scholarly journals The population dynamics of a canonical cognitive circuit

2019 ◽  
Author(s):  
Rishidev Chaudhuri ◽  
Berk Gerçek ◽  
Biraj Pandey ◽  
Adrien Peyrache ◽  
Ila Fiete
Keyword(s):  
Neural Circuit ◽  
Internal Noise ◽  
Population Level ◽  
Dimensional Manifold ◽  
Circuit Representation ◽  
Attractor Dynamics ◽  
Set Up ◽  
Low Dimensional ◽  
Low Dimensional Manifold ◽  
External Stimuli

AbstractThe brain constructs distributed representations of key low-dimensional variables. These variables may be external stimuli or internal constructs of quantities relevant for survival, such as a sense of one’s location in the world. We consider that the high-dimensional population-level activity vectors are the fundamental representational currency of a neural circuit, and these vectors trace out a low-dimensional manifold whose dimension and topology matches those of the represented variable. This manifold perspective — applied to the mammalian head direction circuit across rich waking behaviors and sleep — enables powerful inferences about circuit representation and mechanism, including: Direct visualization and blind discovery that the network represents a one-dimensional circular variable across waking and REM sleep; fully unsupervised decoding of the coded variable; stability and attractor dynamics in the representation; the discovery of new dynamical trajectories during sleep; the limiting role of external rather than internal noise in the fidelity of memory states; and the conclusion that the circuit is set up to integrate velocity inputs according to classical continuous attractor models.

scholarly journals A theory of joint attractor dynamics in the hippocampus and the entorhinal cortex accounts for artificial hippocampal remapping and individual grid cell field-to-field variability

2020 ◽  
Author(s):  
Haggai Agmon ◽  
Yoram Burak
Keyword(s):  
Entorhinal Cortex ◽  
Activity Patterns ◽  
Grid Cell ◽  
Mechanistic Explanation ◽  
Place Cells ◽  
Dimensional Manifold ◽  
Grid Cells ◽  
Attractor Dynamics ◽  
Low Dimensional ◽  
Low Dimensional Manifold

ABSTRACTThe representation of position in the brain is distributed across multiple neural populations. Grid cell modules in the medial entorhinal cortex (MEC) express activity patterns that span a low-dimensional manifold which remains stable across different environments. In contrast, the activity patterns of hippocampal place cells span distinct low-dimensional manifolds in different environments. It is unknown how these multiple representations of position are coordinated. Here we develop a theory of joint attractor dynamics in the hippocampus and the MEC. We show that the system exhibits a coordinated, joint representation of position across multiple environments, consistent with global remapping in place cells and grid cells. We then show that our model accounts for recent experimental observations that lack a mechanistic explanation: variability in the firing rate of single grid cells across firing fields, and artificial remapping of place cells under depolarization, but not under hyperpolarization, of layer II stellate cells of the MEC.

scholarly journals Low-dimensional manifold of actin polymerization dynamics

2017 ◽  
Vol 19 (12) ◽  
pp. 125012 ◽  
Author(s):  
Carlos Floyd ◽  
Christopher Jarzynski ◽  
Garegin Papoian
Keyword(s):  
Actin Polymerization ◽  
Dimensional Manifold ◽  
Low Dimensional ◽  
Low Dimensional Manifold

scholarly journals Latent learning drives sleep-dependent plasticity in distinct CA1 subpopulations

2020 ◽  
Author(s):  
Wei Guo ◽  
Jie J. Zhang ◽  
Jonathan P. Newman ◽  
Matthew A. Wilson
Keyword(s):  
Hippocampal Neurons ◽  
Dimensional Manifold ◽  
Latent Learning ◽  
Neural Ensembles ◽  
Correlated Activity ◽  
Place Fields ◽  
Internal States ◽  
Low Dimensional ◽  
Low Dimensional Manifold ◽  
The Brain

AbstractLatent learning allows the brain the transform experiences into cognitive maps, a form of implicit memory, without reinforced training. Its mechanism is unclear. We tracked the internal states of the hippocampal neural ensembles and discovered that during latent learning of a spatial map, the state space evolved into a low-dimensional manifold that topologically resembled the physical environment. This process requires repeated experiences and sleep in-between. Further investigations revealed that a subset of hippocampal neurons, instead of rapidly forming place fields in a novel environment, remained weakly tuned but gradually developed correlated activity with other neurons. These ‘weakly spatial’ neurons bond activity of neurons with stronger spatial tuning, linking discrete place fields into a map that supports flexible navigation.

