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      Two types of criticality in the brain

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          Abstract

          Neural networks with tightly balanced excitatory and inhibitory coupling show high computational performance. They operate close to a critical point characterized by the joint activation of large populations of neurons. Yet, macaque motor cortex shows very different dynamics with weak fluctuations on macroscopic scales. In this light motor cortex seems to operate in a sub-optimal regime. Here we show the opposite: The large dispersion of correlations across neurons is a signature of a rich dynamical repertoire, hidden from macroscopic brain signals, but essential for high performance in such concepts as reservoir computing. Our findings suggest a refinement of the view on criticality in neural systems: network topology and heterogeneity endow the brain with two complementary substrates for critical dynamics of largely different complexity.

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          Decorrelated neuronal firing in cortical microcircuits.

          Correlated trial-to-trial variability in the activity of cortical neurons is thought to reflect the functional connectivity of the circuit. Many cortical areas are organized into functional columns, in which neurons are believed to be densely connected and to share common input. Numerous studies report a high degree of correlated variability between nearby cells. We developed chronically implanted multitetrode arrays offering unprecedented recording quality to reexamine this question in the primary visual cortex of awake macaques. We found that even nearby neurons with similar orientation tuning show virtually no correlated variability. Our findings suggest a refinement of current models of cortical microcircuit architecture and function: Either adjacent neurons share only a few percent of their inputs or, alternatively, their activity is actively decorrelated.
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            Distinct recurrent versus afferent dynamics in cortical visual processing.

            How intracortical recurrent circuits in mammalian sensory cortex influence dynamics of sensory representation is not understood. Previous methods could not distinguish the relative contributions of recurrent circuits and thalamic afferents to cortical dynamics. We accomplish this by optogenetically manipulating thalamus and cortex. Over the initial 40 ms of visual stimulation, excitation from recurrent circuits in visual cortex progressively increased to exceed direct thalamocortical excitation. Even when recurrent excitation exceeded thalamic excitation, upon silencing thalamus, sensory-evoked activity in cortex decayed rapidly, with a time constant of 10 ms, which is similar to a neuron's integration time window. In awake mice, this cortical decay function predicted the time-locking of cortical activity to thalamic input at frequencies <15 Hz and attenuation of the cortical response to higher frequencies. Under anesthesia, depression at thalamocortical synapses disrupted the fidelity of sensory transmission. Thus, we determine dynamics intrinsic to cortical recurrent circuits that transform afferent input in time.
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              Quantum Field Theory in the Large N Limit: a review

              We review the solutions of O(N) and U(N) quantum field theories in the large \(N\) limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large \(N\), the method relies on constructing effective field theories for composite fields after integration over the original degrees of freedom. We first solve a general scalar \(U(\phib^2)\) field theory for \(N\) large and discuss various non-perturbative physical issues such as critical behaviour. We show how large \(N\) results can also be obtained from variational calculations.We illustrate these ideas by showing that the large \(N\) expansion allows to relate the \((\phib^2)^2\) theory and the non-linear \(\sigma\)-model, models which are renormalizable in different dimensions. Similarly, a relation between \(CP(N-1)\) and abelian Higgs models is exhibited. Large \(N\) techniques also allow solving self-interacting fermion models. A relation between the Gross--Neveu, a theory with a four-fermi self-interaction, and a Yukawa-type theory renormalizable in four dimensions then follows. We discuss dissipative dynamics, which is relevant to the approach to equilibrium, and which in some formulation exhibits quantum mechanics supersymmetry. This also serves as an introduction to the study of the 3D supersymmetric quantum field theory. Large \(N\) methods are useful in problems that involve a crossover between different dimensions. We thus briefly discuss finite size effects, finite temperature scalar and supersymmetric field theories. We also use large \(N\) methods to investigate the weakly interacting Bose gas. The solution of the general scalar \(U(\phib^2)\) field theory is then applied to other issues like tricritical behaviour and double scaling limit.
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                Author and article information

                Journal
                29 November 2017
                Article
                1711.10930
                4aba00c7-3c8c-413d-9956-a3e1f7ca068c

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                cond-mat.dis-nn q-bio.NC

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