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Definitions for the following terms?

Richard Norman rsnorman at mediaone.net
Tue Jul 10 22:00:29 EST 2001

On 10 Jul 2001 17:57:48 -0700, jonesmat at physiology.wisc.edu (Matt
Jones) wrote:

>"Isidore" <isidore at mailandnews.com> wrote in message news:<PoJ27.2$ln3.148 at typhoon.nyu.edu>...
>> Hi everyone,
>>     I'm a high school student trying to read a neuroscience paper and
>> understand it well. There are some keywords listed at the top of the page
>> that I'm not exactly clear on. They aren't explicitly alluded to in my
>> textbook (although perhaps they are by another name).  If someone could help
>> clarify these for me, I'd appreciate it.
>> renewal process: Is this just referring to the process the neuron has to go
>> through before it fires another action potential (absolute refractory
>> period, relative refractory period, etc.?)
>> integrate-and-fire: Is this just referring to the neuron firing when
>> threshold is reached? Why do they call it INTEGRATE-and-fire? Is there any
>> alternative to integrate-and-fire? What is a leaky integrate-and-fire
>> neuron?
>> interval distribution: Is this just the lapses between the action
>> potentials?
>>         Thanks for your time,
>>             Isidore
>As usual, Richard Norman has given a very good response already (Hi
>Richard!). But I've been studying up on spiketrain analysis alot
>lately, and thought I might give another response, since its still
>fresh in my mind.
>(I'm a bit shaky on this first one, but here's what I think the answer
>A renewal process is a kind of "counting" process. Counting process
>means that the signal generated by the process comes in discrete
>units, like ticks of a clock, rather than a continuous flow, like
>water flowing from a tap. So a counting process is characterized by
>things like the frequency of ticks (or spikes, in this case) or the
>number of ticks in a certain timeframe. A renewal process produces
>ticks or spikes in such a way that there is no correlation between the
>time of one spike and any other. That is, observing a spike at any
>particular time doesn't convey any information about when the next
>spike will occur, or about when the preceeding spike occurred. In more
>technical language, a renewal process has a flat autocorrelation
>Integrate-and-fire is a possible model for how neurons examine their
>synaptic inputs and then decide when to fire a spike. In this model,
>they literally integrate (i.e., as in integration, from calculus)
>their inputs over time. Integration is pretty much the same thing as
>just keeping a running sum. So suppose the inputs (e.g., synaptic
>potentials) came in the following order with the following sizes:
>2, 3, 2, 5, 1 ...
>then an integrate-and-fire neuron would integrate these as follows:
>2, 5, 7, 12, 13 .... (i.e., add each number to the previous sum)
>If the spike firing threshold was set at a value of, say, 10, then the
>neuron would have fired a spike between the 3rd and 4th inputs because
>the value 12 is above threshold. A critical feature of an
>integrate-and-fire neuron  is that it -resets- itself to zero every
>time it fires a spike, and starts the sum all over again.
>A leaky integrate-and-fire neuron is an integrate-and-fire neuron that
>has trouble remembering how high it has counted, but in a very
>particular way. It doesn't just forget, it -subtracts- a certain
>amount from the count at each new moment in time. A neuron like this
>will need to receive several inputs close together in time in order to
>reach threshold at all. The time it takes for the count to decay to
>about 1/3 of its value is called the "integration time constant", and
>tells you about how close together in time the inputs have to be in
>order to add up to a value that will reach threshold. A really leaky
>integrator will require multiple almost simultaneous inputs to reach
>threshold, and can therefore be considered a "coincidence detector".
>By the way, in my opinion, real neurons are not integrate-and-fire
>devices, leaky or otherwise.
>Finally, an interval distribution is -not- the time between spikes
>(that's the interspike interval), but is the -distribution- of
>interspike intervals.  In this case, "distribution" means essentially
>a histogram of the probability of seeing a certain interval. To make
>one, you create a list of all the interspike intervals, sort them by
>duration, and group them together into "bins" of a certain size (i.e.,
>if the binwidth is 10 milliseconds, then any intervals between 0-10 ms
>would fall in the first bin, between 11-20 ms in the second bin, etc).
>Then you count how many intervals fell into each bin, and make a graph
>of the count versus the time at the middle of each bin (5, 15, 25 ms,
>etc). Often, you divide the count in each bin by the total number of
>counts before making the graph. This converts the counts into
>The interspike interval (ISI) distribution is a summary of the
>spiketrain that tells its mean rate, and the variability or spread
>around that mean, as well as giving an indication of whether spikes
>occur in bursts or clusters, etc.
>People often make a big deal about Poisson spike processes, which have
>an exponential interspike interval distribution. This is because the
>Poisson process is what you would expect to see if neurons encoded
>information solely through the mean rate of spiking, where each spike
>occurs at a random time (imagine rolling dice at each moment to decide
>whether to fire a spike or not - that would produce a Poisson
>process). This is a nice simple way of thinking about neurons because
>it doesn't call for understanding anything about them except their
>spike rate. More complicated schemes would use encoding by exact spike
>times, and it would probably (no, definitely) be a lot more difficult
>to figure out. So people often draw exponential curves over their ISI
>distributions and conclude that they are "Poisson-like", I think
>because it makes trying to understand the brain seem like it might
>actually be possible instead of hopelessly complicated.
>There are some problems with this: 1) If you look at most of them, the
>exponential curves don't really fit the ISI distributions very well.
>2) They -shouldn't- fit very well, because we know neurons do have
>refractory periods (which means they can't generate enough brief ISIs
>to really be Poisson). 3) Regardless of how well they fit, any highly
>efficient code, no matter how complex and precise, will always tend
>toward a Poisson ISI (there is a mathematical proof of that statement
>by the late, great Claude Shannon, published in 1949).
>So both noisy rate codes and excruciatingly complex and precise timing
>codes -both- predict a Poisson ISI distribution, which makes worrying
>about whether ISIs are exponential or not seem pretty uninformative as
>far as figuring out how neurons encode information.
>Out of curiousity, what paper are you reading?

Thanks, Matt. I knew someone else would come in who really knew
something about spike train analysis.  OK, so I was a math major as an
undergraduate and in fact took courses on probablilty theory and
random processes.  But that was forty years ago!   I do have a lot of
experience, though,  trying to get college sophomores and juniors
through their first hard-core neuro papers.  And I would never let one
start out with spike train analysis (biology students usually have no
math background or interest, unfortunately)

And, Isidore, I am also interested in what paper you have -- and how
and why you got it.  I'll bet this group could help steer you into a
good reading program, if you have the time and interest.  

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