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

@article{citeulike:672143, abstract = {10.1073/pnas.0510673103 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 \^{a}€œwindow of attention,\^{a}€ 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 \^{a}€œconcepts\^{a}€ that are relevant to the text. As the reader follows a text, the \^{a}€œvector of attention\^{a}€ traces out a trajectory of directions in this \^{a}€œconcept space.\^{a}€ 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\^{a}€™s memory in reenacting some of the multidimensionality of the thoughts being expressed.}, author = {Alvarez-Lacalle, E. and Dorow, B. and Eckmann, J. P. and Moses, E.}, citeulike-article-id = {672143}, citeulike-linkout-0 = {http://dx.doi.org/10.1073/pnas.0510673103}, citeulike-linkout-1 = {http://www.pnas.org/content/103/21/7956.abstract}, citeulike-linkout-2 = {http://www.pnas.org/content/103/21/7956.full.pdf}, citeulike-linkout-3 = {http://www.pnas.org/cgi/content/abstract/103/21/7956}, citeulike-linkout-4 = {http://view.ncbi.nlm.nih.gov/pubmed/16698933}, citeulike-linkout-5 = {http://www.hubmed.org/display.cgi?uids=16698933}, day = {23}, doi = {10.1073/pnas.0510673103}, journal = {PNAS}, keywords = {attention, correlation, law, power, svd, text, trajectory}, month = {May}, number = {21}, pages = {7956--7961}, posted-at = {2006-05-27 16:12:57}, priority = {3}, title = {Hierarchical structures induce long-range dynamical correlations in written texts}, url = {http://dx.doi.org/10.1073/pnas.0510673103}, volume = {103}, year = {2006} }

TY - JOUR ID - citeulike:672143 L3 - citeulike-article-id:672143 N2 - 10.1073/pnas.0510673103 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. IS - 21 JF - PNAS EP - 7961 TI - Hierarchical structures induce long-range dynamical correlations in written texts VL - 103 SP - 7956 KW - attention KW - correlation KW - law KW - power KW - svd KW - text KW - trajectory AU - Alvarez-Lacalle, E AU - Dorow, B AU - Eckmann, JP AU - Moses, E PY - 2006/05/23/ UR - http://dx.doi.org/10.1073/pnas.0510673103 ER -