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In this letter, we first derive the analytical channel impulse response for a cylindrical synaptic channel surrounded by glial cells and validate it with particle-based simulations. Afterwards, we provide an accurate analytical approximation for the long-time decay rate of the channel impulse response by employing Taylor expansion to the characteristic equations that determine the decay rates of the system. We validate our approximation by comparing it with the numerical decay rate obtained from the characteristic equation. Overall, we provide a fully analytical description for the long-time behavior of synaptic diffusion, e.g., the clean-up processes inside the channel after communication has long concluded.
We first review traditional approaches to memory storage and formation, drawing on the literature of quantitative neuroscience as well as statistical physics. These have generally focused on the fast dynamics of neurons; however, there is now an incr
We show that the local Spike Timing-Dependent Plasticity (STDP) rule has the effect of regulating the trans-synaptic weights of loops of any length within a simulated network of neurons. We show that depending on STDPs polarity, functional loops are
We derive analytical formulae for the firing rate of integrate-and-fire neurons endowed with realistic synaptic dynamics. In particular we include the possibility of multiple synaptic inputs as well as the effect of an absolute refractory period into the description.
Protein synthesis-dependent, late long-term potentiation (LTP) and depression (LTD) at glutamatergic hippocampal synapses are well characterized examples of long-term synaptic plasticity. Persistent increased activity of the enzyme protein kinase M (
In continuous attractor neural networks (CANNs), spatially continuous information such as orientation, head direction, and spatial location is represented by Gaussian-like tuning curves that can be displaced continuously in the space of the preferred