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eightwings
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08-07-05, 09:11 am |
 Post subject: No Feed-forward Hierarchy |
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No Feed-forward Hierarchy
The brain could not possibly have a feed-forward hierarchy of memory sequences of the type that could lead to an invariant grandmother cell. The psychological record on stimulus response timing refutes it. Why? Because, it would take way too long for signals to travel up to the top of the tree: there would have to be a lot of levels to obtain a grandmother-type cell, way too many to account for the fast response timing observed in biological systems.
None other than Rodney Brooks (MIT AI Lab) said: "the connectivity diameter of the brain is only five or six neurons, if you view it as a graph, so there must be all these quick connections of sensing to action..." (source: Edge.org)
Brooks has used his model of minimal computation between sensing and action to great advantage in his subsumption architecture. Hawkins himself maintained that the brain is essentially a large sheet of neurons six or seven layers deep. How does one get a feed-forward hierarchy of the type that would lead to a grandmother cell from six levels? Assuming that one could use feedback to generate an open-ended hierarchy, the problem that immediately arises is one of slow response. This is not observed in either animals or humans even though the brain uses relatively slow neurons.
Flat Hierarchy
Having said that, I agree with Hawkins that memory is organized as a hierarchy, but it is not a feed-forward perceptual hierarchy. It is a flat hierarchy used for controlling the activation of groups of motor sequences and for the sharing and/or nesting of motor behavior. Besides, what good is memory if it does not produce motor behavior?
One could ask: what does a brain do with a firing grandmother cell? What sort of motor behavior can it perform with a single firing cell? Answer: None. The reason, in my opinion, is that a grandmother-type cell is not the end point of a perceptual hierarchy. On the contrary, it is a control cell that is used to harness a group of memory sequence cells that are related to grandma. Later, the control cell can be used to activate and deactivate the group according to attentional necessity. How is this done? That is, how does the brain know how to group related cells together? In my opinion, it does it via trial and error, by eliminating all cells from the group that are in conflict. A conflict is simply a motor command error.
It is known that there is massive feedback between the basal ganglia and the cerebral cortex. What does Mr. Hawkins say about the linkage between memory and motor behavior?
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Louis Savain
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Orion
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08-13-05, 05:59 am |
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| Quote: | | what does a brain do with a firing grandmother cell? What sort of motor behavior can it perform with a single firing cell? Answer: None. [...] On the contrary, it is a control cell that is used to harness a group of memory sequence cells that are related to grandma. |
So is it a single cell, or isn't it? First you say it can't be, then you assert that it is. I'd say that the idea that there needs to be an invarient cell for grandma is in both models, yours and his. Therefore, this argument can be interpreted as disprooving BOTH models:
| Quote: | there would have to be a lot of levels to obtain a grandmother-type cell, way too many to account for the fast response timing observed in biological systems.
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It doesn't much matter if the single cell is motor or sensory, does it? Both could trigger a motor response in a similar way. Both would have to account for the same level of complexity and context-sensitivity in that response.
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eightwings
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08-13-05, 03:20 pm |
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| Orion wrote: | | Quote: | | what does a brain do with a firing grandmother cell? What sort of motor behavior can it perform with a single firing cell? Answer: None. [...] On the contrary, it is a control cell that is used to harness a group of memory sequence cells that are related to grandma. |
So is it a single cell, or isn't it? First you say it can't be, then you assert that it is. I'd say that the idea that there needs to be an invarient cell for grandma is in both models, yours and his. Therefore, this argument can be interpreted as disprooving BOTH models:. |
You are either misinterpreting or you misread what I wrote. I certainly believe in the existence of grandmother-type cells. I just do not accept for a moment that a grandmother cell is the end point of a bottom-up perceptual hierarchy. I believe in both bottom-up perceptual learning and top-down concept formation. A grandmother cell is what I call an invariant concept cell.
| Orion wrote: | | Quote: | there would have to be a lot of levels to obtain a grandmother-type cell, way too many to account for the fast response timing observed in biological systems.
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It doesn't much matter if the single cell is motor or sensory, does it? Both could trigger a motor response in a similar way. Both would have to account for the same level of complexity and context-sensitivity in that response. |
In my opinion, a grandmother cell is neither a sensory nor a motor cell. It is a concept delineation cell. It is used for both attention (focusing on a single subject/concept) and for behavior selection and credit assignment. As an attention cell, it create a sort of canalization of sensory and motor channels. As a motivation cell, it receives either credit (or blame) for the actions of the memory sequences under its control. This means that grandmother cells are closely associated with the amygdala, the center of pain and pleasure processing.
