  Environmental signals sensed by nervous systems are often represented in
spike trains carried from sensory neurons to higher neural functions where
decisions and functional actions occur. Information about the environmental
stimulus is contained (encoded) in the train of spikes. We show how to "read"
the encoding using state space methods of nonlinear dynamics. We create a
mapping from spike signals which are output from the neural processing system
back to an estimate of the analog input signal. This mapping is realized
locally in a reconstructed state space embodying both the dynamics of the
source of the sensory signal and the dynamics of the neural circuit doing the
processing. We explore this idea using a Hodgkin-Huxley conductance based
neuron model and input from a low dimensional dynamical system, the Lorenz
system. We show that one may accurately learn the dynamical input/output
connection and estimate with high precision the details of the input signals
from spike timing output alone. This form of "reading the neural code" has a
focus on the neural circuitry as a dynamical system and emphasizes how one
interprets the dynamical degrees of freedom in the neural circuit as they
transform analog environmental information into spike trains.
