Toward a quantitative characterization of patient-therapist communication.

The efficacy of psychotherapy, in its many and varied forms, is one of the most intensely contested issues in clinical practice. Though many theories have been advanced, quantitative evidence in their defense is limited. This contribution is directed to relatively unambitious objectives. Rather than establish yet another qualitative theory of psychotherapeutic practice, we wish to contribute to the construction of research methodologies that can quantitatively characterize the dynamic patterns of patient-therapist communication. It is hoped that a theoretical understanding of psychotherapy might eventually emerge naturally from a growing body of quantitative data.

Dynamics of brain electrical activity.

In addition to providing important theoretical insights into chaotic deterministic systems, dynamical systems theory has provided techniques for analyzing experimental data. These methods have been applied to a variety of physical and chemical systems. More recently, biological applications have become important. In this paper, we report applications of one of these techniques, estimation of a signal's correlation dimension, to the characterization of human electroencephalographic (EEG) signals and event-related brain potentials (ERPs). These calculations demonstrate that the magnitude of the technical difficulties encountered when attempting to estimate dimensions from noisy biological signals are substantial. However, these results also suggest that this procedure can provide a partial characterization of changes in cerebral electrical activity associated with changes in cognitive behavior that complements classical analytic procedures.

Periodic metabolic systems: oscillations in multiple-loop negative feedback biochemical control networks.

For a general multiple loop feedback inhibition system in which the end product can inhibit any or all of the intermediate reactions it is shown that biologically significant behaviour is always confined to a bounded region of reaction space containing a unique equilibrium. By explicit construction of a Liapunov function for the general n dimensional differential equation it is shown that some values of reaction parameters cause the concentration vector to approach the equilibrium asymptotically for all physically realizable initial conditions. As the parameter values change, periodic solutions can appear within the bounded region. Some information about these periodic solutions can be obtained from the Hopf bifurcation theorem. Alternatively, if specific parameter values are known a numerical method can be used to find periodic solutions and determine their stability by locating a zero of the displacement map. The single loop Goodwin oscillator is analysed in detail. The methods are then used to treat an oscillator with two feedback loops and it is found that oscillations are possible even if both Hill coefficients are equal to one.