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Louis Savain
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Orion
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08-21-05, 10:56 am |
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Alright.
The memory-prediction framework does fail to completely explain motor behavior.
However, why would perceptual ideas need to be tweaked by motor-learning? The memory-prediction framework shows that they can develop largely on their own. They do trigger action, of course, but not directly; reactions are situation-dependant, and I'd say that the complexity of the situation-dependance is high enough that we need some linkage of a motor heirarchy and a sensory heirarchy (as suggested by the seperate motor and sensory areas recognized by neurology) is needed. If the grandmother-cell denotes the sensory concept of grandma, what motor concept does it demote?
There might be some sort of association-area between the sensory heirarchy and the motor one, representing ideas that include both sense and movement (not merely both sense and self-sense); but I'm unsure as to the learning methods employed. To me, your conflict-based method can only be a partial learning method. How does it produce benificial behavior? Doesn't it merely produce consistant behavior?
It seems like your "controll-cell" is obviously doing double duty, by representing both senses and actions. Such a cell might exist, but it seems like it would rely on lower cells that represented the varios sensory and motor concepts; in otherwords, the "grandmother cell" would be lower in the heirarchy.
Of course, you'd probably know more than me.
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eightwings
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08-22-05, 11:28 am |
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| Quote: | | However, why would perceptual ideas need to be tweaked by motor-learning? The memory-prediction framework shows that they can develop largely on their own. |
Certainly, perceptual knowledge has little to do with motor learning. I don't think I said that. However, there is no doubt in my mind that concept formation is a motor learning problem. Furthermore, I disagree that true invariant concepts can be learned in the brain via perceptual learning alone. Like I said many times, the connectivity diameter of the brain is only about six neurons, which leaves about three neurons (or levels) to build an invariant recognition tree. It's just physically and logically impossible.
| Quote: | | If the grandmother-cell denotes the sensory concept of grandma, what motor concept does it demote? |
That is just it. I does not. There is no such a think as a sensory concept. A sensory percept, yes. A concept is somehting else and is formed in a top-down manner. It is beneficial to look at a brain's hemisphere as consisting of two major complementary subsystems, one for perception, and the other for concept formation. The former deals with sensory signals and their temporal relationships while the latter has to do with motor signals and command timing. The two are tightly integrated.
There seems to be a general consensus among AI researchers that perceptual memory is organized as a probabilistic hierarchical tree. Sensory signals are supposed to travel up the nodes of the tree and a probabilistic associative value is encoded into each node. The accepted wisdom is that this is the most practical way to predict the probability that a node will fire. Needless to say, I disagree with this approach. Not because I think it is dumb (I, too, used to think it was the way to go), but because I have discovered a completely different model that solves several problems in that approach.
A major problem with the probabilistic node model is that it does not take the common sense logic of sequences into consideration. For examples, we know that a door cannot be opened unless it is first closed and vice versa; and we know that we cannot empty a cup unless we first fill it. This is part of what I have been calling the Principle of Complementarity. Complementary logic is not only imposed by the environment, it is expected by the innate functional organization of the brain.
| Quote: | | There might be some sort of association-area between the sensory heirarchy and the motor one, representing ideas that include both sense and movement (not merely both sense and self-sense); but I'm unsure as to the learning methods employed. To me, your conflict-based method can only be a partial learning method. How does it produce benificial behavior? Doesn't it merely produce consistant behavior? |
In my opinion there is a very minimal hierarchical processing in the sensory cortices and it is driven entirely via massive feedback and works on a fixed time scale. A huge number of temporal correlations are learned in the sensory cortices. There is no time for the deep hierarchical pyramid proposed by Hawkins. Fast sensorimotor responses is the norm. The sensory cortices send their output to the cerebral cortex where they are organized as sequences for the purpose of prediction and motor command generation. These are grouped into coherent clusters. Each group is a sensori-motor behavioral cluster of compatible nodes. A group has a control cell (a grandmother-type cell) which also receives motivational inputs from the Amygdala. Groups compete for activation based on motivational experience and on the level of stimulus activity (salience). If grandma appears in the picture, a huge number of memory nodes fire and this activity will wake up the grandmother cell which will in turn wake up all the cells in the group associated with grandma. Now, if a lion appears in the picture, the lion cell will override grandma's cell because it has a higher motivational value having to do with survival. It will cause grandma's cell to deactivate its group temporarily. It's a shift in attention. The bottom-up perceptual pyramid does not provide a mechanism for attention. At least, I don't know of any.
