It is not hard to write a first order formula which is true for a given graph G but is false for any graph not isomorphic to G. The smallest number D(G) of nested quantifiers in a such formula can serve as a measure for the “first order complexity” of G. Here, this parameter is studied for random graphs. We determine it asymptotically when the edge probability p is constant; in fact, D(G) is of...

Acoustic differences between the vowels in filled pauses and ordinary lexical items such as nouns and verbs were examined to know if there was systematic difference of voice-quality. Statistical test of material taken from the Corpus of Spontaneous Japanese showed that, in most cases, there was significant difference of acoustic features like F0, F1, F2, intensity, jitter, shimmer, TL, H1-H2, H...

Quantum information spreading and scrambling in many-body systems attract interest these days. Tripartite mutual (TMI) based on operator-based entanglement entropy (EE) is an efficient tool for measuring them. In this paper, we study random spin chains that exhibit phase transitions accompanying nontrivial changes topological properties. their diagrams, there are two types of localized (MBL) st...