Walter J. Freeman 

Neurophysiology Lab 

The Freeman Laboratory for Nonlinear Neurodynamics  

Department of Molecular & Cell BiologyDivision of Neurobiology, Donner 101University of California at Berkeley

Berkeley CA 94720-3206 USATel 510-642-4220

Fax 510-643-9290

Introduction 

Our aim is to understand the ways in which the immense numbers of neurons in thehuman 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 ofneural 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 ofautonomous robots, neural correlates of consciousness, epileptic seizure modelingand prediction, and the uses of brain imaging to understand the neural mechanisms

of perception, cognition, and creativity in constructing representations of meaning.

Synopsis 

Our group develops data-driven brain theory by analysis of action potentials and

 brain waves (electroencephalograms, EEG, local field potentials, LFP) recordedwith high-density electrode arrays fixed on or in animal and human subjects whoare 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 brainactivity patterns that we find in three-layered paleocortex and six-layeredneocortex. 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 thatthese 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 optimizedspatiotemporal EEG patterns from high-density arrays as projections of activityfrom infinite-dimensional brain state space into a finite n-space defined by the n-

dimensions of our electrode arrays. We use nonlinear mapping andmultidimensional 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 ofneural populations that supports rapid and widespread state transitions by virtue ofsmall-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 locallyis homeostatically regulated by neural thresholds and refractory periods. We use

our K sets to model neural instabilities that underlie the onset of epileptic seizuresand 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 corticalself-organized criticality creates a pseudo-equilibrium in brain dynamics, that letsus 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 phasetransition 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; andthen high-energy pattern broadcast over divergent-convergent axonal corticaloutput 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 corticaltransmission. The power-law and fractal distributions of EEG parameters enable us

to display the scale-free dynamics of cortex as macroscopic cortical statetransitions, 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 KIset 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 andcontrol systems for guidance of navigation and decision-making by autonomous

robots in complex environments. At present we are developing the KV set as aninstrument to analyze the properties of neocortex in human perception. This new

knowledge provides us with the neural correlates of consciousness and variousstates 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 theontological interrelation of an intentional system with its environment includingother intentional systems.