61 research outputs found
What grid cells convey about rat location
We characterize the relationship between the simultaneously recorded quantities of rodent grid cell firing and the position of the rat. The formalization reveals various properties of grid cell activity when considered as a neural code for representing and updating estimates of the rat's location. We show that, although the spatially periodic response of grid cells appears wasteful, the code is fully combinatorial in capacity. The resulting range for unambiguous position representation is vastly greater than the ≈1–10 m periods of individual lattices, allowing for unique high-resolution position specification over the behavioral foraging ranges of rats, with excess capacity that could be used for error correction. Next, we show that the merits of the grid cell code for position representation extend well beyond capacity and include arithmetic properties that facilitate position updating. We conclude by considering the numerous implications, for downstream readouts and experimental tests, of the properties of the grid cell code
Simultaneous embedding of multiple attractor manifolds in a recurrent neural network using constrained gradient optimization
The storage of continuous variables in working memory is hypothesized to be
sustained in the brain by the dynamics of recurrent neural networks (RNNs)
whose steady states form continuous manifolds. In some cases, it is thought
that the synaptic connectivity supports multiple attractor manifolds, each
mapped to a different context or task. For example, in hippocampal area CA3,
positions in distinct environments are represented by distinct sets of
population activity patterns, each forming a continuum. It has been argued that
the embedding of multiple continuous attractors in a single RNN inevitably
causes detrimental interference: quenched noise in the synaptic connectivity
disrupts the continuity of each attractor, replacing it by a discrete set of
steady states that can be conceptualized as lying on local minima of an
abstract energy landscape. Consequently, population activity patterns exhibit
systematic drifts towards one of these discrete minima, thereby degrading the
stored memory over time. Here we show that it is possible to dramatically
attenuate these detrimental interference effects by adjusting the synaptic
weights. Synaptic weight adjustments are derived from a loss function that
quantifies the roughness of the energy landscape along each of the embedded
attractor manifolds. By minimizing this loss function, the stability of states
can be dramatically improved, without compromising the capacity.Comment: To be presetned at the Thirty-seventh Conference on Neural
Information Processing Systems (NeurIPS 2023
An Efficient Coding Theory for a Dynamic Trajectory Predicts non-Uniform Allocation of Grid Cells to Modules in the Entorhinal Cortex
Grid cells in the entorhinal cortex encode the position of an animal in its
environment using spatially periodic tuning curves of varying periodicity.
Recent experiments established that these cells are functionally organized in
discrete modules with uniform grid spacing. Here we develop a theory for
efficient coding of position, which takes into account the temporal statistics
of the animal's motion. The theory predicts a sharp decrease of module
population sizes with grid spacing, in agreement with the trends seen in the
experimental data. We identify a simple scheme for readout of the grid cell
code by neural circuitry, that can match in accuracy the optimal Bayesian
decoder of the spikes. This readout scheme requires persistence over varying
timescales, ranging from ~1ms to ~1s, depending on the grid cell module. Our
results suggest that the brain employs an efficient representation of position
which takes advantage of the spatiotemporal statistics of the encoded variable,
in similarity to the principles that govern early sensory coding.Comment: 23 pages, 5 figures. Supplemental Information available from the
authors on request. A previous version of this work appeared in abstract form
(Program No. 727.02. 2015 Neuroscience Meeting Planner. Chicago, IL: Society
for Neuroscience, 2015. Online.
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Order and Stochastic Dynamics in Drosophila Planar Cell Polarity
Cells in the wing blade of Drosophila melanogaster exhibit an in-plane polarization causing distal orientation of hairs. Establishment of the Planar Cell Polarity (PCP) involves intercellular interactions as well as a global orienting signal. Many of the genetic and molecular components underlying this process have been experimentally identified and a recently advanced system-level model has suggested that the observed mutant phenotypes can be understood in terms of intercellular interactions involving asymmetric localization of membrane bound proteins. Among key open questions in understanding the emergence of ordered polarization is the effect of stochasticity and the role of the global orienting signal. These issues relate closely to our understanding of ferromagnetism in physical systems. Here we pursue this analogy to understand the emergence of PCP order. To this end we develop a semi-phenomenological representation of the underlying molecular processes and define a “phase diagram” of the model which provides a global view of the dependence of the phenotype on parameters. We show that the dynamics of PCP has two regimes: rapid growth in the amplitude of local polarization followed by a slower process of alignment which progresses from small to large scales. We discuss the response of the tissue to various types of orienting signals and show that global PCP order can be achieved with a weak orienting signal provided that it acts during the early phase of the process. Finally we define and discuss some of the experimental predictions of the model.Other Research Uni
Manning condensation in two dimensions
We consider a macroion confined to a cylindrical cell and neutralized by
oppositely charged counterions. Exact results are obtained for the
two-dimensional version of this problem, in which ion-ion and ion-macroion
interactions are logarithmic. In particular, the threshold for counterion
condensation is found to be the same as predicted by mean-field theory. With
further increase of the macroion charge, a series of single-ion condensation
transitions takes place. Our analytical results are expected to be exact in the
vicinity of these transitions and are in very good agreement with recent
Monte-Carlo simulation data.Comment: 4 pages, 4 figure
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Bayesian Model of Dynamic Image Stabilization in the Visual System
Humans can resolve the fine details of visual stimuli although the image projected on the retina is constantly drifting relative to the photoreceptor array. Here we demonstrate that the brain must take this drift into account when performing high acuity visual tasks. Further, we propose a decoding strategy for interpreting the spikes emitted by the retina, which takes into account the ambiguity caused by retinal noise and the unknown trajectory of the projected image on the retina. A main difficulty, addressed in our proposal, is the exponentially large number of possible stimuli, which renders the ideal Bayesian solution to the problem computationally intractable. In contrast, the strategy that we propose suggests a realistic implementation in the visual cortex. The implementation involves two populations of cells, one that tracks the position of the image and another that represents a stabilized estimate of the image itself. Spikes from the retina are dynamically routed to the two populations and are interpreted in a probabilistic manner. We consider the architecture of neural circuitry that could implement this strategy and its performance under measured statistics of human fixational eye motion. A salient prediction is that in high acuity tasks, fixed features within the visual scene are beneficial because they provide information about the drifting position of the image. Therefore, complete elimination of peripheral features in the visual scene should degrade performance on high acuity tasks involving very small stimuli.Molecular and Cellular Biolog
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