Application of chaos theory to biology and medicine.

The application of "chaos theory" to the physical and chemical sciences has resolved some long-standing problems, such as how to calculate a turbulent event in fluid dynamics or how to quantify the pathway of a molecule during Brownian motion. Biology and medicine also have unresolved problems, such as how to predict the occurrence of lethal arrhythmias or epileptic seizures. The quantification of a chaotic system, such as the nervous system, can occur by calculating the correlation dimension (D2) of a sample of the data that the system generates. For biological systems, the point correlation dimension (PD2) has an advantage in that it does not presume stationarity of the data, as the D2 algorithm must, and thus can track the transient non-stationarities that occur when the systems changes state. Such non-stationarities arise during normal functioning (e.g., during an event-related potential) or in pathology (e.g., in epilepsy or cardiac arrhythmogenesis). When stochastic analyses, such as the standard deviation or power spectrum, are performed on the same data they often have a reduced sensitivity and specificity compared to the dimensional measures. For example, a reduced standard deviation of heartbeat intervals can predict increased mortality in a group of cardiac subjects, each of which has a reduced standard deviation, but it cannot specify which individuals will or will not manifest lethal arrhythmogenesis; in contrast, the PD2 of the very same data can specify which patients will manifest sudden death. The explanation for the greater sensitivity and specificity of the dimensional measures is that they are deterministic, and thus are more accurate in quantifying the time-series. This accuracy appears to be significant in detecting pathology in biological systems, and thus the use of deterministic measures may lead to breakthroughs in the diagnosis and treatment of some medical disorders.     

Improving assignment preference through interspersing additional problems: Brief versus easy problems

College students were exposed to a control mathematics assignment containing 16 three-digit by two-digit multiplication (3×2) problems and two experimental assignments that contained 16 equivalent 3×2 problems and six additional interspersed problems. On one experimental assignment, 4-digit plus 4-digit problems (4+4) were interspersed. On the other experimental assignment, 2-digit divided by 1-digit with whole number answers problems (2/1) were interspersed. When given a choice, significantly more students choose the 2/1 assignment over the control and 1+4 assignment. Students also ranked the 2/1 sheet as requiring less time to complete than the control or 4+4 assignment but no differences were found on assignment difficulty rankings between the 4+4 and 2/1 assignments. No differences were found on accuracy levels or rates of responding on the target 3×2 problems across assignments. Results showed that interspersing additional problems that take relatively less time to complete may be more important for altering student preference for assignments than interspersing easier problems. Discussion focuses on schedules of reinforcement and resource efficient procedures for increasing student preference for assignment without compromising curricula integrity.     

Application of chaos theory to a model biological system: Evidence of self-organization in the intrinsic cardiac nervous system

The neural organization that determines the specific beat-to-beat pattern of cardiac behavior is expected to be demonstrated in the independent regulation of the RR intervals (chronotropy) and the corresponding QT subintervals (inotropy), as the former defines the rate of contraction and the latter has a linear negative correlation with the peak pressure inside the contracting ventricular muscles. The neurons of the isolated cardiac nervous system, many of which are located in the fat-pads of the heart, exhibit the same types of mechanical and chemical receptors and the same types of cholinergic and noradrenergic effectors as those found in the neural superstructure. In the surgically isolated and perfused rabbit heart we studied the responses of the QT and RR intervals evoked by block of coronary blood flow. We found that if we separated each RR cycle into QT and RR-QT components, then the dynamics of variation for each subinterval series often had the same fractional number of degrees of freedom (i.e., chaotic dimensions), a finding which suggests they are both regulated by the same underlying system. The ischemia/anoxia evoked transient dimensional increases and separations between the two subinterval series that, after the temporary divergence, reconverged to having the same lower value. The dimensional fluctuations occurred repeatedly and preceded or coincided with alterations in the magnitude and sign of the slope of QT vs RR-QT. We interpret the dimensional fluctuations of the two subinterval series as correlates of adaptation-dependent self-organization and reorganization in the underlying intrinsic cardiac nervous system during accumulating ischemia/anoxia. Such attempts at functional reorganization in this simple neurocardiac system may explain the transient dimensional changes in the RR intervals that precedes by 24 hrs the occurrences of fatal ventricular fibrillation in high-risk cardiac patients.     

EFFECTS OF HIGH-PREFERENCE SINGLE-DIGIT MATHEMATICS PROBLEM COMPLETION ON MULTIPLE-DIGIT MATHEMATICS PROBLEM PERFORMANCE

The purpose of this study was to examine the effects of a sequence of three single-digit (1 digit × 1 digit) multiplication problems on the latency to initiate multiple-digit (3 digit × 3 digit) multiplication problems for 2 students in an alternative education school. Data showed that (a) during the preference assessment, both students selected the single-digit problems in a majority of the sessions, and (b) intervention resulted in a decrease in latency between problems for both students. Results are discussed in relation to using high-preference sequences to promote behavioral momentum in academic content areas.     

THE EFFECTS OF ORAL PRESENTATION PREVIEWING RATES ON READING PERFORMANCE

A multielement design was used to compare the effects of rapid oral presentation and slow oral presentation during listening previewing on rates of accurate oral rereading. The participants were 2 elementary students with reading skills deficits. For both students, rates of accurate oral rereading were higher when adults reduced their oral reading rates as students read silently.     

The Effects of Response Repetitions on Sight Word Acquisition for Students with Mild Disabilities

Single response learning trials, defined in terms of the three-term contingency model, were compared with repeated response learning trials. The purpose of Study 1 was to assess the effectiveness and efficiency of single and repeated response learning trials on sight word remediation. In Study 1, one single response learning trial having one response opportunity per word was compared to one repeated response learning trial having five response opportunities. In Study 2, three single response trials were compared to three repeated response trials. In both studies, the training conditions were compared using an alternating treatments design. Measuring the cumulative number of sight words mastered showed the training conditions equally effective. However, measuring (a) the mean duration of training sessions, (b) the cumulative frequency of words mastered per session duration, (c) the mean number of training sessions per word required for mastery, and (d) the training time per mastered word showed that the single response condition was more efficient. Discussion focuses on the need to include training data when determining best practices for teaching.