scholarly journals Training and spontaneous reinforcement of neuronal assemblies by spike timing plasticity

2016 ◽  
Author(s):  
Gabriel Koch Ocker ◽  
Brent Doiron
Keyword(s):  
Neural Coding ◽  
Large Scale ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spike Timing ◽  
Temporal Correlations ◽  
Time Correlations ◽  
Low Dimensional ◽  
Large Scale Simulations ◽  
Fast Spike

AbstractThe synaptic connectivity of cortex is plastic, with experience shaping the ongoing interactions between neurons. Theoretical studies of spike timing–dependent plasticity (STDP) have focused on either just pairs of neurons or large-scale simulations. A simple analytic account for how fast spike time correlations affect both micro- and macroscopic network structure is lacking. We develop a low-dimensional mean field theory for STDP in recurrent networks and show the emergence of assemblies of strongly reciprocally coupled neurons with shared stimulus preferences. After training this connectivity is actively reinforced by spike train correlations during the spontaneous dynamics. Furthermore, the stimulus coding by cell assemblies is actively maintained by these internally generated spiking correlations, suggesting a new role for noise correlations in neural coding. Assembly formation has been often associated with firing rate-based plasticity schemes; our theory provides an alternative and complementary framework, where fine temporal correlations and STDP form and actively maintain learned structure in cortical networks.

scholarly journals Training and Spontaneous Reinforcement of Neuronal Assemblies by Spike Timing Plasticity

2018 ◽  
Vol 29 (3) ◽  
pp. 937-951 ◽  
Author(s):  
Gabriel Koch Ocker ◽  
Brent Doiron
Keyword(s):  
Neural Coding ◽  
Large Scale ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spike Timing ◽  
Strongly Coupled ◽  
Temporal Correlations ◽  
Time Correlations ◽  
Low Dimensional ◽  
Large Scale Simulations

Abstract The synaptic connectivity of cortex is plastic, with experience shaping the ongoing interactions between neurons. Theoretical studies of spike timing-dependent plasticity (STDP) have focused on either just pairs of neurons or large-scale simulations. A simple analytic account for how fast spike time correlations affect both microscopic and macroscopic network structure is lacking. We develop a low-dimensional mean field theory for STDP in recurrent networks and show the emergence of assemblies of strongly coupled neurons with shared stimulus preferences. After training, this connectivity is actively reinforced by spike train correlations during the spontaneous dynamics. Furthermore, the stimulus coding by cell assemblies is actively maintained by these internally generated spiking correlations, suggesting a new role for noise correlations in neural coding. Assembly formation has often been associated with firing rate-based plasticity schemes; our theory provides an alternative and complementary framework, where fine temporal correlations and STDP form and actively maintain learned structure in cortical networks.

scholarly journals Assembly formation is stabilized by Parvalbumin neurons and accelerated by Somatostatin neurons

2021 ◽  
Author(s):  
Fereshteh Lagzi ◽  
Martha Canto Bustos ◽  
Anne-Marie Oswald ◽  
Brent Doiron
Keyword(s):  
Large Scale ◽  
Mean Field ◽  
Spike Timing ◽  
Excitatory Synapses ◽  
Mean Field Models ◽  
Stdp Rule ◽  
Somatostatin Neurons ◽  
Large Scale Simulations ◽  
The Brain ◽  
Parvalbumin Neurons

AbstractLearning entails preserving the features of the external world in the neuronal representations of the brain, and manifests itself in the form of strengthened interactions between neurons within assemblies. Hebbian synaptic plasticity is thought to be one mechanism by which correlations in spiking promote assembly formation during learning. While spike timing dependent plasticity (STDP) rules for excitatory synapses have been well characterized, inhibitory STDP rules remain incomplete, particularly with respect to sub-classes of inhibitory interneurons. Here, we report that in layer 2/3 of the orbitofrontal cortex of mice, inhibition from parvalbumin (PV) interneurons onto excitatory (E) neurons follows a symmetric STDP function and mediates homeostasis in E-neuron firing rates. However, inhibition from somatostatin (SOM) interneurons follows an asymmetric, Hebbian STDP rule. We incorporate these findings in both large scale simulations and mean-field models to investigate how these differences in plasticity impact network dynamics and assembly formation. We find that plasticity of SOM inhibition builds lateral inhibitory connections and increases competition between assemblies. This is reflected in amplified correlations between neurons within assembly and anti-correlations between assemblies. An additional finding is that the emergence of tuned PV inhibition depends on the interaction between SOM and PV STDP rules. Altogether, we show that incorporation of differential inhibitory STDP rules promotes assembly formation through competition, while enhanced inhibition both within and between assemblies protects new representations from degradation after the training input is removed.

