https://meet.google.com/wfh-rekd-etw Cecilia Romaro, Antonio Carlos Roque, Jose Roberto Castilho Piqueira Studying the dynamics of a neuron network has been a challenge to computational Neuroscience [1,2]. Doing so in a neuron network with topographic organization is even more demanding due to the boundary condition, i.e. the interruption of the topographic pattern of connection in network edges, which changes network boundary activity. The neurons on the edge of the network present underside behavior due to a lack (or excess) of connections and a torus solution may introduce undesired oscillations. Facing such strain, this work presents a method based on mean field potential (i.e. first and second-order statistics of neuron network dynamics) to sustain neuron boundary activity – such as neurons on the core of the layer network activity – without introducing an oscillation component.
This method is based on the rescaling presented on CNS previous works (CNS-2018) and consists of:
Step 1: Calculating the scale factor k_i for any neuron i in network as follows: For a neuron i, k_i is given by the average of total number of connections received divided by the average of total number of connections that would be received IF the network had no boundaries – was a set of infinity neurons;
Step 2: Increasing the synaptic weights by dividing them by the square root of the scale factor;
Step 3: Providing each cell with a DC input current with a value corresponding to the total input lost due to network edge (boundary cut).
In essence, the boundary correction method numerically estimates the normalized density function of connection on the first step, then weights each neuron connection based on this density, and finally balances the threshold to grant the neuron/layer activity. This method was successfully applied on consolidated models such as Brunel [1] and PD [2], among others.
Firstly the models were reimplemented and the results were reproduced. Secondly, a topographic patter of connection was introduced to the models including the consideration that neurons near each other have a higher probability of connection then those further from each other. A different activity rises on both network boundary neurons and sometimes on core neurons. This method was applied and the activities were driven back to the original ones.
The algorithmic of rescaling method can be found in any one of example- application available in GitHub (https://github.com/ceciliaromaro/recoup-the- first-and-second-order-statistics-of-neuron-network-dynamics)
Acknowledgements
This work was produced as part of the activities of FAPESP Research, Disseminations and Innovation Center for Neuromathematics (Grant 2013/07699-0, S. Paulo Research Foundation).
References
[1] Brunel, N.Dynamics of sparsely connected networks of excitatory and inhibitory spikingneurons.Journal of computational neuroscience 8, 3 (2000), 183–208
[2] Potjans TC and Diesmann M (2014). The cell-type specific cortical microcircuit: relating structure and activity in a full-scale spiking network model. Cerebral Cortex 24:785-806.
