1. Some thoughts on a language coordination game using Izhikevich networks.
2. ROUGH notes on neural evolution and language learning.
3. Publication in PLoS ONE. Copying and Evolution of Neuronal Topology.
1. Frameworks for simulating Izhikevich neurons in C++.
2. A version of the code used to generate results for the PLoS ONE paper above.
3. A Cocoa GUI for constructing and simulating spiking neural networks.
1. Distributed coding by single spikes in the bullfrog vestibular nerve: a basis for dynamical computation in neural systems. "Single spikes may be treated as operends in neural computation" because single spikes carried some information about the head state of the frog.
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1. Brian (SNN simulator Python).
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Despite considerable effort the functional role of oscillations remains unclear (Lisman, 2005. Hippocampus 15:913-922). The role of gamma oscillation in solving the binding problem was considered by Singer and von der Malsberg.
Here I summarize the paper by Yamaguchi (2003) Biol. Cybernetics. 89 1-9, that gives a model of how temporal input sequences can be encoded by STDP recurrent networks. Theta phase precession is generated in entorhinal cortex by phase locking between neural oscillations activated within theta frequency range and the local field theta rhythm. The gradual phase shift of neurons in ECII is inherited by CA3 and CA1. STDP in CA3 encodes the temporal sequence.
Questions.
1. Does phase precession occur in a passive listening case where there is no actual movement (of a rat through a maze), e.g. when music is played and one is subsequently asked whether one heard that piece of music before? In this case, does a temporal representation of that music appear locked to a theta rhythm in EC?
2. How does phase locking in a coupled neural oscillator system work? a. Feed input vector into the array of neural units in EC. There is overlap between receptive fields of these units, which gives a population code of a given event at time t. b. The internal parameter of each unit gradually changes so that its frequency increases. A neural unit oscillates in the ON state and is at rest in the OFF state. c. LFP acts as reference oscillator.
The equation above shows the rate of change of oscillation phase of the ith oscillator. The native frequency of LFP is w0. wi is the native frequency of the ith unit. Cos of phase i is the membrane potential of unit i.
Bi(t) in 1 is shown above. The second term is behaviour dependent input and and the last is input from the LFP theta with constant k. When the Ith unit is off, Ii(t) = 0, wi(t) = w0, and Bi(t) = Beta. When a unit is on then wi(t) and Bi(t) are changed. When a unit is activated, its native frequency gradually increases linearly according to the following equation...
4
where deltaW and Ws are positive constants.
The neurons from ECII project to CA3 CA3 is fully recurrently connected, with STDP at each synapse. There is THETA modulation of PLASTICITY in CA3. Indivduals units from CA3 project to all CA1 neurons with STDP weights as well. ECIII projects to CA1 with fixed topographic connections. ECII projects to ECIII, ECIII also recieves inputs, ECIII lags behind ECII by quarter of a theta cycle!
The theta oscillations are described by the equations above. You can see they are coupled together (by phase-locking). ECII activation is described by...
i.e. it recieves inputs, as described by equation 4 above. This results in the following equations describing time-evolution of the other layers.
Where P is an output function...
The results from a numerical simulation are shown below...
The input sequence is shown at the top, with the neurons in ECII shown next. The sequence of inputs is CONVERTED into a set of phase shifted oscillations. NOTE that this all happens in one trial. The cleverness of the theta rhythm is that it solves the problem of the discrepency between the time scale of behavioural sequences and the timescale of STDP. Memory retrieval is tested by presenting only the first 3 input stimuli which allows CA3, CA1 and ECIII to reproduce the rest of the sequence...
ECIII is considered the DECODER. How is this different from what we wanted to achieve in our experiment?
1. We wanted to have ALL these dynamics, sure (possibly in simplified form) but we also wanted to see how these memories could get transferred to cortex.
2. How crucial is it to model CA3 AND CA1 and two types of ECII and ECIII?
Yamaguchi accepts that a crucial requirement for the above model is the gradual increase in native frequency of neurons in EC. There is evidence for such oscillations. There appears to be no role for multiple copies being made of an input sequence, nor for storage of MANY distinct input sequences in a network. This may require a cortical store. But then the question is, how to retrieve that store by presenting partial input sequences? The first step is to replicate the crucial aspects of the above model so that a C++ function exists to convert an environmental input sequence (e.g. a tune) into theta encoded components.
Software to simulate EC1 (Yamaguchi) with CA3 is available here.
Chialvo, D.R. and Bak, P. Learning from mistakes. (1998) Download ps.
Sporns, O. Chialvo, D.R. Kaiser, M. Hilgetag, C.C. Organization, Development and Function of Complex Brain Networks. (2004) Trands in Cognitive Sciences. 8(9), 418-425 Download pdf.