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 specifity 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 aredeterministic, and thus are moreaccurate 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.     

Low-dimensional chaos maps learning in a model neuropil (olfactory bulb)

Quantification of a chaotic system can be made by calculating the correlation dimension (D2) of the data that the system generates (Packard et al., 1980). The D2 algorithm, however, requires stationarity of the generator, a feature that biological data rarely reflect (Mayer-Kress et al., 1988). So we developed the “point correlation dimension” (PD2), an algorithm that accurately tracks D2 in linked data of different dimensions (Carpeggiani et al., 1991). We now present a mathematical argument that, for stationary data, individual PD2s converge to D2 and we demonstrate that the algorithm rejects contributions made by bursts of noise. Data were obtained from the surface of the olfactory bulb of the conscious rabbit (64 electrodes, 640 Hz each, 1.3 sec epochs) before and after presentation of a novel or habituated odor. D2 could be calculated in only 1 of 10 novel-odor trials, whereas PD2 could be calculated in all. Both algorithms indicated that a novel odor evokes a spatially uniform dimensional increase. The PD2 uniquely exhibited the dimensional decreases that occur during inspiration and the gradients of mean dimension present during the nonstimulated control state. These control gradients remained unchanged without odor experience, but showed spatially specific PD2 increases following odor habituation. It is interpreted that, 1) the PD2 issensitive, accurate, and appropriate for dimensional assessment of biological data, 2) that during analysis of unfamiliar information a singleglobal process is transiently evoked in the neuropil, and 3) after experience multiplespatially specific processes tonically map the sites of learning. Grant Support: National Institutes of Health, HL 31164 and NS27745     

Neighborhood frequency effects and letter visibility in visual word recognition

Two experiments are described that measured lexical decision latencies and errors to five-letter French words with a single higher frequency orthographic neighbor and control words with no higher frequency neighbors. The higher frequency neighbor differed from the stimulus word by either the second letter (e.g.,astre-autre) or the fourth letter (chope-chose). Neighborhood frequency effects were found to interact with this factor, and significant interference was observed only tochope-type words. The effects of neighborhood frequency were also found to interact with the position of initial fixation in the stimulus word (either the second letter or the fourth letter). Interference was greatly reduced when the initial fixation was on the critical disambiguating letter (i.e., the letterp inchope). Moreover, word recognition was improved when subjects initially fixated the second letter relative to when they initially fixated the fourth letter of a five-letter word, but this second-letter advantage practically disappeared when the stimulus differed from a more frequent word by its fourth letter. The results are interpreted in terms of the interaction between visual and lexical factors in visual word recognition.     

Increasing the intelligibility of speech through multiple phonemic restorations

Outside of the laboratory, listening conditions are often less than ideal, and when attending to sounds from a particular source, portions are often obliterated by extraneous noises. However, listeners possess rather elegant reconstructive mechanisms. Restoration can be complete, so that missing segments are indistinguishable from those actually present and the listener is unaware that the signal is fragmented. This phenomenon, called temporal induction (TI), has been studied extensively with nonverbal signals and to a lesser extent with speech. Earlier studies have demonstrated that TI can produce illusory continuity spanning gaps of a few hundred milliseconds when portions of a signal are replaced by a louder sound capable of masking the signal were it actually present. The present study employed various types of speech signals with periodic gaps and measured the effects upon intelligibility produced by filling these gaps with noises. Enhancement of intelligibility through multiple phonemic restoration occurred when the acoustic requirements for TI were met and when sufficient contextual information was available in the remaining speech fragments. It appears that phonemic restoration is a specialized form of TI that uses linguistic skills for the reconstruction of obliterated speech.     

