International Journal of Modern Physics B, Dec 1, 1988
The series analysis of the low temperature expansion of the checkerboard q-state Potts model in a... more The series analysis of the low temperature expansion of the checkerboard q-state Potts model in a magnetic field initiated in two previous papers is continued. In particular algebraic varieties of the parameter space (corresponding or generalizing the so-called disorder solutions), the checkerboard Potts model and its Bethe approximation are indistinguishable as far as one is concerned with the partition function and its first order derivatives. The difference between the two models occurs for higher order derivatives. In particular one gives the exact expression of the (low temperature expansion of the) susceptibility of the checkerboard Ising model in zero magnetic field on one of these varieties.
Persistent activity in cortex is the neural correlate of workingmemory (WM). In persistent activi... more Persistent activity in cortex is the neural correlate of workingmemory (WM). In persistent activity, spike trains are highly irregular, even more than in baseline. This seemingly innocuous feature challenges our current understanding of the synaptic mechanisms underlying WM. Here we argue that in WM the prefrontal cortex (PFC) operates in a regime of balanced excitation and inhibition and that the observed temporal irregularity reflects this regime. We show that this requires that nonlinearities underlying the persistent activity are primarily in the neuronal interactions between PFC neurons.We also show that short-term synaptic facilitation can be the physiological substrate of these nonlinearities and that the resulting mechanism of balanced persistent activity is robust, in particular with respect to changes in the connectivity. As an example, we put forward a computational model of the PFC circuit involved in oculomotor delayed response task. The novelty of this model is that re...
Electrical synapses are ubiquitous in the mammalian CNS. Particularly in the neocortex, electrica... more Electrical synapses are ubiquitous in the mammalian CNS. Particularly in the neocortex, electrical synapses have been shown to connect low-threshold spiking (LTS) as well as fast spiking (FS) interneurons. Experiments have highlighted the roles of electrical synapses in the dynamics of neuronal networks. Here we investigate theoretically how intrinsic cell properties affect the synchronization of neurons interacting by electrical synapses. Numerical simulations of a network of conductance-based neurons randomly connected with electrical synapses show that potassium currents promote synchrony, whereas the persistent sodium current impedes it. Furthermore, synchrony varies with the firing rate in qualitatively different ways depending on the intrinsic currents. We also study analytically a network of quadratic integrate-and-fire neurons. We relate the stability of the asynchronous state of this network to the phase-response function (PRF), which characterizes the effect of small pertu...
The Journal of neuroscience : the official journal of the Society for Neuroscience, Jan 14, 2016
Absence seizures are characterized by brief interruptions of conscious experience accompanied by ... more Absence seizures are characterized by brief interruptions of conscious experience accompanied by oscillations of activity synchronized across many brain areas. Although the dynamics of the thalamocortical circuits are traditionally thought to underlie absence seizures, converging experimental evidence supports the key involvement of the basal ganglia (BG). In this theoretical work, we argue that the BG are essential for the maintenance of absence seizures. To this end, we combine analytical calculations with numerical simulations to investigate a computational model of the BG-thalamo-cortical network. We demonstrate that abnormally strong striatal feedforward inhibition can promote synchronous oscillatory activity that persists in the network over several tens of seconds as observed during seizures. We show that these maintained oscillations result from an interplay between the negative feedback through the cortico-subthalamo-nigral pathway and the striatal feedforward inhibition. T...
We try to elucidate the role played by different symmetries in simple models of statistical mecha... more We try to elucidate the role played by different symmetries in simple models of statistical mechanics. Starting with obvious symmetries for the partition function and combining them with duality relations we obtain a set of constraints on the possible algebraic varieties relevant for the integrable manifolds and the phase diagram of the lattice model. When imposing in addition the inversion relation special polynomials are obtained, which are close and sometimes identical to the set of equations defining the parameter subspace of the integrable models. Our procedure is detailed on the q-state chiral Potts models on a square lattice, in particular for q=3 and 4.