My contention is that the grandmother cell harnesses memory nodes on the basis of their non-conflicting behavior, not on the basis of some probabilistic value encoded into each node. As far as the connection between movement and memory sequences is concerned, there is no doubt in my mind that it is a direct link. There is no time to waste computing a lot of stuff during motor behavior. Motor commands in a group are chosen if they do not create motor conflicts.
| Quote: | | It seems like your "controll-cell" is obviously doing double duty, by representing both senses and actions. Such a cell might exist, but it seems like it would rely on lower cells that represented the varios sensory and motor concepts; in otherwords, the "grandmother cell" would be lower in the heirarchy. |
In my opinion, there is just a two-level hierarchy of groups. It is a top down hierarchy. The grandmother cell is at the top and may control a large number of subgroups.
| Quote: | | Of course, you'd probably know more than me. |
Believe it or not, I don't know any of this stuff and I am not making any claims that I figured any of it out. Someone else did and I am memrely digging from a source. I am reporting what I have been able to uncover and understand so far.
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Louis Savain
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chatham
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08-30-05, 09:06 am |
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| Quote: | | A major problem with the probabilistic node model is that it does not take the common sense logic of sequences into consideration. For examples, we know that a door cannot be opened unless it is first closed and vice versa; and we know that we cannot empty a cup unless we first fill it. This is part of what I have been calling the Principle of Complementarity |
I think you're making a straw man here. I don't know of any professional AI researcher who would advocate the probabilistic node model of perceptual memory and ALSO maintain that it does not receive input from previous activations (in your example, whether the door was just opened or closed.) So in my opinion, your principle of complementarity is a "given" of what you call the probabilistic node model.
What I don't understand about all this talk of a grandmother cell - and I admit that I may not be familiar with the relevant research (please cite) - is why it has to be a single cell. Why could "grandmother" not be encoded by a distributed set of neurons throughout the top 1 or 2 levels in the hierarchy, instead of just a single neuron?
Another way of attacking the idea of a "grandmother" cell would be this: if you were to destroy that single neuron, would the patient no longer be capable of thinking of grandmother?
Of course not. So why are we pretending as though there is a single neuron responsible for it? |
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Don
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08-30-05, 11:59 am |
| Post subject: Exciting grandmothers |
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Chatham wrote:
| Quote: | | I don't know of any professional AI researcher who would advocate the probabilistic node model of perceptual memory and ALSO maintain that it does not receive input from previous activations. |
If I understand Chatham correctly, I don't think I subscribe to the "previous activation" model, nor do I think Grossberg does. But then, it may be argued we're not "AI researchers" but rather "natural intelligence" researchers. Indeed, in Grossberg's general model of serial learning and performance, one might say the probability of node B firing depends upon the deactivation of node A: in learning or performing the sequence "AB" there is no cerebral excitatory signal from node A to node B. [The emphasis on cerebral is critical here; there is AB excitation in cerebellar cortices via the parallel fibers, but most people wouldn't call the cerebellum "cognitive" or "intelligent" in the most human sense.]
I agree with Chatham on "grandmother cells":
| Quote: | | Why could "grandmother" not be encoded by a distributed set of neurons throughout the top 1 or 2 levels in the hierarchy, instead of just a single neuron? |
However, once we get into distributed subnets the boundaries of the hierarchy itself start getting so fuzzy, and I don't find it very helpful to continue to think in terms of classical "hierarchies".
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Lawrence Phillia
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08-30-05, 01:30 pm |
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| Whether its a single neuron or a population of neurons appears abit misleading and irrelevant , dont we actually mean the dynamic synaptic connection patterns between the neurons ? Since a single neuron can have thousands of dendrites with as many , if not more, associated synapses it could "encode" a meriade of states. If we look at this as a contribution to a population vector the magnetude and resolution of the network is only increased . |
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chatham
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08-30-05, 05:26 pm |
| Post subject: Re: Exciting grandmothers |
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Hi Don, thanks for responding.
| Don wrote: | | Indeed, in Grossberg's general model of serial learning and performance, one might say the probability of node B firing depends upon the deactivation of node A: in learning or performing the sequence "AB" there is no cerebral excitatory signal from node A to node B. [The emphasis on cerebral is critical here; there is AB excitation in cerebellar cortices via the parallel fibers, but most people wouldn't call the cerebellum "cognitive" or "intelligent" in the most human sense.] |
I didn't mean to say that the inputs from previous activations are necessarily excitatory, or that they come from the neocortex (or any other brain area) in particular.
And a quick potshot: most people wouldn't call a disembodied inferior temporal cortex "cognitive" or "intelligent" in the most human sense either. That doesn't mean that "cognitive" or "intelligent" behavior doesn't arise from its interaction with other brain areas.
