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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... 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.
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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... 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...
ABSTRACT
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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... 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...
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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... 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...
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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... 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.
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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... 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.
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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... 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...
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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... 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 ...
Research Interests: Neuroscience, Psychology, Working Memory, Medicine, Prefrontal Cortex, and 14 moreHumans, Neuronal Plasticity, Memoria, Neurons, Novelty, SYNAPSES, Short Term Memory, Dinamica, Enseñanza - Aprendizaje Ciencias Naturales Y Exactas, Action Potentials, Ciencias Fisicas, Psychology and Cognitive Sciences, Medical and Health Sciences, and plasticidad
Research Interests: Neuroscience, Computer Science, Computational Biology, Nonlinear dynamics, Biology, and 15 moreElectroencephalography, Medicine, Biological Sciences, Global change, Mathematical Sciences, Animals, Contrast sensitivity, Oscillations, Gamma Band, Layered Structure, Neuronal Activity, Local Field Potential, Network Model, Chaotic, and Gamma band activity
Research Interests: Neuroscience, Computer Science, Electrophysiology, Biology, Medicine, and 15 moreBiological Sciences, High Frequency, Humans, Computer Simulation, Mathematical Sciences, Animals, Conductance, Neuron, Nonlinear Dynamic System, Neocortex, Action Potentials, Interneurons, Bursting, Intracellular recording, and Firing pattern
It is shown that the low temperature expansion of the partition function, magnetization and nearest neighbour correlation functions of the q-state checkerboard Potts model in a magnetic field drastically simplify on a very simple... more
It is shown that the low temperature expansion of the partition function, magnetization and nearest neighbour correlation functions of the q-state checkerboard Potts model in a magnetic field drastically simplify on a very simple algebraic variety. These four formal constraints on the expansions are also analysed in the framework of the resummed low temperature expansions and the large q expansions. These exact results are generalized straightforwardly to higher dimensional hypercubic lattices and also to some random problems.
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Research Interests: Biology and Basal ganglia
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Research Interests: Neuroscience, Cognitive Science, Algorithms, Electrophysiology, Animal Behavior, and 15 moreMedicine, Applied Animal Behavior, Movement disorders, Movement, Female, Animals, Oscillations, Neurons, European, Globus Pallidus, Basal ganglia, Macaca Mulatta, Disease Progression, Neurosciences, and Parkinsonism
Research Interests: Neuroscience, Chemistry, Electrophysiology, Deep Brain Stimulation, Medicine, and 15 moreBrain, Female, Animals, Oscillations, Neurons, Neurotoxins, Neuronal Activity, Basal ganglia, Macaca Mulatta, Action Potentials, Correlation function, High Frequency Stimulation, Medical and Health Sciences, MPTP, and Electric stimulation
It is now widely believed that decisions are guided by a small number of internal subjective variables that determine choice preference. The process of learning manifests as a change in the state of these variables. It is not clear how to... more
It is now widely believed that decisions are guided by a small number of internal subjective variables that determine choice preference. The process of learning manifests as a change in the state of these variables. It is not clear how to find the neural correlates of these variables, in particular because their state cannot be directly measured or controlled by the experimenter. Rather, these variables reflect the history of the subject’s actions and reward experience. We seek to construct a behavioral model that captures the dynamics of learning and decision making, such that the internal variables of this model will serve as a proxy for the subjective variables. We use the theory of reinforcement learning in order to find a behavioral model that best captures the learning dynamics of monkeys in a two-armed bandit reward schedule. We consider two families of learning algorithms: value function estimation and direct policy optimization. In the former, the values of the alternative ...
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Recent evidence points to involvement of central nervous system oscillators in Parkinson's disease (PD) rest tremor. It remains unknown whether one or multiple oscillators cause tremor in multiple limbs. Based on the prediction that... more
Recent evidence points to involvement of central nervous system oscillators in Parkinson's disease (PD) rest tremor. It remains unknown whether one or multiple oscillators cause tremor in multiple limbs. Based on the prediction that multiple oscillators would cause low coherence even with similar average frequency, we studied 22 PD patients using accelerometers on multiple limbs. Records were digitized and spectral analysis was performed. Peak frequencies in the arms, legs, and chin were similar, indicating that biomechanical factors did not determine the frequency. Coherence between different axes of individual accelerometers and between different segments of the same limb was high. However, coherence between tremor in different limbs was low. There was no consistent pattern across patients of ipsi- vs. contralateral predominance of coherence. These data suggest that tremor in PD is generated by multiple oscillatory circuits, which operate on similar frequencies.