On axiomatization of many-valued logics associated with formalization of plausible reasonings

This paper studies a class of infinite-valued predicate logics. A sufficient condition for axiomatizability of logics from that class is given.To the memory of Jerzy Supecki     

Context effects in stroop-like word and picture processing

Presents a series of 6 experiments in which Stroop-like effects were generated by modally pure color-color, picture-picture, and word-word stimuli instead of the usual modally mixed color-word or picture-word stimuli. Naming, reading, and categorization tasks were applied. The Stroop inhibition was preserved with these stimuli but unexpectedly showed a semantic gradient only in the naming and not in the reading task. Word categorizing was slower and more interference prone than picture categorizing. These and other results can be captured by a model with two main assumptions: (a) semantic memory and the lexicon are separate, and (b) words have privileged access to the lexicon, whereas pictures and colors have privileged access to the semantic network. Such a model is developed and put to an initial test.     

Parent attributions of emotion to their children and the cues children use in perceiving their own emotions

A number of studies have demonstrated stable individual differences in the cues that generate emotions and other feeling states. These differences are assumed to arise from the cues parents use to identify their children's emotional states. As children learn about their own emotional states, they come to rely on these same cues. To test one implication of their view, the facial expressions of children (N=41) were manipulated and their feelings assessed. Some children reported emotions consistent with their expressions, while others reported emotions appropriate to the situation. In a separate procedure, their mothers were asked to identify the emotional states of children whose expressions were inconsistent with an account of their circumstances. Mothers who paid more attention to their children's expressive behavior had children who were more responsive to their own expressive behavior. In contrast, the mothers who were more responsive to situational cues had children whose emotions arose from the situational cues as well.The authors would like to thank numerous teachers and administrators of the Worcester Public School system in Worcester, Massachusetts, for their assistance.     

Spatial frequencies and the cerebral hemispheres: contrast sensitivity, visible persistence, and letter classification

The hypothesis that the two cerebral hemispheres are specialized for processing different visual spatial frequencies was investigated in three experiments. No differences between the left and right visual fields were found for: (1) contrast-sensitivity functions measured binocularly with vertical gratings ranging from 0.5 to 12 cycles per degree (cpd); (2) visible persistence durations for 1- and 10-cpd gratings measured with a stimulus alternation method; and (3) accuracy (d') and reaction times to correctly identify digitally filtered letters as targets (L or H) or nontargets (T or F). One significant difference, however, was found: In Experiment 3, a higher decision criterion (beta) was used when filtered letters were identified in the right visual field than when they were identified in the left. The letters were filtered with annular, 1-octave band-pass filters with center spatial frequencies of 1, 2, 4, 8, and 16 cpd. Combining four center frequencies with three letter sizes (0.5 degrees, 1 degree, and 2 degrees high) made some stimuli equivalent in distal spatial frequency (cycles per object) and some equivalent in proximal spatial frequency (cycles per degree). The effective stimulus in the third experiment seemed to be proximal spatial frequency (cycles per degree) not distal (cycles per object). We conclude that each cerebral hemisphere processes visual spatial frequency information with equal accuracy but that different decision rules are used.     

Attention deficit disorder with hyperactivity and methylphenidate: The effects of dose and mastery level on children's learning performance

This investigation examined the relationship between methylphenidate (MPH) and the learning and recall of paired associations by children with attention deficit disorder with hyperactivity (ADDH). Forty-five children with ADDH were randomly assigned to one of three groups (novel, partial mastery, and mastery learning) that varied in the amount of previous learning of paired associations and participated in a double-blind, placebo-control, repeated-measures-across-dose (crossover) design. Each child received four doses of MPH (5 mg, 10 mg, 15 mg, and 20 mg) and a placebo in a random, counterbalanced sequence. The results indicated that both the rate of acquisition and accuracy in learning paired associations were significantly, but differentially, affected by MPH dose and the degree of learning mastery. The implications of these results for psychopharmacological research and the monitoring of psychostimulant effects on children's learning performance in academic settings are discussed.The authors wish to acknowledge and express their sincere appreciation to the graduate and undergraduate student members of the Children's Learning Clinic.