Eric, Actually I am looking for a function A =f(N,S,O).
If one leaves out the O, and merely wants to find the number of subcombinations of size S that can be formed from a population of size N, just apply the standard formula for combinations. But adding the limitation that none of the combinations in A is allowed to overlap by more than O with any other combination in A makes things much more complex, and way beyond my understanding. Ed Porter -----Original Message----- From: Eric Burton [mailto:[EMAIL PROTECTED] Sent: Wednesday, October 15, 2008 8:05 PM To: [email protected] Subject: Re: [agi] Who is smart enough to answer this question? >Is anybody on this list smart and/or knowledgeable enough to come up with a >formula for the following (I am not): I don't think I'm the person to answer this for you. But I do have some insights. >Given N neural net nodes, what is the number A of unique node assemblies >(i.e., separate subsets of N) of size S that can have less than O >overlapping nodes, with the population of any other such node assembly >similarly selected from the N nodes to have the same size S and less than >the same O overlapping nodes with any other such node assembly. Good question. Let's call the function that returns A for N, "f(N)", and continue. >For example, if you have 1 billion nodes (N = 1G), how many cell assemblies >(A) of size 10,000 (S=10K) will have less than 5,000 nodes (0 = 5K) in >common with the population of any other node assembly. So at this point we are seeking f(1000000000), which I'm going to go ahead and call P. >Its easy to figure out how many unique cell assemblies drawn from a >population of N nodes that can have a size S, but I haven't a clue, other >than by computational exploration to figure out how many will each have less >than a given level of overlap with any other unique cell assemblies. This is why we have f. >And for anyone who knows how to solve the above, if possible, could you also >please also tell me, once you have close to A node assemblies selected that >have less than O overlap, how can you rapidly determine the population of a >new node assembly that has less than O overlap? For my purposes, f is a black box. You'd have to delve into its internals to answer this yourself. >This is not just an meaningless math problem. >A lot of people believe the human brain uses cell assemblies to represent >nodes in a representation of semantic knowledge. Such cell assemblies >create problems with current computer hardware because they tend to require >very high internal bandwidth, but in future architectures this problem may >not exist, and if the number of cell assemblies that can be created with a >sufficiently low cross-talk is large relative to the number of nodes, the >use of cell assemblies can allow for redundancy, high representational >capacity, and gradual degrading of memories over time to make room for more >memories. Hence, I suppose, the value of your inquiry. If I'm visualizing the issue correctly you'd like a function that returns the number of unique neural nets with a number of nodes either less or greater than n and interconnects either less or greater than i... I'll reiterate that I'm not a student of mathematics and aren't qualified to address the details of the problem. But surely this function is what we've been calling f. I'd welcome corrections and clarifications. I may not understand the question. Eric B ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?&; Powered by Listbox: http://www.listbox.com ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
