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closeCould Information Sources be part of the fly brain?
Posted by Dick_Windecker on 03 Jun 2007 at 18:50 GMT
One of the implications of the work referred to in my previous comment is that it is ALWAYS possible to de-compose a Stochastic Sequential Machine (SSM) into a deterministic Sequential Machine, some of whose inputs are provided by Simple Information Sources (SISs). A SIS has no logical inputs and only one output. It has no internal structure. So it has no memory. When required, it produces an output according to fixed probabilities. For example: pulse 30% of the time, no pulse 70% of the time. The fact that a SSM can always be decomposed this way does not mean that any particular implemetation has to be constructed this way. However, it seems to me sensible to consider the possibility that Nature might have invented SISs as a way to introduce nondeterministic behavior into otherwise deterministic nervous systems. Such SISs might be single specialized neurons. Or they might be other structures. In any case, I suggest trying to interpret the data on fruit flies to see if they support the possibility that the fruit fly brain contains several SISs. If the answer is yes, then it would be an interesting experiment to look to see if they actually exist.
RE: Could Information Sources be part of the fly brain?
BjoernBrembs replied to Dick_Windecker on 10 Jul 2007 at 12:05 GMT
In some way, the noise present in any system such as a brain is an "information source" in the sense of Shannon and Weaver. I don't think you need specialized neurons for that, but I wouldn't want to exclude anything beforehand.
One way I would dare to speculate about this question in the light of our current results, is to envisage the brain as a system where one of its fundamental properties is based on nonlinearly amplifying the variability brought about by noise. The degree of this amplification appears to be specific both in time and in space (i.e., circuit).
I guess this makes for a fairly long-winded "probably" :-)
RE: RE: Could Information Sources be part of the fly brain?
Dick_Windecker replied to BjoernBrembs on 24 Jul 2007 at 16:29 GMT
Yes, the whole brain could be considered to be an Information Source, presumably a very complex one.
However, with respect to the question of the ultimate source of nondeterministic behavior, I think there is another, slightly higher-level question that possibly can be, and probably should be, answered first. Is the nondeterministic behavior of the organism as a whole: 1) the result of nondeterministic behavior of individual neurons that produce output signals with specific nondeterministic characteristics, or 2) the result of some “emergent” property of much larger aggregates of neurons? There are a lot of significant implications, in either case.
My suggestion that you look to see if the fly behavior could be described by a Stochastic Sequential Machine is one way of starting to get at the answer to this question. If the fly behavior can be described by a SSM, this would suggest that the first alternative, above, is more likely, although this would not be conclusive. But it would be a first, easy step. If the fly behavior can be described by a SSM, then there is a second, harder step that would be definitive. This second step is outlined below (at a high level). Also listed are some of the implications if the answer, after both steps, is the first alternative, above.
But first, I think I may have been a little sloppy in my use of the term Stochastic Sequential Machine (and Information Source as a special case) in my previous comments. To be clear, a SSM is a purely mathematical construct. It can be decomposed into simpler parts. Such a decomposition is called a “realization”. But a realization is still a purely mathematical construct. Any given SSM may have many realizations. Finally, it is possible to construct real, physical systems that embody a particular realization of a SSM. That is, such physical systems have real physical components whose behavior corresponds to the behavior of the parts of the realization. And, of course, the behavior of the whole aligns with the behavior described by the SSM.
My previous comments suggested that there might be a possibility that the observed nondeterministic behavior of the fly could be described by a SSM. If this can be determined to be the case, then the second step is to address the question: can the SSM be decomposed into simpler parts (that is, “realized”) in such a way that the simpler parts align with parts of the fly nervous system, presumably individual neurons? That is, does the fly nervous system embody in physical “hardware” one realization of this SSM? If the question in this second step can be answered in the affirmative, then we would be quite sure that the nondeterministic behavior of the fly relies on the nondeterministic behavior of individual neurons.
From a mathematical point of view, a SSM can always be decomposed into a deterministic Sequential Machine, some of whose inputs are Simple Information Sources. But there are many other possible decompositions as well, including ones involving more complex Information Sources. If any (even partial) decomposition can be shown to align (partially) with the fly nervous system, using Simple Information Sources or not, it would imply that the source of the fly’s nondeterministic behavior is very likely to be at the cellular level, and not some property of a larger aggregate.
If it eventually turns out that the nondeterministic behavior of the whole is derived from the nondeterministic behavior of individual neurons, then one implication is, I think, that it is unlikely that the probability distribution of the process that underlies nondeterministic behavior at the cellular level is at all discernable or recognizable at the level of observed macroscopic behavior. The reason is that it is likely there would be too much processing in between – thresholding, selecting (conditionally), combining (with time delays), etc.
I think a further implication is that it is likely that there are a lot of probability distributions that can adequately serve the needs of providing nondeterministic behavior at the cellular level, although some distributions might have properties that give them advantages over others. I suspect that among the distributions that can work are ones that are associated with processes that are understandable in terms of classical physics, such as the Gaussian distribution. Since selection works on changing incrementally, and improving, what is already existing, not necessarily finding what is optimum, it is hard to say what process nature might have chosen to use for this. Some pretty sophisticated experiments might be required to determine the process.
Anyway, I think it is worth working through the two steps outlined above because, if it turns out that the source of nondeterministic behavior is at the cellular level, the implications are very far-reaching. There is only one place to start: at the first step. That is, looking to see if the fly behavior can be described by a SSM.
