretation of a graph G if a morphic image of H is (isomorphic to) a subgraph of G. A graph H can be seen to be n-colorable iff H is an interpretation of K, (the complete graph on n vertices): hence colorability is a special case of the concept of interpretation. In this paper the complexity of the general coloring problem, i.e., of deciding for a given graph G whethe...