Existence, learning, and replication of periodic motions in recurrent neural networks.

A class of recurrent neural networks is shown to possess a stable limit cycle. A gradient type algorithm is used to modify the parameters of the network so that it learns and replicates autonomously a time varying periodic signal. The results are applied to controlling the repetitive motion of a two-link robot manipulator.

Existence and learning of oscillations in recurrent neural networks.

In this paper we study a particular class of -node recurrent neural networks (RNN's). In the 3-node case we use monotone dynamical systems theory to show, for a well-defined set of parameters, that, generically, every orbit of the RNN is asymptotic to a periodic orbit. Then we investigate whether RNN's of this class can adapt their internal parameters so as to "learn" and then replicate autonomously (in feedback) certain external periodic signals. Our learning algorithm is similar to identification algorithms in adaptive control theory. The main feature of the algorithm is that global exponential convergence of parameters is guaranteed. We also obtain partial convergence results in the -node case.

Lung compliance and its transient elevations measured with pulse-flow method.

We describe a pulse-flow method of measuring static lung compliance (CL) that is sensitive to rapid transients in CL. CL is measured by blowing air at a constant flow into the mouth and lungs for 2 s and calculated by dividing airflow in 1/s by the change in transpulmonary pressure in CMH2O/s. Pulse and static inspiratory CL was measured in five normals, four obstructives, five obese, and two patients with pulmonary fibrosis, Pulse CL after tidal breathing was correlated with static CL measured after deep breaths (r = 0.96). Pulse CL after deep breaths was higher than pulse CL after tidal breathing (p less than 0.01) and then static CL after deep breaths (p less than 0.05). In all subjects the lower the forced expiratory volume in 1 s, expressed as a percentage of vital capacity (FEV1/FVC), the greater the increase in pulse CL after a deep breath will be (r = 0.93). After deep breaths pulse CL fell from maximum CL to base-line CL at a rate related to 1/t2 where t equals the time in seconds from the last deep breath. We conclude that the increase in CL after a deep breath is related to the degree of airway obstruction and that the subsequent fall in CL is related to 1/t2.

A pulse method of measuring respiratory system compliance.

We describe a new method of measuring respiratory system compliance (Crs) that appears to detect whether respiratory muscles are relaxed. A pulse airflow, 0.3/s, is blown into the mouth through a pneumotachograph. Mouth pressure is recorded on the abscissa of an oscilloscope. Inflated volume, integrated from the flow signal, is recorded on the ordinate. After an initial step shift of pressure related to the flow resistance of the subject, pressure increases linearly at a rate inversely proportional to Crs. Crs is calculated from the slope of the volume-pressure line. With relaxed subjects, repeated pulses yield straight lines with similar slopes (mean coef of variation = 4.8%). When subjects are not relaxed, the pulse produces irregular lines. In 15 normal subjects who could relax. Crs averaged 0.86 +/- 0.016 (SD) 1/cmH2O. When normalized for body size by dividing by the vital capacity, the mean value was 0.021 +/- 0.0024 cmH2O-1, which agrees with published values. We conclude that the pulse method accurately measures Crs and has the advantage of detecting respiratory muscle relaxation.