The distribution ofin vivoaverage firing rates within local cortical networks has been reported t... more The distribution ofin vivoaverage firing rates within local cortical networks has been reported to be highly skewed and long tailed. The distribution of average single-cell inputs, conversely, is expected to be Gaussian by the central limit theorem. This raises the issue of how a skewed distribution of firing rates might result from a symmetric distribution of inputs. We argue that skewed rate distributions are a signature of the nonlinearity of thein vivo f–Icurve. Duringin vivoconditions, ongoing synaptic activity produces significant fluctuations in the membrane potential of neurons, resulting in an expansive nonlinearity of thef–Icurve for low and moderate inputs. Here, we investigate the effects of single-cell and network parameters on the shape of thef–Icurve and, by extension, on the distribution of firing rates in randomly connected networks.
Neurons in primary visual cortex (V1) display substantial orientation selectivity even in species... more Neurons in primary visual cortex (V1) display substantial orientation selectivity even in species where V1 lacks an orientation map, such as in mice and rats. The mechanism underlying orientation selectivity in V1 with such a salt-and-pepper organization is unknown; it is unclear whether a connectivity that depends on feature similarity is required, or a random connectivity suffices. Here we argue for the latter. We study the response to a drifting grating of a network model of layer 2/3 with random recurrent connectivity and feedforward input from layer 4 neurons with random preferred orientations. We show that even though the total feedforward and total recurrent excitatory and inhibitory inputs all have a very weak orientation selectivity, strong selectivity emerges in the neuronal spike responses if the network operates in the balanced excitation/inhibition regime. This is because in this regime the (large) untuned components in the excitatory and inhibitory contributions approx...
Persistent activity in cortex is the neural correlate of working memory (WM). In persistent activ... more Persistent activity in cortex is the neural correlate of working memory (WM). In persistent activity, spike trains are highly irregular, even more than in baseline. This seemingly innocuous feature challenges our current understanding of the synaptic mechanisms underlying WM. Here we argue that in WM the prefrontal cortex (PFC) operates in a regime of balanced excitation and inhibition and that the observed temporal irregularity reflects this regime. We show that this requires that nonlinearities underlying the persistent activity are primarily in the neuronal interactions between PFC neurons. We also show that short-term synaptic facilitation can be the physiological substrate of these nonlinearities and that the resulting mechanism of balanced persistent activity is robust, in particular with respect to changes in the connectivity. As an example, we put forward a computational model of the PFC circuit involved in oculomotor delayed response task. The novelty of this model is that ...
International Journal of Modern Physics B, Dec 1, 1988
The series analysis of the low temperature expansion of the checkerboard q-state Potts model in a... more The series analysis of the low temperature expansion of the checkerboard q-state Potts model in a magnetic field initiated in two previous papers is continued. In particular algebraic varieties of the parameter space (corresponding or generalizing the so-called disorder solutions), the checkerboard Potts model and its Bethe approximation are indistinguishable as far as one is concerned with the partition function and its first order derivatives. The difference between the two models occurs for higher order derivatives. In particular one gives the exact expression of the (low temperature expansion of the) susceptibility of the checkerboard Ising model in zero magnetic field on one of these varieties.
Persistent activity in cortex is the neural correlate of workingmemory (WM). In persistent activi... more Persistent activity in cortex is the neural correlate of workingmemory (WM). In persistent activity, spike trains are highly irregular, even more than in baseline. This seemingly innocuous feature challenges our current understanding of the synaptic mechanisms underlying WM. Here we argue that in WM the prefrontal cortex (PFC) operates in a regime of balanced excitation and inhibition and that the observed temporal irregularity reflects this regime. We show that this requires that nonlinearities underlying the persistent activity are primarily in the neuronal interactions between PFC neurons.We also show that short-term synaptic facilitation can be the physiological substrate of these nonlinearities and that the resulting mechanism of balanced persistent activity is robust, in particular with respect to changes in the connectivity. As an example, we put forward a computational model of the PFC circuit involved in oculomotor delayed response task. The novelty of this model is that re...
Electrical synapses are ubiquitous in the mammalian CNS. Particularly in the neocortex, electrica... more Electrical synapses are ubiquitous in the mammalian CNS. Particularly in the neocortex, electrical synapses have been shown to connect low-threshold spiking (LTS) as well as fast spiking (FS) interneurons. Experiments have highlighted the roles of electrical synapses in the dynamics of neuronal networks. Here we investigate theoretically how intrinsic cell properties affect the synchronization of neurons interacting by electrical synapses. Numerical simulations of a network of conductance-based neurons randomly connected with electrical synapses show that potassium currents promote synchrony, whereas the persistent sodium current impedes it. Furthermore, synchrony varies with the firing rate in qualitatively different ways depending on the intrinsic currents. We also study analytically a network of quadratic integrate-and-fire neurons. We relate the stability of the asynchronous state of this network to the phase-response function (PRF), which characterizes the effect of small pertu...
