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Burak, Yoram

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Burak

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Yoram

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Burak, Yoram
Author's Publications: search.filters.isAuthorOfPublication.a57fc457-06d1-486c-824f-61a8996e5284

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    Bayesian Model of Dynamic Image Stabilization in the Visual System
    (Proceedings of the National Academy of Sciences, 2010) Burak, Yoram; Rokni, Uri; Meister, Markus; Sompolinsky, Haim
    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.
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    Accurate Path Integration in Continuous Attractor Network Models of Grid Cells
    (Public Library of Science, 2009) Burak, Yoram; Fiete, Ila R.
    Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of ∼10–100 meters and ∼1–10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.
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    Order and Stochastic Dynamics in Drosophila Planar Cell Polarity
    (Public Library of Science, 2009) Burak, Yoram; Shraiman, Boris I.
    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.