Hierarchical structures induce long-range dynamical correlations in written texts.

Thoughts and ideas are multidimensional and often concurrent, yet they can be expressed surprisingly well sequentially by the translation into language. This reduction of dimensions occurs naturally but requires memory and necessitates the existence of correlations, e.g., in written text. However, correlations in word appearance decay quickly, while previous observations of long-range correlations using random walk approaches yield little insight on memory or on semantic context. Instead, we study combinations of words that a reader is exposed to within a "window of attention," spanning about 100 words. We define a vector space of such word combinations by looking at words that co-occur within the window of attention, and analyze its structure. Singular value decomposition of the co-occurrence matrix identifies a basis whose vectors correspond to specific topics, or "concepts" that are relevant to the text. As the reader follows a text, the "vector of attention" traces out a trajectory of directions in this "concept space." We find that memory of the direction is retained over long times, forming power-law correlations. The appearance of power laws hints at the existence of an underlying hierarchical network. Indeed, imposing a hierarchy similar to that defined by volumes, chapters, paragraphs, etc. succeeds in creating correlations in a surrogate random text that are identical to those of the original text. We conclude that hierarchical structures in text serve to create long-range correlations, and use the reader's memory in reenacting some of the multidimensionality of the thoughts being expressed.

The topological relationship between the large-scale attributes and local interaction patterns of complex networks.

Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the underlying reasons for the variable quantity of different subgraph types, their propensity to form clusters, and their relationship with the networks' global organization remain poorly understood. Here we show that a network's large-scale topological organization and its local subgraph structure mutually define and predict each other, as confirmed by direct measurements in five well studied cellular networks. We also demonstrate the inherent existence of two distinct classes of subgraphs, and show that, in contrast to the low-density type II subgraphs, the highly abundant type I subgraphs cannot exist in isolation but must naturally aggregate into subgraph clusters. The identified topological framework may have important implications for our understanding of the origin and function of subgraphs in all complex networks.