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## Project Overview: Spike Train Definition

• Spike trains are the time-series 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 "pulse-coded" signals (i.e., action potentials) to represent the information encoded by a neuron. The message encoded by a neuron is embedded by a time-series 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 time-of-arrival of the signal. These pulse-coded digital signals are hybrid between the binary-code (used by modern-day digital computers) and the time-code. It is the time-of-occurrence 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 point-event. 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

• Reverse-engineering 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 reverse-engineering 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: Black-Box Approach in Spike Train Analysis

• Black-box approach is a classical reverse-engineering approach to deduce the working principles of a "black-box" (an unknown box) based on the input and output signals applied to the black-box without opening up the black-box. That is, we can deduce the principles of operation mathematically by analyzing the signals going into the black-box and the signals coming out of the black-box. Based on these input/output signal relationships, we can deduce what the black-box is computing without the need to open up the black-box or look into the content of the black-box.
• What is essential in the black-box approach is the input/output relationship. By knowing the input/output relationships, a mathematical formulation of the black-box can be deduced. Although the specific details inside the black-box 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 black-box will produce light-energy 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 black-box approach is to deduce what is inside the black-box just by analyzing the input-output signals of the black-box 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 black-box 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 (black-box) 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 one-to-one mapping function, rather it is a many-to-many mapping. Furthermore, the mapping function is non-unique, i.e., it is non-deterministic. 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 stimulus-response 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) Real-Time Estimation of Predictive Firing Rate. Neurocomputing, 52-54: 637-641. [Reprint.pdf]
• See publication: Tam, D. C. (2002) A spike train analysis for quantifying inhibitory near synchrony in spike firings. Neurocomputing, 44-46: 1149-1153. [Reprint.pdf]
• See publication: Tam, D. C. (2002) An alternate burst analysis for detecting intra-burst firings based on inter-burst periods. Neurocomputing, 44-46: 1155-1159. [Reprint.pdf]
• See publication: Tam, D. C. (2001) A multi-unit spike train analysis for quantifying phase-relationships of near-synchrony firings. Neurocomputing. 38-40: 945-949. [Reprint.pdf]
• See publication: Tam, D. C. (2001) A spike train analysis for correlating burst firings in neurons. Neurocomputing. 38-40: 951-955. [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: 309-326. [Reprint.pdf]
• See publication: Tam, D. C. (1999) A spike train analysis for detecting temporal integration in neurons. Neurocomputing. 26-27: 1055-1060. [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. 31-49.
• See publication: Tam, D. C. (1998) A cross-interval spike train analysis: the correlation between spike generation and temporal integration of doublets. Biological Cybernetics. 78: 95-106. [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. 633-638.
• See publication: Tam, D. C. and Fitzurka, M. A. (1997) Inter-arrival 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.189-195.
• 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. 299-303.
• See publication: Fitzurka, M. A. and Tam, D. C. (1997) Hybrid analyses of neuronal spike train data for pre-and post-cross intervals in relation to interspike interval differences. In: Computational Neuroscience: Trends in Research. (J. M. Bower, eds.) Plenum Pub., San Diego, CA. pp. 81-86.
• See publication: Tam, D. C. (1996) A Time-scale 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. 465-470.
• 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. 429-434.
• 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. 435-440.
• See publication: Tam, D. C. and Fitzurka, M. A. (1995) A stochastic time-series analysis for detecting excitation-inhibition 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. 921-931.
• 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. 990-1008.
• 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. 73-78.
• See publication: Tam, D. C. (1994) A multi-conditional correlation statistics for detecting spatio-temporally correlated firing patterns. In: Computation in Neurons and Neural Systems. (F. H. Eeckman and J. M. Bower eds.) Kluwer Academic Publishers, Norwell, MA. pp. 33-38.
• See publication: Tam, D. C. (1994) A hybrid time-shifted neural network for analyzing biological neuronal spike trains. Progress in Neural Networks Vol. 2, pp. 129-146.
• See publication: Tam, D. C. and Gross G. W. (1994) Dynamical changes in neuronal network circuitries using multi-unit spike train analysis. In: Enabling Technologies for Cultured Neural Networks. (T. McKenna & D. A. Stenger, eds.) Academic Press, San Diego, CA. pp. 319-345.
• See publication: Tam, D. C. and Gross G. W. (1994) Post-conditional correlation between neurons in cultured neuronal networks Proceedings of the World Congress on Neural Networks. San Diego, CA, June 5-9, 1994. Vol. 2, pp. 792-797.
• See publication: Gross G. W. and Tam, D. C. (1994) Pre-conditional correlation between neurons in cultured networks. Proceedings of the World Congress on Neural Networks. San Diego, CA, June 5-9, 1994. Vol. 2, pp. 786-791.
• See publication: Tam, D. C. (1993) Computation of cross-correlation function by a time-delayed neural network. In: Intelligent Engineering Systems through Artificial Neural Networks. Vol. 3. pp. 51-55.
• See publication: Tam, D. C. (1993) A new conditional correlation statistics for detecting spatio-temporally correlated firing patterns in a biological neuronal network. Proceedings of the World Congress on Neural Networks, July 1993. Vol. 2. pp. 606-609.
• See publication: Tam, D. C. (1993) Novel cross-interval maps for identifying attractors from multi-unit 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. 65-77.
• See publication: Tam, D. C. (1993) A multi-neuronal vectorial phase-space 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. 49-53.
• 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. 44-47.
• See publication: Tam, D. C. (1992) Vectorial phase-space 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. 97-102.
• See publication: Tam, D. C. (1992) A novel vectorial phase-space analysis of spatio-temporal firing patterns in biological neural networks. Proceedings of the Simulation Technology Conference. Nov., 1992, pp. 556-564.
• See publication: Tam, D. C. (1991) Signal processing in multi-threshold neurons. In: Single Neuron Computation (T. McKenna, J. Davis, and S. F. Zornetzer, eds.) Academic Press, San Diego. pp. 481-501.
• 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. 282-288.
• See publication: Tam, D. C. (1990) Decoding of firing intervals in a temporal-coded spike train using a topographically mapped neural network. Proceedings of the International Joint Conference on Neural Networks, June, 1990. Vol. 3, pp. III-627-632.
• See publication: Tam, D. C. (1990) Temporal-spatial coding transformation: Conversion of frequency-code to place-code via a time-delayed neural network. Proceedings of the International Joint Conference on Neural Networks (H. Caudill, eds.), Jan., 1990. Vol. 1, pp. I-130?-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. I-781-786.
• See publication: Tam, D. C., Ebner, T. J., and Knox, C. K. (1988) Cross-interval histogram and cross-interspike interval histogram correlation analysis of simultaneously recorded multiple spike train data. Journal of Neuroscience Methods, 23: 23-33. [Reprint.pdf]