The Journal of neuroscience : the official journal of the Society for Neuroscience, Jan 14, 2016
Absence seizures are characterized by brief interruptions of conscious experience accompanied by ... more Absence seizures are characterized by brief interruptions of conscious experience accompanied by oscillations of activity synchronized across many brain areas. Although the dynamics of the thalamocortical circuits are traditionally thought to underlie absence seizures, converging experimental evidence supports the key involvement of the basal ganglia (BG). In this theoretical work, we argue that the BG are essential for the maintenance of absence seizures. To this end, we combine analytical calculations with numerical simulations to investigate a computational model of the BG-thalamo-cortical network. We demonstrate that abnormally strong striatal feedforward inhibition can promote synchronous oscillatory activity that persists in the network over several tens of seconds as observed during seizures. We show that these maintained oscillations result from an interplay between the negative feedback through the cortico-subthalamo-nigral pathway and the striatal feedforward inhibition. T...
We try to elucidate the role played by different symmetries in simple models of statistical mecha... more We try to elucidate the role played by different symmetries in simple models of statistical mechanics. Starting with obvious symmetries for the partition function and combining them with duality relations we obtain a set of constraints on the possible algebraic varieties relevant for the integrable manifolds and the phase diagram of the lattice model. When imposing in addition the inversion relation special polynomials are obtained, which are close and sometimes identical to the set of equations defining the parameter subspace of the integrable models. Our procedure is detailed on the q-state chiral Potts models on a square lattice, in particular for q=3 and 4.
The distribution ofin vivoaverage firing rates within local cortical networks has been reported t... more The distribution ofin vivoaverage firing rates within local cortical networks has been reported to be highly skewed and long tailed. The distribution of average single-cell inputs, conversely, is expected to be Gaussian by the central limit theorem. This raises the issue of how a skewed distribution of firing rates might result from a symmetric distribution of inputs. We argue that skewed rate distributions are a signature of the nonlinearity of thein vivo f–Icurve. Duringin vivoconditions, ongoing synaptic activity produces significant fluctuations in the membrane potential of neurons, resulting in an expansive nonlinearity of thef–Icurve for low and moderate inputs. Here, we investigate the effects of single-cell and network parameters on the shape of thef–Icurve and, by extension, on the distribution of firing rates in randomly connected networks.
Neurons in primary visual cortex (V1) display substantial orientation selectivity even in species... more Neurons in primary visual cortex (V1) display substantial orientation selectivity even in species where V1 lacks an orientation map, such as in mice and rats. The mechanism underlying orientation selectivity in V1 with such a salt-and-pepper organization is unknown; it is unclear whether a connectivity that depends on feature similarity is required, or a random connectivity suffices. Here we argue for the latter. We study the response to a drifting grating of a network model of layer 2/3 with random recurrent connectivity and feedforward input from layer 4 neurons with random preferred orientations. We show that even though the total feedforward and total recurrent excitatory and inhibitory inputs all have a very weak orientation selectivity, strong selectivity emerges in the neuronal spike responses if the network operates in the balanced excitation/inhibition regime. This is because in this regime the (large) untuned components in the excitatory and inhibitory contributions approx...
Persistent activity in cortex is the neural correlate of working memory (WM). In persistent activ... more Persistent activity in cortex is the neural correlate of working memory (WM). In persistent activity, spike trains are highly irregular, even more than in baseline. This seemingly innocuous feature challenges our current understanding of the synaptic mechanisms underlying WM. Here we argue that in WM the prefrontal cortex (PFC) operates in a regime of balanced excitation and inhibition and that the observed temporal irregularity reflects this regime. We show that this requires that nonlinearities underlying the persistent activity are primarily in the neuronal interactions between PFC neurons. We also show that short-term synaptic facilitation can be the physiological substrate of these nonlinearities and that the resulting mechanism of balanced persistent activity is robust, in particular with respect to changes in the connectivity. As an example, we put forward a computational model of the PFC circuit involved in oculomotor delayed response task. The novelty of this model is that ...
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