Or maybe I misunderstood your point.
In any case it's a pleasure to have you here. |
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eightwings
Joined: 07 Aug 2005
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09-01-05, 11:05 am |
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| chatham wrote: | | Quote: | | A major problem with the probabilistic node model is that it does not take the common sense logic of sequences into consideration. For examples, we know that a door cannot be opened unless it is first closed and vice versa; and we know that we cannot empty a cup unless we first fill it. This is part of what I have been calling the Principle of Complementarity |
I think you're making a straw man here. I don't know of any professional AI researcher who would advocate the probabilistic node model of perceptual memory and ALSO maintain that it does not receive input from previous activations (in your example, whether the door was just opened or closed.) So in my opinion, your principle of complementarity is a "given" of what you call the probabilistic node model. |
Well, if this were the case, Bayesian networks would have given rise to common sense intelligence by now. One reason that it has not is that there is more to intelligence than perception. The ability to aggregate multiple memory sequences into coherent contexts is a must.
| Quote: | | What I don't understand about all this talk of a grandmother cell - and I admit that I may not be familiar with the relevant research (please cite) - is why it has to be a single cell. |
Here is an article about a recent experiment. The grandmother cell is no longer a mere a hypothesis. It is a fact.
| Quote: | | Why could "grandmother" not be encoded by a distributed set of neurons throughout the top 1 or 2 levels in the hierarchy, instead of just a single neuron? |
Well, it is so encoded. The problem is that we need a mechanism to harness memory sequences to form single concepts. This is a top-down learning process, not a bottom-up feed-forward pyramid as Hawkins and others have suggested. The connectivity diameter of the brain leaves only about two or three neurons/levels for a hierarchical tree. Not nearly enough to produce a grandmother cell using a multi-level Bayesian network. Also, the pyramid hypothesis cannot account for the fast stimulus response time observed in humans and animals.
| Quote: | Another way of attacking the idea of a "grandmother" cell would be this: if you were to destroy that single neuron, would the patient no longer be capable of thinking of grandmother?
Of course not. So why are we pretending as though there is a single neuron responsible for it? |
I both agree and disagree. There are indeed single neurons in the hippocampus responsible for concept formation and attention. However there is a lot of overlapping between concepts. So destroying a grandmother cell would cripple a small part of our conceptual framework related to grandma. Notice that in the referred experiment, just mentioning the name of a person or showing the name written on a piece of paper is enough to activate the cell associated with the person.
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Louis Savain
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chatham
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09-02-05, 08:41 am |
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| eightwings wrote: | | The connectivity diameter of the brain leaves only about two or three neurons/levels for a hierarchical tree. Not nearly enough to produce a grandmother cell using a multi-level Bayesian network. |
I am still thinking about everything else you said, but I wanted to point out that I think you're misunderstanding the connectivity diameter idea.
Connectivity diameter in the context of the brain would be a measure of the shortest path between the two most distant neurons in any given brain area. It is equivalent to the diameter of a circle, in which a straight line (the shortest distance between any two points) is drawn between the two most distant points (those lying opposite each other on the circumference of the circle). Many paths LONGER than the diameter are possible between those two most distant points (you could draw a line that curves back on itself and goes in loopdy-loops).
Likewise, many paths longer than the "connectivity diameter" of the brain are possible even between geographically close neurons. The connecticity diameter does not stipulate that longer paths are not possible (including those making 'grandmother clusters' possible in a Bayesian network), but only that the existence of a shorter path between any two distant neurons is unlikely. |
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Don
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09-03-05, 01:25 pm |
| Post subject: Motor behavior and connectivity diameter |
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I think Chatham makes an excellent point here:
| Quote: | | Likewise, many paths longer than the "connectivity diameter" of the brain are possible even between geographically close neurons. |
At them moment I'm listening to Kyung Wha Chung playing the Bartok Violin Concerto and I'm asking myself, "Does eightwings think this this 'motor performance' is organized in a top-down command hierarchy 3 or 4 or 5 levels deep??" By my understanding, where the cortical branching factor <= 4, he is almost right. She couldn't pull it off with a tree of leaf circumference 4^^4, but 4^^5 might *just barely* do. I suspect if we talked about a "grandmother network rooted in the hippocampus", those of us on these threads would be close to a consensus.
