Nonlinear oscillations in discrete and continuous systems

The first thesis topic is a perturbation method for resonantly coupled nonlinear oscillators. By successive near-identity transformations of the original equations, one obtains new equations with simple structure that describe the long time evolution of the motion. This technique is related to two-timing in that secular terms are suppressed in the transformation equations. The method has some important advantages. Appropriate time scalings are generated naturally by the method, and don't need to be guessed as in two-timing. Furthermore, by continuing the procedure to higher order, one extends (formally) the time scale of valid approximation. Examples illustrate these claims. Using this method, we investigate resonance in conservative, non-conservative and time dependent problems. Each example is chosen to highlight a certain aspect of the method.

The second thesis topic concerns the coupling of nonlinear chemical oscillators. The first problem is the propagation of chemical waves of an oscillating reaction in a diffusive medium. Using two-timing, we derive a nonlinear equation that determines how spatial variations in the phase of the oscillations evolves in time. This result is the key to understanding the propagation of chemical waves. In particular, we use it to account for certain experimental observations on the Belusov-Zhabotinskii reaction.

Next, we analyse the interaction between a pair of coupled chemical oscillators. This time, we derive an equation for the phase shift, which measures how much the oscillators are out of phase. This result is the key to understanding M. Marek's and I. Stuchl's results on coupled reactor systems. In particular, our model accounts for synchronization and its bifurcation into rhythm splitting.

Finally, we analyse large systems of coupled chemical oscillators. Using a continuum approximation, we demonstrate mechanisms that cause auto-synchronization in such systems.

Neural representation of auditory temporal structure

Neurons in the songbird forebrain nucleus HVc are highly sensitive to auditory temporal context and have some of the most complex auditory tuning properties yet discovered. HVc is crucial for learning, perceiving, and producing song, thus it is important to understand the neural circuitry and mechanisms that give rise to these remarkable auditory response properties. This thesis investigates these issues experimentally and computationally.

Extracellular studies reported here compare the auditory context sensitivity of neurons in HV c with neurons in the afferent areas of field L. These demonstrate that there is a substantial increase in the auditory temporal context sensitivity from the areas of field L to HVc. Whole-cell recordings of HVc neurons from acute brain slices are described which show that excitatory synaptic transmission between HVc neurons involve the release of glutamate and the activation of both AMPA/kainate and NMDA-type glutamate receptors. Additionally, widespread inhibitory interactions exist between HVc neurons that are mediated by postsynaptic GABA_A receptors. Intracellular recordings of HVc auditory neurons in vivo provides evidence that HV c neurons encode information about temporal structure using a variety of cellular and synaptic mechanisms including syllable-specific inhibition, excitatory post-synaptic potentials with a range of different time courses, and burst-firing, and song-specific hyperpolarization.

The final part of this thesis presents two computational approaches for representing and learning temporal structure. The first method utilizes comput ational elements that are analogous to temporal combination sensitive neurons in HVc. A network of these elements can learn using local information and lateral inhibition. The second method presents a more general framework which allows a network to discover mixtures of temporal features in a continuous stream of input.

Primary cosmic-ray positrons and negatrons in 1968 at energies between 11 and 204 MeV

The cosmic-ray positron and negatron spectra between 11 and 204 MeV have been measured in a series of 3 high-altitude balloon flights launched from Fort Churchill, Manitoba, on July 16, July 21, and July 29, 1968. The detector system consisted of a magnetic spectrometer utilizing a 1000-gauss permanent magnet, scintillation counters, and a lucite Čerenkov counter.

Launches were timed so that the ascent through the 100 g/cm² level of residual atmosphere occurred after the evening geomagnetic cutoff transition. Data gathered during ascent are used to correct for the contribution of atmospheric secondary electrons to the flux measured at float altitude. All flights floated near 2.4 g/cm².

A pronounced morning intensity increase was observed in each flight. We present daytime positron and negatron data which support the interpretation of the diurnal flux variation as a change in the local geomagnetic cutoff. A large diurnal variation was observed in the count rate of positrons and negatrons with magnetic rigidities less than 11 MV and is evidence that the nighttime cutoff was well below this value.

