
Project Overview: Spike Train Definition
 Spike trains are the timeseries electrical signals
recorded from individual neurons in the brain. They
are essentially the action potentials (nerve impulses)
generated by neurons. Spike trains are the signals
generated by neurons used to communicate with one another.
 Neurons use a series of "pulsecoded" signals
(i.e., action potentials) to represent the information
encoded by a neuron. The message encoded by a neuron
is embedded by a timeseries of spike train. Since
all action potentials are essentially identifical to
one another (i.e., same amplitude and same width),
they represent the digital signals used by neurons
where the signal is conveyed not by the amplitude of
the signal, but by the timeofarrival of the signal.
These pulsecoded digital signals are hybrid between
the binarycode (used by modernday digital computers)
and the timecode. It is the timeofoccurrence of
the spike that encodes the parameter/content of the
signal.
 Mathematically, spike trains belong to a class of
a process called "point process." A point
process is a natural process that is characterized
by the occurrence of a pointevent. A point event is
an event that occurs as a point in time or a point
in space. Mathematically, a point does not occupy any
finite time or finite space, rather it signifies the
onset of an event in time or the limit of an event
in space. In other words, a point is infinitestimally
small. Usually a point is used to signify the onset
of event.
 Although action potentials do occupy finite time,
the time of occurrence (or the onset of an action potential)
can be considered as a "point." Thus, the
analysis of the signal contents encoded by neurons
can be treated as a point process, which allows us
to simplify the complex problem into elegant mathematics.
Project Overview: Spike Train Analysis
 Mathematically, spike train analysis is essentially
an analysis of the point process encoded by the spike
train.
 Physiologically, spike train analysis is used to
deduce the functions of a neural circuitry based on
the spike train signals recorded from neurons. In other
words, it extracts the underlying functional circuitry
of a neural network based solely on the spike train
signals.
Project Overview: Reverse Engineering in Spike Train
Analysis
 Reverseengineering is a branch of engineering that
extract the underlying principles of operation of an
unknown machine by analyzing the (signal) contents
of the machine. It is the principles for cracking the
code, or figuring out what is not known inside the
box (or under the hood).
 In many ways, biology is essentially reverseengineering
the principles of biological systems. The unknown machines
are the biological organisms. We dissect them to figure
out how it works, that is essentially opening up the
hood and figure out how a car works (if we didn't know
how cars work before).
Project Overview: BlackBox Approach in Spike Train Analysis
 Blackbox approach is a classical reverseengineering
approach to deduce the working principles of a "blackbox" (an
unknown box) based on the input and output signals
applied to the blackbox without opening up the blackbox.
That is, we can deduce the principles of operation
mathematically by analyzing the signals going into
the blackbox and the signals coming out of the blackbox.
Based on these input/output signal relationships, we
can deduce what the blackbox is computing without
the need to open up the blackbox or look into the
content of the blackbox.
 What is essential in the blackbox approach is the
input/output relationship. By knowing the input/output
relationships, a mathematical formulation of the blackbox
can be deduced. Although the specific details inside
the blackbox can be different from implementation
to implementation, the overall function is the same.
For instance, the input/output function of a lamp is:
given the input of some electrical energy, the blackbox
will produce lightenergy as output. This lamp can
be implemented as a incandescent lamp or a flourescent
lamp or a laser lamp, but the function is essentially
the same. What is important is figuring out "what
it does," not "how it does." There can
be many different ways to accomplish the same function.
 In other words, a blackbox approach is to deduce
what is inside the blackbox just by analyzing the
inputoutput signals of the blackbox without opening
up to see what is inside. In biology, it is a nice
approach to study what an organism does without dissecting
the organism. Dissecting an organism is not only an
invasive technique, but also destroy the normal operating
function of the organism and perturbing the system
in such a way that prevents us from finding out the
true unperturbed functions.
 Therefore, the blackbox approach to spike train
analysis allows us to deduce what is the principles
of operation of the brain without opening up the brain
to see what is inside, just by examining the neural
signals generated by the neurons.
Rationale
 The basis behind spike train analysis is to deduce
the principles of operation of a neural network (blackbox)
by the spike train signals recorded from these neurons.
That is, given a set of spike train signals representing
the input/output or intermediate signal of a network,
how can we deduce what the network is computing?
 Mathematically, we are looking at the input/output
mapping function of the system. Now, this mapping function
is not a simple onetoone mapping function, rather
it is a manytomany mapping. Furthermore, the mapping
function is nonunique, i.e., it is nondeterministic.
In other words, the mapping function is a probablistic
function. This is why given the same stimulus to an
animal, the response is variable – not always
the same each time. The stimulusresponse function
is variable because the underlying neural network producing
the mapping function is probablistic.
Research Objectives
 The objective is to analyze a set of spike train
signals recorded from a large number of (~100) neurons
in the brain to deduce the function of the underlying
neural circuitry.