So I wonder if maybe the wide-ranging debate over "grandmother cells" vs. "grandmother nets" hasn't taken us a bit off-topic?? Somewhere at the beginning of these threads was eightwings question about "layers vs. cortical diameter". My problem is this:
Hawkins pays lots of lip service to Mountcastle and his cortical "columns", but the end of the book is all about "cortical layers". So what is it?? Is the unit of cortical computation the "column", which is perpendicular to the cortical plane?? Or is it the "layer", parallel to the cortical plane??
might just pull it off with a tree of leaf dimension
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eightwings
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09-04-05, 11:31 am |
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| chatham wrote: | | eightwings wrote: | | The connectivity diameter of the brain leaves only about two or three neurons/levels for a hierarchical tree. Not nearly enough to produce a grandmother cell using a multi-level Bayesian network. |
I am still thinking about everything else you said, but I wanted to point out that I think you're misunderstanding the connectivity diameter idea. |
I don't think so.
| Quote: | | Connectivity diameter in the context of the brain would be a measure of the shortest path between the two most distant neurons in any given brain area. It is equivalent to the diameter of a circle, in which a straight line (the shortest distance between any two points) is drawn between the two most distant points (those lying opposite each other on the circumference of the circle). Many paths LONGER than the diameter are possible between those two most distant points (you could draw a line that curves back on itself and goes in loopdy-loops). |
That's not it at all. As far as I know, the term "connectivity diameter of the brain" was coined by Dr. Rodney Brooks, director of the AI lab at MIT. Brooks is no lightweight. He is the co-founder of I-robot (Roomba) and his subsumption architecture is being used in robots on Mars. Here's what Brooks said in an interview with Edge.org:
| Quote: | | ... what must be happening in biological systems is that sensing is connected to action very quickly. The connectivity diameter of the brain is only five or six neurons, if you view it as a graph, so there must be all these quick connections of sensing to action... |
What Brooks means is that a sensory signal travels no more than five or six neurons before reaching the motor layer. There is no point in arguing over the meaning of the term, in my opinion. It is clear from the context. Brooks is famous for proposing that there is minimal computation taking place between sensing and action. I agree with him 100%. It is crucial to survival. In fact, if one take out the sensor and effector layer, there is only a diameter of three or four neurons left. But it get worse. If one posits that half of the diameter is used for motor learning and the other for sensory/perceptual learning, that leaves only a two-neuron diameter for a perceptual pyramid or hierarchy. You're not going to get a grandmother-type cell out of that, I don't care how good you are.
But there is more. Psychology teaches us that the reaction time of human beings to a visual stimulus is about 180 ms or less. Assuming a 30 ms reaction time per neuron, this is hardly enough time for a sensory signal to go up a multi-level perceptual hierarchy and make it to the motor layer.
Personally, I believe that the connectivity diameter of the brain to be no more than four neurons if one take out the sensor and effector layers. There is a sensory discrete signal separation layer, a coincidence layer, a sequence/prediction layer and the motor coordination layer. In addition, there is a concept formation subnetwork which sits on top of the sequence layer. The cerebellum is a separate supervised motor behavior network with direct sensor to effector connections. Although very useful, it is really not needed for adaptive intelligence. Some animals don't have a cerebellum and a few humans are born without one.
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Louis Savain
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chatham
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09-05-05, 09:22 am |
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| eightwings wrote: | | That's not it at all. As far as I know, the term "connectivity diameter of the brain" was coined by Dr. Rodney Brooks, director of the AI lab at MIT. Brooks is no lightweight. |
Not sure what Brooks' credentials have to do with you being correct about his use of the term connectivity diameter.
from: http://faculty.washington.edu/~krumme/207/networks.html
| Quote: | "Diameter of a network: Number of links in the shortest path between the furthest pair of nodes.
Analytical significance: It is needed to identify the number of matrix multiplications (using the adjacency matrix) needed to fill all the "boxes" in the "solution matrix" (i.e. to assure that all nodes are directly or indirectly linked to each other when assessing the accessibility of the network's nodes; more specifically, the adjacency matrix has to be taken to the power of the diameter)." |
also from http://people.hofstra.edu/geotrans/eng/ch2en/meth2en/ch2m2en.html
| Quote: | | "Diameter (d). The length of the shortest path between the most distanced nodes of a graph is the diameter. d measures the extent of a graph and the topological length between two nodes" |
also from http://www.cs.uidaho.edu/~casey931/mega-math/gloss/graph/grdiam.html
| Quote: | The diameter of a graph is the longest distance you can find between two vertices.
When you are measuring distances to determine a graph's diameter, recall that if 2 vertices have many paths of different distances connecting them, you can only count the shortest one. |
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eightwings
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09-05-05, 01:57 pm |
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| Quote: | | Not sure what Brooks' credentials have to do with you being correct about his use of the term connectivity diameter. |
Alright. This disscussion is not going anywhere, in my opinion. It was nice chatting with you.
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Louis Savain
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