Using nighttime data we derive extraterrestrial positron and negatron spectra. The positron-to-total-electron ratio which we measure indicates that the interstellar secondary, or collision, source contributes ≾50 percent of the electron flux within this energy interval. By comparing our measured positron spectrum with the positron spectrum calculated for the collision source we derive the absolute solar modulation for positrons in 1968. Assuming negligible energy loss during modulation, we derive the total interstellar electron spectrum as well as the spectrum of directly accelerated, or primary, electrons. We examine the effect of adiabatic deceleration and find that many of the conclusions regarding the interstellar electron spectrum are not significantly altered for an assumed energy loss of up to 50 percent of the original energy.

Identification and characterization of the egg-laying hormone from the neurosecretary bag cells of Aplysia

This investigation has resulted in the chemical identification and isolation of the egg-laying hormone from Aplysia californica, Aplysia vaccaria, and Aplysia dactylomela. The hormone, which was originally identified as the Bag Cell-Specific protein (BCS protein) on polyacrylamide gels, is a polypeptide of molecular weight ≈ 6000, which is localized in the neurosecretory bag cells of the parietovisceral ganglion and the surrounding connective tissue sheath which contains the bag cell axons. All three species produce a hormone of similar molecular weight, but varying electrophoretic mobility as determined on polyacrylamide gels. As tested, the hormone is completely cross-reactive among the three species.

Although the bag cells of sexually immature animals contain the active hormone, sexual maturation of the animal results in a 10-fold increase in the BCS protein content of these neurons.

A seasonal variation in the BCS protein content was also observed, with 150 times more hormone contained in the bag cells of Aplysia californica in August than in January. This correlates well with the variation in the animals' ability to lay eggs throughout the year (Strumwasser et al., 1969). There are some indications that the receptivity of the animal to the available hormone also fluctuates during the year, being lower in winter than in swmner. The seasonal rhythm of the other species, Aplysia vaccaria and Aplysia dactylomela, has not been investigated.

A polyacrylamide gel electrophoresis analysis of water-soluble proteins in Aplysia californica revealed several other nerve-specific proteins. One of these is also located in the bag cell somas and stains turquoise with Amido Schwarz. The function of this protein has not been investigated.

Circadian clock mutants of Drosophila melanogaster

Three mutants of Drosophila melanogaster have been isolated in which the free-running period of the circadian eclosion rhythm and the adult locomotor activity rhythm is affected. One mutant is arrhythmic, another has a short period of 19 hours, and the third has a long period of 28 hours. The mutants retain their phenotypes over the temperature range 18° to 25° C. All three mutants map near the tip of the X chromosome (distal to the centromere). By deficiency mapping, the short-period mutation has been localized to the 3B1-2 region. Complementation tests show that all three mutations affect the same functional gene.

Analysis of activity rhythms of individual mosaic flies indicates that the site of action of the short-period mutation is probably located in the head of the fly. A few activity patterns of split-head and mixed-head mosaics appear to possess both mutant and heterozygous components, suggesting that the fly head may contain two complete clocks capable of maintaining their periodicities independently.

The short-period mutation affects both the duration of the light-insensitive part of the oscillation and the degree to which the clock can be reset during the light-sensitive part of the oscillation.

Both the short-period and long-period mutant eclosion rhythms can be entrained to a period of 24 hours by a 12:12 light-dark cycle having a light intensity at least two orders of magnitude greater than that required to entrain the normal rhythm. The arrhythmic mutant does not entrain under these conditions. In the presence of a temperature cycle, however, the arrhythmic mutant does entrain, but its rhythm damps out when the temperature cycle is removed.

Evidence is presented that Pittendrigh's two-oscillator model for the clock in D. pseudoobscura applies to D. melanogaster as well. The three clock mutations primarily affect the light- sensitive driving oscillator. The arrhythmic mutation appears to have eliminated the driving oscillator while leaving the temperature-sensitive driven oscillator relatively intact.