42 research outputs found
The complexity of dynamics in small neural circuits
Mean-field theory is a powerful tool for studying large neural networks.
However, when the system is composed of a few neurons, macroscopic differences
between the mean-field approximation and the real behavior of the network can
arise. Here we introduce a study of the dynamics of a small firing-rate network
with excitatory and inhibitory populations, in terms of local and global
bifurcations of the neural activity. Our approach is analytically tractable in
many respects, and sheds new light on the finite-size effects of the system. In
particular, we focus on the formation of multiple branching solutions of the
neural equations through spontaneous symmetry-breaking, since this phenomenon
increases considerably the complexity of the dynamical behavior of the network.
For these reasons, branching points may reveal important mechanisms through
which neurons interact and process information, which are not accounted for by
the mean-field approximation.Comment: 34 pages, 11 figures. Supplementary materials added, colors of
figures 8 and 9 fixed, results unchange
Mean Field description of and propagation of chaos in recurrent multipopulation networks of Hodgkin-Huxley and Fitzhugh-Nagumo neurons
We derive the mean-field equations arising as the limit of a network of
interacting spiking neurons, as the number of neurons goes to infinity. The
neurons belong to a fixed number of populations and are represented either by
the Hodgkin-Huxley model or by one of its simplified version, the
Fitzhugh-Nagumo model. The synapses between neurons are either electrical or
chemical. The network is assumed to be fully connected. The maximum
conductances vary randomly. Under the condition that all neurons initial
conditions are drawn independently from the same law that depends only on the
population they belong to, we prove that a propagation of chaos phenomenon
takes places, namely that in the mean-field limit, any finite number of neurons
become independent and, within each population, have the same probability
distribution. This probability distribution is solution of a set of implicit
equations, either nonlinear stochastic differential equations resembling the
McKean-Vlasov equations, or non-local partial differential equations resembling
the McKean-Vlasov-Fokker- Planck equations. We prove the well-posedness of
these equations, i.e. the existence and uniqueness of a solution. We also show
the results of some preliminary numerical experiments that indicate that the
mean-field equations are a good representation of the mean activity of a finite
size network, even for modest sizes. These experiment also indicate that the
McKean-Vlasov-Fokker- Planck equations may be a good way to understand the
mean-field dynamics through, e.g., a bifurcation analysis.Comment: 55 pages, 9 figure
Stationary-State Statistics of a Binary Neural Network Model with Quenched Disorder
We study the statistical properties of the stationary firing-rate states of a
neural network model with quenched disorder. The model has arbitrary size,
discrete-time evolution equations and binary firing rates, while the topology
and the strength of the synaptic connections are randomly generated from known,
generally arbitrary, probability distributions. We derived semi-analytical
expressions of the occurrence probability of the stationary states and the mean
multistability diagram of the model, in terms of the distribution of the
synaptic connections and of the external stimuli to the network. Our
calculations rely on the probability distribution of the bifurcation points of
the stationary states with respect to the external stimuli, which can be
calculated in terms of the permanent of special matrices, according to extreme
value theory. While our semi-analytical expressions are exact for any size of
the network and for any distribution of the synaptic connections, we also
specialized our calculations to the case of statistically-homogeneous
multi-population networks. In the specific case of this network topology, we
calculated analytically the permanent, obtaining a compact formula that
outperforms of several orders of magnitude the
Balasubramanian-Bax-Franklin-Glynn algorithm. To conclude, by applying the
Fisher-Tippett-Gnedenko theorem, we derived asymptotic expressions of the
stationary-state statistics of multi-population networks in the
large-network-size limit, in terms of the Gumbel (double exponential)
distribution. We also provide a Python implementation of our formulas and some
examples of the results generated by the code.Comment: 30 pages, 6 figures, 2 supplemental Python script
Microwave imaging of magnetohydrodynamic instabilities in fusion plasma
Microwave imaging diagnostics are extremely useful for observing magnetohydrodynamic (MHD) instabilities in magnetic fusion plasmas. Two imaging diagnostics will be available on the WEST tokamak. A method was developed to reconstruct electron density maps from electron density profiles measured by ultrafast reflectometry, a technique based on FM-CW radar principle. It relies on plasma rotation to perform 2D reconstruction. An Electron Cyclotron Emission Imaging (ECEI) diagnostic will image directly the temperature fluctuations. It will be equivalent to 24 stacked vertically radiometers, each probing a spot of few centimetres. These two complementary techniques will contribute to the validation of MHD models.ope
Quantitative assessment based on kinematic measures of functional impairments during upper extremity movements: a review
Quantitative measures of human movement quality are important for discriminating healthy and pathological conditions and for expressing the outcomes and clinically important changes in subjects' functional state. However the most frequently used instruments for the upper extremity functional assessment are clinical scales, that previously have been standardized and validated, but have a high subjective component depending on the observer who scores the test. But they are not enough to assess motor strategies used during movements, and their use in combination with other more objective measures is necessary. The objective of the present review is to provide an overview on objective metrics found in literature with the aim of quantifying the upper extremity performance during functional tasks, regardless of the equipment or system used for registering kinematic data
Bridging the gap between robotic technology and health care
Although technology and computation power have become more and more present in our daily lives, we have yet to see the same tendency in robotics applied to health care. In this work we focused on the study of four distinct applications of robotic technology to health care, named Robotic Assisted Surgery, Robotics in Rehabilitation, Prosthetics and Companion Robotic Systems. We identified the main roadblocks that are limiting the progress of such applications by an extensive examination of recent reports. Based on the limitations of the practical use of current robotic technology for health care we proposed a general modularization approach for the conception and implementation of specific robotic devices. The main conclusions of this review are: (i) there is a clear need of the adaptation of robotic technology (closed loop) to the user, so that robotics can be widely accepted and used in the context of heath care; (ii) for all studied robotic technologies cost is still prohibitive and limits their wide use. The reduction of costs influences technology acceptability; thus innovation by using cheaper computer systems and sensors is relevant and should be taken into account in the implementation of robotic systems