The Freeman Laboratory for Nonlinear Neurodynamics
Department of Molecular & Cell Biology
Division of Neurobiology, Donner 101
University of California at Berkeley
Berkeley CA 94720-3206 USA
Our aim is to understand the ways in which the immense numbers of neurons in the human brain cooperate and coordinate their activities in creating intelligent behavior. We use recordings of the action potentials and electric field potentials in animals and scalp EEG from human volunteers to get the data we need to build theories of brain function. We use the brain theory to design and refine the electrode arrays that are necessary to observe and measure the spatial patterns of neural activity that create and control intentional behavior. We apply the optimized brain theory broadly in clinical, industrial, scientific and philosophical settings to such classic tasks as biologically motivated pattern recognition, navigation of autonomous robots, neural correlates of consciousness, epileptic seizure modeling and prediction, and the uses of brain imaging to understand the neural mechanisms of perception, cognition, and creativity in constructing representations of meaning.
Our group develops data-driven brain theory by analysis of action potentials and brain waves (electroencephalograms, EEG, local field potentials, LFP) recorded with high-density electrode arrays fixed on or in animal and human subjects who are engaged in goal-directed behavior. We use the theory to design data processing algorithms that enhance the spatial and temporal resolution of the textures of brain activity patterns that we find in three-layered paleocortex and six-layered neocortex. We maximize the neural correlates of behavior using our optimized measurements of the spatiotemporal patterns of amplitude modulation and phase modulation in the beta and gamma frequency ranges of the EEG. We find that these spatial AM patterns and PM patterns repeat at frequencies in the theta and alpha ranges.
Using the optimized data patterns we construct a hierarchy of models of cortical nonlinear neurodynamics: Katchalsky sets ("K sets"). We regard the optimized spatiotemporal EEG patterns from high-density arrays as projections of activity from infinite-dimensional brain state space into a finite n-space defined by the n-dimensions of our electrode arrays. We use nonlinear mapping and multidimensional scaling into 2-space to identify itinerant chaotic trajectories through sequences of nonconvergent attractor ruins in the attractor landscapes of brain state space. The attractors are created and modified by reinforcement learning based on classical and operant conditioning. Neural modeling includes demonstrations of the neural mechanisms that ensure in all cortices the stability of neural populations that supports rapid and widespread state transitions by virtue of small-world and scale-free network architecture. Neocortex is unique among cortices in maintaining global self-organized criticality, in which the critical order parameter is the global level of neural synaptic interaction that everywhere locally is homeostatically regulated by neural thresholds and refractory periods. We use our K sets to model neural instabilities that underlie the onset of epileptic seizures and may enable new methods for seizure prediction.
We use our brain theory to analyze and model neural mechanisms of perception following sensation and of category learning ("Aha!" learning by abstraction) as distinct from generalization gradients. A major discovery is evidence that cortical self-organized criticality creates a pseudo-equilibrium in brain dynamics, that lets us model cortical mesoscopic state transitions as analogous to phase transitions in near-equilibrium nonliving systems like boiling or condensing water. Using the Hilbert transform we show that each state transition has 4 stages: a 1st order phase transition that resets the phase of beta-gamma EEG oscillations in a discontinuity of the cortical dynamics; pattern selection in the attractor landscape by phase re-synchronization in n-space; a 2nd order phase transition that leads to pattern stabilization by dramatic decrease in the rate of change in the order parameter; and then high-energy pattern broadcast over divergent-convergent axonal cortical output pathways, during which the rate of free energy dissipation is maximized. The ratio of rate of free energy dissipation to the rate of change in order parameter defines the pragmatic information, which is maximized during cortical transmission. The power-law and fractal distributions of EEG parameters enable us to display the scale-free dynamics of cortex as macroscopic cortical state transitions, that at times cover an entire cerebral hemisphere almost instantaneously even in humans, and that we propose as the neural mechanism that forms Gestalts (unified multisensory percepts).
Applications of our K-sets include clinical and industrial settings. We use the KI set to analyze local homeostasis that ensures the stability of neural populations. The KII set serves to model 1st order state transitions as Hopf bifurcations and allows us to embody the dynamics of neural populations in VLSI hardware, The KIII set is a powerful and versatile device that serves for pattern classification using the chaotic attractors with fractal basins of attraction as our memory bank in adaptive landscapes to capture the effectiveness of biological pattern recognition. We use the KIV set modeling the limbic system to design and build command and control systems for guidance of navigation and decision-making by autonomous robots in complex environments. At present we are developing the KV set as an instrument to analyze the properties of neocortex in human perception. This new knowledge provides us with the neural correlates of consciousness and various states of awareness and sleep. Applications in neurophilosophy include reformulations of classic concepts of intentionality, causality, emotion, the perception of time, and the neurobiology of meaning, which we characterize as the ontological interrelation of an intentional system with its environment including other intentional systems.