Specific Goals
 The goal is to derive the probablistic input/ouput
mapping function of the neural network based on the
set of spike train signals recorded simultaneously
from many neurons within a network.
The Challenge
 Find the probabilistic mapping functions such that
they represent the internal processing functions for
massively parallel operation.
The Solutions
 See publication: Tam, D. C. (2003) RealTime Estimation
of Predictive Firing Rate. Neurocomputing, 5254: 637641.
[Reprint.pdf]
 See publication: Tam, D. C. (2002) A spike train
analysis for quantifying inhibitory near synchrony
in spike firings. Neurocomputing, 4446: 11491153.
[Reprint.pdf]
 See publication: Tam, D. C. (2002) An alternate burst
analysis for detecting intraburst firings based on
interburst periods. Neurocomputing, 4446: 11551159.
[Reprint.pdf]
 See publication: Tam, D. C. (2001) A multiunit spike
train analysis for quantifying phaserelationships
of nearsynchrony firings. Neurocomputing. 3840: 945949.
[Reprint.pdf]
 See publication: Tam, D. C. (2001) A spike train
analysis for correlating burst firings in neurons.
Neurocomputing. 3840: 951955. [Reprint.pdf]
 See publication: Fitzurka, M. A. and Tam, D. C. (1999)
A joint interspike interval difference stochastic spike
train analysis: detecting local trends in the temporal
firing patterns of single neurons. Biological Cybernetics.
80: 309326. [Reprint.pdf]
 See publication: Tam, D. C. (1999) A spike train
analysis for detecting temporal integration in neurons.
Neurocomputing. 2627: 10551060. [Reprint.pdf]
 See publication: Tam, D. C. (1999) Spike train analysis
for detecting oscillations and synchronous firing among
neurons in networks. In: Oscillations in Neural Systems.
(D. S. Levin, V. R. Brown and V. T. Shirey, eds.) Lawrence
Erlbaum Assoc. Pub., Mahwah, NJ. pp. 3149.
 See publication: Tam, D. C. (1998) A crossinterval
spike train analysis: the correlation between spike
generation and temporal integration of doublets. Biological
Cybernetics. 78: 95106. [Reprint.pdf]
 See publication: Tam, D. C. (1998) Regularity in
spike firing with random inputs detected by method
extracting contribution of remporal integration of
a pair of incoming spikes to the firing of a neuron.
In: Computational Neuroscience: Trends in Research.
(J. M. Bower, eds.) Plenum Pub., San Diego, CA. pp.
633638.
 See publication: Tam, D. C. and Fitzurka, M. A. (1997)
Interarrival time spike train analyses for detecting
spatial and temporal summation in neurons. In: Computational
Neuroscience: Trends in Research. (J. M. Bower, eds.)
Plenum Pub., San Diego, CA. pp.189195.
 See publication: Fitzurka, M. A. and Tam, D. C. (1997)
A joint cross interval difference analysis for detecting
coupling trends between neurons. In: Computational
Neuroscience: Trends in Research. (J. M. Bower, eds.)
Plenum Pub., San Diego, CA. pp. 299303.
 See publication: Fitzurka, M. A. and Tam, D. C. (1997)
Hybrid analyses of neuronal spike train data for preand
postcross intervals in relation to interspike interval
differences. In: Computational Neuroscience: Trends
in Research. (J. M. Bower, eds.) Plenum Pub., San Diego,
CA. pp. 8186.
 See publication: Tam, D. C. (1996) A Timescale invariant
method for detection of changes and oscillations in
neuronal firing intervals. In: Computational Neuroscience.
(J. M. Bower, eds.) Academic Press, San Diego, CA.
pp. 465470.
 See publication: Fitzurka, M. A. and Tam, D. C. (1996)
First order interspike interval difference phase plane
analysis of neuronal spike train data. In: Computational
Neuroscience. (J. M. Bower, eds.) Academic Press, San
Diego, CA. pp. 429434.
 See publication: Fitzurka, M. A. and Tam, D. C. (1996)
Second order interspike interval difference phase plane
analysis of neuronal spike train data. In: Computational
Neuroscience. (J. M. Bower, eds.) Academic Press, San
Diego, CA. pp. 435440.
 See publication: Tam, D. C. and Fitzurka, M. A. (1995)
A stochastic timeseries analysis for detecting excitationinhibition
couplings among neurons in a network. In: Computational
Medicine, Public Health and Biotechnology: Building
a Man in the Machine. (M. Witten and D. J. Vincent,
eds.) Mathematical Biology and Medicine, Vol. 5, pp.
921931.
 See publication: Fitzurka, M. A. and Tam, D. C. (1995)
A new statistical measure for detecting trends in the
firing patterns of neurons. In: Computational Medicine,
Public Health and Biotechnology: Building a Man in
the Machine. (M. Witten and D. J. Vincent, eds.) Mathematical
Biology and Medicine, Vol. 5, pp. 9901008.
