Jacek M. Kowalski

Layered neural networks with Gaussian hidden units as universal approximations

A neural network with a single layer of hidden units of gaussian type is proved to be a universal approximator for real-valued maps defined on convex, compact sets of Rn.

Original Contribution: Neuronal networks with spontaneous, correlated bursting activity: Theory and simulations

A model of spontaneously active biological neuronal networks is proposed where each component neuron is an excitable dynamical unit of the Hodgkin-Huxley (HH) type described by a system of ordinary differential equations. Neurotransmitter fluxes are additional state variables in such networks and the action of chemical synapses is modelled by additional kinetic equations. Networks composed of intrinsically inactive units may ignite to one or more correlated bursting patterns. These transitions can be described as bifurcations governed by interaction parameters. Stability problems and classes of synchronized solutions are studied. Networks of this type exhibit rich dynamics (multiple attractors), including the possibility of synchronized chaotic activity. Biological and information processing applications are reviewed and some open mathematical problems are indicated.

Slope analysis of Auditory Brainstem Responses in children at risk of central auditory processing disorders.

The method of slope vectors was used to quantify Auditory Brainstem Responses (ABR) obtained from nine normal children and nine children at risk for central auditory processing disorders (CAPD) with language impairment, for monaural and binaural stimulation conditions. Slopes thus obtained were subjected to K-Means Cluster Analysis. Distinction between the two groups was obtained only for binaural stimulation conditions, wherein all normal children were grouped under cluster 1 with higher slope values and 6 out of 9 CAPD children were grouped under cluster 2 with lower slopes. The results suggest that there may be several subcategories among children who are found to be at risk for CAPD. One of the subcategories may comprise children who exhibit poor ABR morphology, especially during binaural stimulation conditions, which could be due to binaural interference.

DYNAMICS OF BURST PATTERNS GENERATED BY MONOLAYER NETWORKS IN CULTURE

Publisher Summary Over the past few decades, cross-fertilization between the fields of neurophysiology, physics, mathematics, and computer science has helped in the complex efforts to understand the mechanisms used by the central nervous system and has provided a wealth of challenging theoretical problems. On the engineering side, neuronally inspired models and devices have proved themselves very useful in applied pattern recognition and robotics. Artificial neural nets are used commercially for complex technological processes and for providing rapid solutions to optimization problems. This chapter explains how very simple neuronal networks, composed of only a few hundred neurons, can be complicated and dynamically rich. The main challenge is to better control and understand this dynamics at the cellular and ensemble level with emphasis on the emerging network properties. It is also essential to supplement pharmacological manipulations with electrical stimulation of increasing pattern complexity at single electrodes and on a spatial pattern of electrodes. The observed richness of the dynamical repertoire of small neuronal networks serves a definite purpose in living systems, and such studies may become a possible source of inspiration for yet another generation of hardware devices and computing algorithms.

Emergent dynamical properties of biological neuronal ensembles and their theoretical interpretation and significance

New culturing and recording techniques allow long-term, real-time, and multisite monitoring of spontaneous and evoked spike activity from small neuronal networks grown from dissociated embryonic mouse CNS tissue. These systems, typically composed of several hundred neurons, generate complex spatio-temporal spike and burst patterns and exhibit interesting dynamical properties that are generally non-linear and non-stationary with a multitude of inter-state transitions. We have observed network self-activation (or “ignition”) to bursting states; complex oscillatory bursting as a basic activity mode of a cellular group; simple, regular oscillations during disinhibition; transient synchronization or approximate phase-locking within active groups; dynamical recruitment with spike frequency-dependent activation of additional neurons and their incorporation into a common network pattern; and dynamical competition among different active cell groups. In addition to providing a rich test-bed for the application of n...

Dynamical instabilities in a CO2 laser with an externally modulated optical feedback

CO2 lasers are very sensitive to optical feedback and can be driven into a large variety of dynamical states by an external modulation of the feedback parameters. We report on the experimental results concerning instabilities of CO2 lasers induced by either an additional passive resonator of periodically varying geometrical length or an refractive index modulation in the external cavity by an electro- optical modulator. Experimental results show the presence of stable periodic orbits of different periods, bistability of periodic orbits and chaotic attractors with complex transition scenarios.

Studying chaos in carbon-dioxide lasers in a graduate level optical laboratory

Carbon-dioxide lasers are well-known example of optical systems, which can exhibit complex transitions from the CW to the chaotic regime in the intensity caused by the modulation of various systems parameters. They can demonstrate classical bifurcation scenarios with period doubling, bistability, and chaotic attractors. We report on a new method of observing chaos in carbon-dioxide lasers where the simple technique of modulation of the optical feedback parameters is applied. In this approach the parameters of the carbon-dioxide laser itself remain unchanged and modulation is carried out externally. This leads to a system which can be easily assembled and studied in a graduate laboratory. Experimental results show the presence of stable periodic orbits of different periods, bistability of periodic orbits and chaotic attractors with complex transition scenarios, providing a wealth of examples for the student to investigate.