Multiscale Simulations of Domains in Ferroelectrics

Domain Walls ◽  
2020 ◽  
pp. 311-339
Author(s):  
S. Liu ◽  
I. Grinberg ◽  
A. M. Rappe
Keyword(s):  
Density Functional ◽  
Large Scale ◽  
Mean Field Theory ◽  
Mean Field ◽  
Md Simulations ◽  
Relaxor Ferroelectrics ◽  
Ferroelectric Materials ◽  
Multiscale Simulations ◽  
Challenges And Opportunities ◽  
Physically Based

This chapter focuses on recent studies of ferroelectrics, where large-scale molecular dynamics (MD) simulations using first-principles-based force fields played a central role in revealing important physics inaccessible to direct density functional theory (DFT) calculations but critical for developing physically-based free energy functional for coarse-grained phase-field-type simulations. After reviewing typical atomistic potentials of ferroelectrics for MD simulations, the chapter describes a progressive theoretical framework that combines DFT, MD, and a mean-field theory. It then focuses on relaxor ferroelectrics. By examining the spatial and temporal polarization correlations in prototypical relaxor ferroelectrics with million-atom MD simulations and novel analysis techniques, this chapter shows that the widely accepted model of polar nanoregions embedded in a non-polar matrix is incorrect for Pb-based relaxors. Rather, the unusual properties of theses relaxor ferroelectrics stem from the presence of a multi-domain state with extremely small domain sizes (2–10 nanometers), giving rise to a greater flexibility for polarization rotations and the ultrahigh dielectric and piezoelectric responses. Finally, this chapter discusses the challenges and opportunities for multiscale simulations of ferroelectric materials.

scholarly journals Characteristics of sequential activity in networks with temporally asymmetric Hebbian learning

2020 ◽  
Vol 117 (47) ◽  
pp. 29948-29958
Author(s):  
Maxwell Gillett ◽  
Ulises Pereira ◽  
Nicolas Brunel
Keyword(s):  
Storage Capacity ◽  
Synaptic Weight ◽  
Hebbian Learning ◽  
Mean Field Theory ◽  
Mean Field ◽  
Learning Rule ◽  
Network Activity ◽  
Synaptic Connectivity ◽  
Random Input ◽  
Low Dimensional

Sequential activity has been observed in multiple neuronal circuits across species, neural structures, and behaviors. It has been hypothesized that sequences could arise from learning processes. However, it is still unclear whether biologically plausible synaptic plasticity rules can organize neuronal activity to form sequences whose statistics match experimental observations. Here, we investigate temporally asymmetric Hebbian rules in sparsely connected recurrent rate networks and develop a theory of the transient sequential activity observed after learning. These rules transform a sequence of random input patterns into synaptic weight updates. After learning, recalled sequential activity is reflected in the transient correlation of network activity with each of the stored input patterns. Using mean-field theory, we derive a low-dimensional description of the network dynamics and compute the storage capacity of these networks. Multiple temporal characteristics of the recalled sequential activity are consistent with experimental observations. We find that the degree of sparseness of the recalled sequences can be controlled by nonlinearities in the learning rule. Furthermore, sequences maintain robust decoding, but display highly labile dynamics, when synaptic connectivity is continuously modified due to noise or storage of other patterns, similar to recent observations in hippocampus and parietal cortex. Finally, we demonstrate that our results also hold in recurrent networks of spiking neurons with separate excitatory and inhibitory populations.

RECENT APPLICATIONS OF THE DMRG METHOD

2006 ◽  
Vol 20 (19) ◽  
pp. 2624-2635
Author(s):  
KAREN HALLBERG
Keyword(s):  
Degrees Of Freedom ◽  
Mean Field Theory ◽  
Mean Field ◽  
Finite Size ◽  
Strongly Correlated Systems ◽  
Strongly Correlated ◽  
Correlated Systems ◽  
Infinite Dimensional ◽  
Low Dimensional ◽  
Time Dependent Problems

Since its inception, the DMRG method has been a very powerful tool for the calculation of physical properties of low-dimensional strongly correlated systems. It has been adapted to obtain dynamical properties and to consider finite temperature, time-dependent problems, bosonic degrees of freedom, the treatment of classical problems and non-equilibrium systems, among others. We will briefly review the method and then concentrate on its latest developments, describing some recent successful applications. In particular we will show how the dynamical DMRG can be used together with the Dynamical Mean Field Theory (DMFT) to solve the associated impurity problem in the infinite-dimensional Hubbard model. This method is used to obtain spectral properties of strongly correlated systems. With this algorithm, more complex problems having a larger number of degrees of freedom can be considered and finite-size effects can be minimized.

Optimal attack and defence of large scale networks using mean field theory

2016 ◽  
Author(s):  
Jorge del Val ◽  
Santiago Zazo ◽  
Sergio Valcarcel Macua ◽  
Javier Zazo ◽  
Juan Parras
Keyword(s):  
Field Theory ◽  
Large Scale ◽  
Mean Field Theory ◽  
Mean Field ◽  
Large Scale Networks

Predicted hexagonal titanium nitride monolayer as an intrinsic ferromagnetic semiconductor

2021 ◽  
Author(s):  
Jun Li ◽  
Yuhong Huang ◽  
Hongkuan Yuan ◽  
Hong Chen
Keyword(s):  
Titanium Nitride ◽  
Carrier Transport ◽  
Phonon Dispersion ◽  
Magnetic Semiconductors ◽  
Mean Field Theory ◽  
Mean Field ◽  
Ferromagnetic Semiconductor ◽  
Dynamics Simulation ◽  
Low Dimensional ◽  
Semiconducting Behavior