 See publication: Fitzurka, M. A. and Tam, D. C. (1995)
A new spike train analysis technique for detecting
trends in the firing patterns of neurons. In: The Neurobiology
of Computation. (J. M. Bower, eds.) Kluwer Academic
Publishers, Norwell, MA. pp. 7378.
 See publication: Tam, D. C. (1994) A multiconditional
correlation statistics for detecting spatiotemporally
correlated firing patterns. In: Computation in Neurons
and Neural Systems. (F. H. Eeckman and J. M. Bower
eds.) Kluwer Academic Publishers, Norwell, MA. pp.
3338.
 See publication: Tam, D. C. (1994) A hybrid timeshifted
neural network for analyzing biological neuronal spike
trains. Progress in Neural Networks Vol. 2, pp. 129146.
 See publication: Tam, D. C. and Gross G. W. (1994)
Dynamical changes in neuronal network circuitries using
multiunit spike train analysis. In: Enabling Technologies
for Cultured Neural Networks. (T. McKenna & D.
A. Stenger, eds.) Academic Press, San Diego, CA. pp.
319345.
 See publication: Tam, D. C. and Gross G. W. (1994)
Postconditional correlation between neurons in cultured
neuronal networks Proceedings of the World Congress
on Neural Networks. San Diego, CA, June 59, 1994.
Vol. 2, pp. 792797.
 See publication: Gross G. W. and Tam, D. C. (1994)
Preconditional correlation between neurons in cultured
networks. Proceedings of the World Congress on Neural
Networks. San Diego, CA, June 59, 1994. Vol. 2, pp.
786791.
 See publication: Tam, D. C. (1993) Computation of
crosscorrelation function by a timedelayed neural
network. In: Intelligent Engineering Systems through
Artificial Neural Networks. Vol. 3. pp. 5155.
 See publication: Tam, D. C. (1993) A new conditional
correlation statistics for detecting spatiotemporally
correlated firing patterns in a biological neuronal
network. Proceedings of the World Congress on Neural
Networks, July 1993. Vol. 2. pp. 606609.
 See publication: Tam, D. C. (1993) Novel crossinterval
maps for identifying attractors from multiunit neural
firing patterns. In: Nonlinear Dynamical Analysis of
the EEG. (B. H. Jansen and M. E. Brandt, eds.) World
Scientific Publishing Co., River Edge, NJ. pp. 6577.
 See publication: Tam, D. C. (1993) A multineuronal
vectorial phasespace analysis for detecting dynamical
interactions in firing patterns of biological neural
networks. In: Computational Neural Systems. (F. H.
Eeckman and J. M. Bower, eds.) Kluwer Academic Publishers,
Norwell, MA. pp. 4953.
 See publication: Kenyon, G. T. and Tam, D. C. (1993)
An entropy measure for revealing determinisitc structure
in spike train data. In: Computation Neural Systems.
(F. H. Eeckman and J. M. Bower, eds.) Kluwer Academic
Publishers, Norwell, MA. pp. 4447.
 See publication: Tam, D. C. (1992) Vectorial phasespace
analysis for detecting dynamical interactions in firing
patterns of biological neural networks. Proceedings
of the International Joint Conference on Neural Networks,
June 1992. Vol.3 pp. 97102.
 See publication: Tam, D. C. (1992) A novel vectorial
phasespace analysis of spatiotemporal firing patterns
in biological neural networks. Proceedings of the Simulation
Technology Conference. Nov., 1992, pp. 556564.
 See publication: Tam, D. C. (1991) Signal processing
in multithreshold neurons. In: Single Neuron Computation
(T. McKenna, J. Davis, and S. F. Zornetzer, eds.) Academic
Press, San Diego. pp. 481501.
 See publication: Tam, D. C. (1991) Signal processing
by multiplexing and demultiplexing in neurons. In:
Advances in Neural Information Processing Systems.
(D. S. Touretzky, ed.), Morgan Kaufmann Publishers,
San Mateo, California. pp. 282288.
 See publication: Tam, D. C. (1990) Decoding of firing
intervals in a temporalcoded spike train using a topographically
mapped neural network. Proceedings of the International
Joint Conference on Neural Networks, June, 1990. Vol.
3, pp. III627632.
 See publication: Tam, D. C. (1990) Temporalspatial
coding transformation: Conversion of frequencycode
to placecode via a timedelayed neural network. Proceedings
of the International Joint Conference on Neural Networks
(H. Caudill, eds.), Jan., 1990. Vol. 1, pp. I130?33.
 See publication: Tam, D. C. and Perkel, D. H. (1989)
A model for temporal correlation of biological neuronal
spike trains. Proceedings of the IEEE International
Joint Conference on Neural Networks 1989. Vol. 1, pp.
I781786.
 See publication: Tam, D. C., Ebner, T. J., and Knox,
C. K. (1988) Crossinterval histogram and crossinterspike
interval histogram correlation analysis of simultaneously
recorded multiple spike train data. Journal of Neuroscience
Methods, 23: 2333. [Reprint.pdf]