Large-eddy simulation of direct injection natural gas combustion in a heavy-duty truck engine using modified conditional moment closure model with low-dimensional manifold method

2018 ◽  
Vol 21 (5) ◽  
pp. 824-837 ◽  
Author(s):  
Jian Huang ◽  
Gordon McTaggart-Cowan ◽  
Sandeep Munshi
Keyword(s):  
Natural Gas ◽  
Direct Injection ◽  
Moment Closure ◽  
Dimensional Manifold ◽  
Conditional Moment ◽  
Gas Combustion ◽  
Conditional Moment Closure ◽  
Natural Gas Combustion ◽  
Low Dimensional ◽  
Low Dimensional Manifold

This article describes the application of a modified first-order conditional moment closure model used in conjunction with the trajectory-generated low-dimensional manifold method in large-eddy simulation of pilot ignited high-pressure direct injection natural gas combustion in a heavy-duty diesel engine. The article starts with a review of the intrinsic low-dimensional manifold method for reducing detailed chemistry and various formulations for the construction of such manifolds. It is followed by a brief review of the conditional moment closure method for modelling the interaction between turbulence and combustion chemistry. The high computational cost associated with the direct implementation of the basic conditional moment closure model was discussed. The article then describes the formulation of a modified approach to solve the conditional moment closure equation, whose reaction source terms for the conditional mass fractions for species were obtained by projecting the turbulent perturbation onto the reaction manifold. The main model assumptions were explained and the resulting limitations were discussed. A numerical experiment was conducted to examine the validity the model assumptions. The model was then implemented in a combustion computational fluid dynamics solver developed on an open-source computational fluid dynamics platform. Non-reactive jet simulations were first conducted and the results were compared to the experimental measurement from a high-pressure visualization chamber to verify that the jet penetration under engine relevant conditions was correctly predicted. The model was then used to simulate natural gas combustion in a heavy-duty diesel engine equipped with a high-pressure direct injection system. The simulation results were compared with the experimental measurement from a research engine to verify the accuracy of the model for both the combustion rate and engine-out emissions.

W-LDMM: A Wasserstein driven low-dimensional manifold model for noisy image restoration

2020 ◽  
Vol 371 ◽  
pp. 108-123 ◽  
Author(s):  
Ruiqiang He ◽  
Xiangchu Feng ◽  
Weiwei Wang ◽  
Xiaolong Zhu ◽  
Chunyu Yang
Keyword(s):  
Image Restoration ◽  
Dimensional Manifold ◽  
Noisy Image ◽  
Low Dimensional ◽  
Low Dimensional Manifold

scholarly journals Exploring Chemical Reaction Space With Reaction Difference Fingerprints and Parametric t-SNE

2021 ◽  
Author(s):  
Mikhail Andronov ◽  
Maxim Fedorov ◽  
Sergey Sosnin
Keyword(s):  
Neural Network ◽  
Chemical Reaction ◽  
Deep Neural Network ◽  
Visual Representations ◽  
Dimensional Manifold ◽  
Reaction Space ◽  
Large Databases ◽  
Global Reaction ◽  
Low Dimensional ◽  
Low Dimensional Manifold

<div>Humans prefer visual representations for the analysis of large databases. In this work, we suggest a method for the visualization of the chemical reaction space. Our technique uses the t-SNE approach that is parameterized by a deep neural network (parametric t-SNE). We demonstrated that the parametric t-SNE combined with reaction difference fingerprints can provide a tool for the projection of chemical reactions onto a low-dimensional manifold for easy exploration of reaction space. We showed that the global reaction landscape, been projected onto a 2D plane, corresponds well with already known reaction types. The application of a pretrained parametric t-SNE model to new reactions allows chemists to study these reactions on a global reaction space. We validated the feasibility of this approach for two marketed drugs: darunavir and oseltamivir. We believe that our method can help explore reaction space and inspire chemists to find new reactions and synthetic ways. </div><div><br></div>

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