RE: Could Information Sources be part of the fly brain?
BjoernBrembs replied to Dick_Windecker on 06 Aug 2007 at 07:36 GMT
The strength of the model system Drosophila lies in its powerful genetic toolbox. Hence, the next step will be to genetically block circuits in the fly brain to determine if there is any localized source for the nonlinearity in the behavioral variability. If such a circuit can be localized, your question of local vs. global indeterminism in the brain will also be one step closer to an answer.
My personal speculation would be, at this point in time, that various sources of noise convolve with the overall non-linear instability of the circuits controlling turning behavior in the fly.
But the genetic (actually, transgenic) experiments will eventually put a stop to these speculations and provide us with some new and exciting data from which to move on.
RE: RE: RE: Could Information Sources be part of the fly brain?
alexm replied to Dick_Windecker on 11 Oct 2007 at 07:20 GMT
An SSM can implement arbitrary input-output functions using stochastic logic gates. The crucial point in our experiment is that we investigated fly behavior in the absence of any input (stimulation). To model this situation using an SSM one would not use an input-output mapping, but rather the intrinsically generated output sequences. In terms of SSM theory this activity would be generated by Simple Information Sources (SIS). The parameterization of these SIS is up to the modeler, so he or she decides what probability distribution to use, how to adjust the parameters, and how to combine the outputs.
We made an attempt in this direction in our article when we compared data generated by several stochastic models to the animal data. The models comprise different levels of complexity, like simple Poisson process, cascading and branching Poisson processes, and a nonlinear automat. All these models would have a straightforward formulation in the SSM framework (I think). However, none of the models we tested was able to reproduce the properties of the fly behavior completely. Therefore, the observed behavioral variability must be rooted in aspects of the brain that are not covered by these models. I think that the SSM framework is a useful tool to represent and investigate complex models, and it will be even more valuable afterwards in the steps outlined by Dick Windecker, i.e. mapping such a model to the fly brain and reducing it to its basic functional principles. But what is needed first is an idea for a functional principle of a "spontaneity generator", and the most important tool for this task is a creative human mind.
RE: RE: RE: RE: Could Information Sources be part of the fly brain?
Dick_Windecker replied to alexm on 01 Nov 2007 at 18:42 GMT
I agree that in general, SSMs map inputs to outputs. But I think it is important to keep two things in mind. First, outputs at any given time depend not only on inputs, but on internal states, and internal states can contain information on past inputs, past outputs, and past internal states.
The second thing to keep in mind is that the relationship between SSMs and Information Sources (ISs) is so close that it makes sense, at least to me, to regard the set of ISs as a subset of the set of SSMs. What this means is that the ISs are the subset of SSMs that have the number of inputs, N, equal to zero.
I don’t know of this is the generally accepted view among experts in this field. But it seems natural to me to have as part of the definition of a SSM that it have N inputs, where N >= 0, not N >=1. One of the reasons this seems natural to me is that exactly the same mathematical formalism can be used to describe (analyze) the N = 0 case as the N > 0 case. Also, exactly the same methods of synthesis apply in both cases. An additional reason for taking this point of view, especially in the present context, is that if you have a SSM that has N > 0 inputs, and you fix all N inputs, you get an IS – at least from a mathematical point of view. In any case, an IS, like a more general SSM, can have internal states that can contain information about past outputs and past internal states.
The set of Simple Information Sources (SISs) is a subset of the complete set of ISs. SISs have only one output and also have no internal states. If we take the set of SISs out of the set of all ISs, I would call the remaining subset the set of Complex Information Sources (CISs). Like SSMs in general, CISs can have multiple outputs and can have internal states. Since internal states can give a CIS information about past outputs and also about past internal states, CISs can have very complex behaviors indeed. Such behaviors include, I think, mimicking various common stochastic models or distributions.
If the behavior of the fruit fly, with inputs fixed, can be described as a CIS, then, by looking at the set of possible ways you might synthesize that CIS from simpler parts, you might get insights as to how the fruit fly brain is structured. From a mathematical point of view, all CISs can be synthesized from simpler parts that include only deterministic logic gates and SISs. But there may also be ways of synthesizing a given CIS without using SISs, but using CISs that are simpler than the overall CIS. It is possible that the physical realization of the fruit fly CIS involves only SISs. If so, for reasons I explained earlier, the “spontaneity generator” may not matter much, although it would still certainly be interesting to know what it is. If the physical realization of the fruit fly CIS is based on simpler CISs, not SISs, then the spontaneity generator might matter more. Either way, I don’t see that an understanding of the spontaneity generator is necessarily needed first because it could be so buried within the SISs or CISs that its details are unimportant.
Finally, I would point out that if the behavior of the fruit fly, with inputs fixed, can be described as a CIS, and looking at the possible ways of synthesizing that CIS from simpler parts gives insights as to how the fruit fly brain is structured, then fixing the inputs in a different way might give additional insight into how the fruit fly brain is structured and this might also give insight into how the fruit fly brain works when the inputs are not fixed.
The bottom line is that I am not yet convinced that it would not be worth a bit of effort now to see if the data on fruit fly behavior can be mapped into the mathematical formalism of a CIS. If so, then I think it would also be worth a bit more effort to explore some of the ways such a CIS can be decomposed into simpler parts.