X-Message-Number: 26992 From: Date: Sat, 10 Sep 2005 02:15:55 EDT Subject: Uploading technology (1.iv.2) The column level . Uploading technology (1.iv.2) The column level . The cerebral cortex may be divided into 50 or so cortical areas. Or on a finer scale, into one thousand maps. Each with 300 columns (300,000 columns). There may be five millions cortical bands and 300 millions microcolumns, each with 100 neurons or so. Most channels have a refractory period, so there can't be a new pulse for a given time. A tipical refractory time is 100 ms, in this duration, an action potential travel one or two centimeters in a non myelinated axon or a dendrite. With a density of 60,000 neurons/sq. mm nearly all neurons in a microcolumn can be contacted in less than that time. The network dynamics is then limited by the refractory period, this is the Glauber dynamics. It may be good until the column level. Beyond that, the transmission time is of the same order as the refractory time and there is another dynamics, the Little one. What is interesting with that dynamical change is that neurons from one to another may in fact communicate globally. For one given neuron, each nearby one in the same column is an individual one. Nearby has the meaning of glauber area. Beyond that, the neuron see only another glauber block, that is a pool of 100,000 or so neurons. Each neuron pool works as a black box for the rest of the brain. This open up a possibility for uploading: Assume a simulation is run on a single column, it could be seen as self contained. If all the possible input ar e tested and all output registered or deduced in some way, a black box with a very different technology could be substitued to the neural network and give neverthless the same output. Here is a possibility: The main information between neurons seems to be carried out by firing patterns. Mathematical analysis demonstrates that the pattern number P can't exceed the number N of neurons. Here, "neurons" stand for the simplified W. S. McCulloch and W.Pitts model from the 1943 era. Even being a far simplified version of real neurons, they are interesting because they are universal, that is they can simulate a true neuron if a sufficient number of them is assembled correctly. A real neuron may need one McCulloch-Pitts one at each synapse and each dendrite branching point. This would ask for something as 100,000 McCulloch-Pitts neurons for each biological pyramidal one. One column would need so ten billions elementary neurons. It would not be cost effective to build a brain that way, but it is a theoretical possibility. It tells us that a column can't display more than ten billion different outputs to the outside world. This seems not a very interesting result, neverthless, it brighten when seen another way. Assume the maximum firing rate of a neuron is one pulse every ten millisecond and a pattern has a maximum duration near one second, so it may contain one hundred pulses. Each such pulse may be present or not in an actual pattern, so there is 2 ^100 possibilities or 10^30 possible patterns. Reducing that value to 10^10 is an interesting result. That assume only one action potential kind, if strong and long AP are allowed, the theoretical possibilities jump to 10^60. A 10^10 limit is then even more interesting. One way to interpret these values would be to say that a pattern can't extend for a full second. If it was limited to 150 ms or so, all possibilities would be used. In fact, it seems more natural to lenghten the pattern time and allows a decreasing density of realised possibilities with time. So, short patterns would use nearly all possible combinations and long ones would be only a small subsample of all possibilities. G-protein gated channels would presumably control the pattern lenght and second messenger currents would shift from one pattern to another. There may be more involved combinations between currents, even for fast chemical channels. Given the noisy environment of neurons, it seems a pattern must be recognizable even if it has undergone a lot of alteration. This imply that all possible alteration are not legitimate patterns and so the true repertory of used patterns must be a small subsample of all possibilities. Out of the 10^10 possible AP combinations, may be one out of one thousand would be used. Put another way, a given column would use only 10^7 patterns. From that, may be some thousands would be in regular use. Now what is a pattern? It is a set of action potentials, 64 would be a good maximum limit. Each would be defined by a two bits code, so a pattern is defined by a 128 bits string or 16 bytes. Ten millions would take 160 Mb. If there is 100,000 columns in the cortex, the full repertory would take 16 Tb, that is 32 hard disk, each with a 500 Gb capacity. Using 16 PC each with 2 HD would fit the bill. This bring into play a new comcept : A brain could be simulated as a set comprising 100,000 "black boxes", each simulated using time sharing on a set of PCs. The individual neuron simulation would be limited to a single column with something as 100 to 300 thousands neurons. Using time sharing, this would fit on approximately 10 - 15 current generation FPGAs. The same material device would simulate each column, one after the other and give out its pattern repertory and how they are displayed to the outside given all possible inputs. This brain simulation would be harder to evolve than a full implementation of each individual neuron but it would be a valuable first step using only off the shelf electronics components without recourse to specialised asic neuromorphic chips. Yvan Bozzonetti. 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