We applied this distance measurement to RR interval time series, each at least 2 hours in length, from 40 ostensibly healthy subjects with subgroups of young (10 females and 10 males, average 25.9 years) and elderly (10 females and 10 males, average 74.5 years), a group of subjects (n = 43) with severe congestive heart failure (CHF) (15 females and 28 males, average 55.5 years) and a group of 9 subjects with atrial fibrillation (AF). We measured the average distance between subjects across different groups. We defined the inter-group distance of groups A and B as the average distance between all pairs of subjects where one subject is from group A and the other subject is from group B. We calculated the inter-group distances among all groups of our time series as well as a group of 100 artificial time series of uncorrelated noise (white noise group).
The method for constructing phylogenetic trees is a useful tool to
present our results since the algorithm arranges different groups on a
branching tree to best fit the pairwise distance measurements. Here we
show the result of a rooted tree for the case of 
.
![\includegraphics[width=4in]{fig3.ps}](img33.png) |
We note that the structure of the tree is consistent with the underlying physiology: the further down the branch the more complex the dynamics are. The groups are arranged in the following order (from bottom to top as shown in the above figure): 1) Time series from the healthy young group represent dynamical fluctuations of a highly complex integrative control system. 2) The healthy elderly group represents deviation from the ``optimal'' youthful state, possibly due to decoupling (or drop-out) of components in the integrative control system. 3) Severe damage to the control system is represented by the CHF group. These individuals have profound abnormalities in cardiac function associated with pathologic alterations in both the sympathetic and parasympathetic control mechanisms that regulate beat-to-beat variability. 4) The AF group is an example of a pathologic state in which there appears to be very limited external input on the heartbeat control system. 5) The artificial white noise group represents the extreme case in that only noise and no signal is present. This example demonstrates that the physiologic complexity of human heart beat dynamics can be robustly described by our information categorization method.
The generic concept underlying the information categorization method makes it applicable to a wide range of problems. Recently, as a further proof of principle application, we applied this approach to address a long-standing authorship debate related to Shakespeare’s plays [2]. This work was featured in the Boston Globe (Aug. 5, 2003) and was the basis for the award-winning entry in the Calvin & Rose G. Hoffman Marlowe Memorial Trust 2003 Prize. In addition to being a new approach to forensic text analysis, this method has potential applications in genetic sequence analysis [3].