Two-dimensional (2D) magnetic semiconductors have great promising for energy-efficient ultracompact spintronics due to the low-dimensional ferromagnetic and semiconducting behavior. Here, we predict hexagonal titanium nitride monolayer ($h$-TiN) to be a ferromagnetic semiconductor by investigating stability, magnetism, and carrier transport of $h$-TiN using the first-principles calculations. The thermodynamical stability of $h$-TiN is revealed by phonon dispersion, molecular dynamics simulation and formation energy. The energy band structure shows that $h$-TiN is a ferromagnetic semiconductor with medium magnetic anisotropy, the magnetic moment of 1$\mu_{B}$ and the band gaps of 1.33 and 4.42 eV for spin-up and -down channels, respectively. The Curie temperature of $h$-TiN is estimated to be about 205 K by mean-field theory and not enhanced by the compressive and tensile strains. Higher carrier mobility, in-plane stiffness and conductivity indicate that $h$-TiN has favorable transport performance. The ferromagnetic semiconducting behavior is robust against the external strains, indicating that $h$-TiN could be a rare candidate for nanoscale spintronic devices.

scholarly journals Motivation and challenge to capture both large-scale and local transport in next generation accretion theory

2015 ◽  
Vol 81 (5) ◽  
Author(s):  
Eric G. Blackman ◽  
Farrukh Nauman
Keyword(s):  
Field Theory ◽  
Large Scale ◽  
Mean Field Theory ◽  
Mean Field ◽  
Next Generation ◽  
Dynamo Theory ◽  
Non Local ◽  
Local Transport

Accretion disc theory is less developed than stellar evolution theory although a similarly mature phenomenological picture is ultimately desired. While the interplay of theory and numerical simulations has amplified community awareness of the role of magnetic fields in angular momentum transport, there remains a long term challenge to incorporate the insights gained from simulations into improving practical models for comparison with observations. What has been learned from simulations that can lead to improvements beyond SS73 in practical models? Here, we emphasize the need to incorporate the role of non-local transport more precisely. To show where large-scale transport would fit into the theoretical framework and how it is currently missing, we review why the wonderfully practical approach of Shakura & Sunyaev (Astron. Astrophys., vol. 24, 1973, pp. 337–355, SS73) is necessarily a mean field theory, and one which does not include large-scale transport. Observations of coronae and jets, combined with the interpretation of results from shearing box simulations, of the magnetorotational instability (MRI) suggest that a significant fraction of disc transport is indeed non-local. We show that the Maxwell stresses in saturation are dominated by large-scale contributions and that the physics of MRI transport is not fully captured by a viscosity. We also clarify the standard physical interpretation of the MRI as it applies to shearing boxes. Computational limitations have so far focused most attention toward local simulations, but the next generation of global simulations should help to inform improved mean field theories. Mean field accretion theory and mean field dynamo theory should in fact be unified into a single theory that predicts the time evolution of spectra and luminosity from separate disc, corona and outflow contributions. Finally, we note that any mean field theory, including that of SS73, has a finite predictive precision that needs to be quantified when comparing the predictions to observations.

scholarly journals Dynamics of fingering convection. Part 1 Small-scale fluxes and large-scale instabilities

2011 ◽  
Vol 677 ◽  
pp. 530-553 ◽  
Author(s):  
A. TRAXLER ◽  
S. STELLMACH ◽  
P. GARAUD ◽  
T. RADKO ◽  
N. BRUMMELL
Keyword(s):  
Large Scale ◽  
Molecular Diffusion ◽  
Turbulent Transport ◽  
Mean Field Theory ◽  
Density Ratio ◽  
Mean Field ◽  
Field Measurements ◽  
Small Scale ◽  
Diapycnal Mixing ◽  
Density Ratios

Double-diffusive instabilities are often invoked to explain enhanced transport in stably stratified fluids. The most-studied natural manifestation of this process, fingering convection, commonly occurs in the ocean's thermocline and typically increases diapycnal mixing by 2 orders of magnitude over molecular diffusion. Fingering convection is also often associated with structures on much larger scales, such as thermohaline intrusions, gravity waves and thermohaline staircases. In this paper, we present an exhaustive study of the phenomenon from small to large scales. We perform the first three-dimensional simulations of the process at realistic values of the heat and salt diffusivities and provide accurate estimates of the induced turbulent transport. Our results are consistent with oceanic field measurements of diapycnal mixing in fingering regions. We then develop a generalized mean-field theory to study the stability of fingering systems to large-scale perturbations using our calculated turbulent fluxes to parameterize small-scale transport. The theory recovers the intrusive instability, the collective instability and the γ-instability as limiting cases. We find that the fastest growing large-scale mode depends sensitively on the ratio of the background gradients of temperature and salinity (the density ratio). While only intrusive modes exist at high density ratios, the collective and γ instabilities dominate the system at the low density ratios where staircases are typically observed. We conclude by discussing our findings in the context of staircase-formation theory.

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