1,333 research outputs found
Statistical Mechanics of Recurrent Neural Networks I. Statics
A lecture notes style review of the equilibrium statistical mechanics of
recurrent neural networks with discrete and continuous neurons (e.g. Ising,
coupled-oscillators). To be published in the Handbook of Biological Physics
(North-Holland). Accompanied by a similar review (part II) dealing with the
dynamics.Comment: 49 pages, LaTe
Nonlinear multiplicative dendritic integration in neuron and network models
Neurons receive inputs from thousands of synapses distributed across dendritic trees of complex morphology. It is known that dendritic integration of excitatory and inhibitory synapses can be highly non-linear in reality and can heavily depend on the exact location and spatial arrangement of inhibitory and excitatory synapses on the dendrite. Despite this known fact, most neuron models used in artificial neural networks today still only describe the voltage potential of a single somatic compartment and assume a simple linear summation of all individual synaptic inputs. We here suggest a new biophysical motivated derivation of a single compartment model that integrates the non-linear effects of shunting inhibition, where an inhibitory input on the route of an excitatory input to the soma cancels or âshuntsâ the excitatory potential. In particular, our integration of non-linear dendritic processing into the neuron model follows a simple multiplicative rule, suggested recently by experiments, and allows for strict mathematical treatment of network effects. Using our new formulation, we further devised a spiking network model where inhibitory neurons act as global shunting gates, and show that the network exhibits persistent activity in a low firing regime
Simulation of networks of spiking neurons: A review of tools and strategies
We review different aspects of the simulation of spiking neural networks. We
start by reviewing the different types of simulation strategies and algorithms
that are currently implemented. We next review the precision of those
simulation strategies, in particular in cases where plasticity depends on the
exact timing of the spikes. We overview different simulators and simulation
environments presently available (restricted to those freely available, open
source and documented). For each simulation tool, its advantages and pitfalls
are reviewed, with an aim to allow the reader to identify which simulator is
appropriate for a given task. Finally, we provide a series of benchmark
simulations of different types of networks of spiking neurons, including
Hodgkin-Huxley type, integrate-and-fire models, interacting with current-based
or conductance-based synapses, using clock-driven or event-driven integration
strategies. The same set of models are implemented on the different simulators,
and the codes are made available. The ultimate goal of this review is to
provide a resource to facilitate identifying the appropriate integration
strategy and simulation tool to use for a given modeling problem related to
spiking neural networks.Comment: 49 pages, 24 figures, 1 table; review article, Journal of
Computational Neuroscience, in press (2007
Electroencephalographic field influence on calcium momentum waves
Macroscopic EEG fields can be an explicit top-down neocortical mechanism that
directly drives bottom-up processes that describe memory, attention, and other
neuronal processes. The top-down mechanism considered are macrocolumnar EEG
firings in neocortex, as described by a statistical mechanics of neocortical
interactions (SMNI), developed as a magnetic vector potential . The
bottom-up process considered are waves prominent in synaptic
and extracellular processes that are considered to greatly influence neuronal
firings. Here, the complimentary effects are considered, i.e., the influence of
on momentum, . The canonical
momentum of a charged particle in an electromagnetic field, (SI units), is calculated, where the charge of
is , is the magnitude of the charge of an
electron. Calculations demonstrate that macroscopic EEG can be
quite influential on the momentum of ions, in
both classical and quantum mechanics. Molecular scales of
wave dynamics are coupled with fields developed at macroscopic
regional scales measured by coherent neuronal firing activity measured by scalp
EEG. The project has three main aspects: fitting models to EEG
data as reported here, building tripartite models to develop
models, and studying long coherence times of waves in the
presence of due to coherent neuronal firings measured by scalp
EEG. The SMNI model supports a mechanism wherein the interaction at tripartite synapses, via a dynamic centering
mechanism (DCM) to control background synaptic activity, acts to maintain
short-term memory (STM) during states of selective attention.Comment: Final draft. http://ingber.com/smni14_eeg_ca.pdf may be updated more
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