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Yoram Burak

Publications and source records attributed to Yoram Burak.

14 recordsLinked to original sources
arXiv2023

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.

q-bio.NC↗
arXiv2019

Limits on Spectral Resolution Measurements by Quantum Probes

The limits of frequency resolution in nano-NMR experiments have been discussed extensively in recent years. It is believed that there is a crucial difference between the ability to resolve a few frequencies and the precision of estimating a single one. Whereas the efficiency of single frequency estimation gradually increases with the square root of the number of measurements, the ability to resolve two frequencies is limited by the specific timescale of the signal and cannot be compensated for by extra measurements. Here we show theoretically and demonstrate experimentally that the relationship between these quantities is more subtle and both are only limited by the Cramér-Rao bound of a single frequency estimation.

quant-ph↗
arXiv2017

Continuous parameter working memory in a balanced chaotic neural network

It has been proposed that neural noise in the cortex arises from chaotic dynamics in the balanced state: in this model of cortical dynamics, the excitatory and inhibitory inputs to each neuron approximately cancel, and activity is driven by fluctuations of the synaptic inputs around their mean. It remains unclear whether neural networks in the balanced state can perform tasks that are highly sensitive to noise, such as storage of continuous parameters in working memory, while also accounting for the irregular behavior of single neurons. Here we show that continuous parameter working memory can be maintained in the balanced state, in a neural circuit with a simple network architecture. We show analytically that in the limit of an infinite network, the dynamics generated by this architecture are characterized by a continuous set of steady balanced states, allowing for the indefinite storage of a continuous parameter. In finite networks, we show that the chaotic noise drives diffusive motion along the approximate attractor, which gradually degrades the stored memory. We analyze the dynamics and show that the slow diffusive motion induces slowly decaying temporal cross correlations in the activity, which differ substantially from those previously described in the balanced state. We calculate the diffusivity, and show that it is inversely proportional to the system size. For large enough (but realistic) neural population sizes, and with suitable tuning of the network connections, the proposed balanced network can sustain continuous parameter values in memory over time scales larger by several orders of magnitude than the single neuron time scale.

cond-mat.dis-nn↗
arXiv2016

Shaping neural circuits by high order synaptic interactions

Spike timing dependent plasticity (STDP) is believed to play an important role in shaping the structure of neural circuits. Here we show that STDP generates effective interactions between synapses of different neurons, which were neglected in previous theoretical treatments, and can be described as a sum over contributions from structural motifs. These interactions can have a pivotal influence on the connectivity patterns that emerge under the influence of STDP. In particular, we consider two highly ordered forms of structure: wide synfire chains, in which groups of neurons project to each other sequentially, and self connected assemblies. We show that high order synaptic interactions can enable the formation of both structures, depending on the form of the STDP function and the time course of synaptic currents. Furthermore, within a certain regime of biophysical parameters, emergence of the ordered connectivity occurs robustly and autonomously in a stochastic network of spiking neurons, without a need to expose the neural network to structured inputs during learning.

q-bio.NC↗
arXiv2016

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.

q-bio.NC↗
arXiv2009

Accurate path integration in continuous attractor network models of grid cells

Grid cells in the rodent 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, in previous models suggested for grid cell activity, errors accumulate rapidly in the integration of velocity inputs. To produce grid-cell like responses, these models would require frequent resets triggered by external sensory cues, casting doubt on the dead-reckoning potential of the grid cell system. Here we focus on the accuracy of path integration 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. We consider the role of the network boundary in integration performance, and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We show that the rate at which errors accumulate in the integration of velocity depends on the network's organization and size, and on the intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model can accurately integrate velocity inputs over a maximum of ~10-100 m and ~1-10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in dMEC. 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.

q-bio.NC↗
arXiv2009

Stimulus-dependent correlations in threshold-crossing spiking neurons

We consider a threshold-crossing spiking process as a simple model for the activity within a population of neurons. Assuming that these neurons are driven by a common fluctuating input with Gaussian statistics, we evaluate the cross-correlation of spike trains in pairs of model neurons with different thresholds. This correlation function tends to be asymmetric in time, indicating a preference for the neuron with the lower threshold to fire before the one with the higher threshold, even if their inputs are identical. The relationship between these results and spike statistics in other models of neural activity are explored. In particular, we compare our model with an integrate-and-fire model in which the membrane voltage resets following each spike. The qualitative properties of spike cross correlations, emerging from the threshold-crossing model, are similar to those of bursting events in the integrate-and-fire model. This is particularly true for generalized integrate-and-fire models in which spikes tend to occur in bursts as observed, for example, in retinal ganglion cells driven by a rapidly fluctuating visual stimulus. The threshold crossing model thus provides a simple, analytically tractable description of event onsets in these neurons.

q-bio.NC↗
arXiv2007

Electrostatic Interactions of Asymmetrically Charged Membranes

We predict the nature (attractive or repulsive) and range (exponentially screened or long-range power law) of the electrostatic interactions of oppositely charged and planar plates as a function of the salt concentration and surface charge densities (whose absolute magnitudes are not necessarily equal). An analytical expression for the crossover between attractive and repulsive pressure is obtained as a function of the salt concentration. This condition reduces to the high-salt limit of Parsegian and Gingell where the interaction is exponentially screened and to the zero salt limit of Lau and Pincus in which the important length scales are the inter-plate separation and the Gouy-Chapman length. In the regime of low salt and high surface charges we predict - for any ratio of the charges on the surfaces - that the attractive pressure is long-ranged as a function of the spacing. The attractive pressure is related to the decrease in counter-ion concentration as the inter-plate distance is decreased. Our theory predicts several scaling regimes with different scaling expressions for the pressure as function of salinity and surface charge densities. The pressure predictions can be related to surface force experiments of oppositely charged surfaces that are prepared by coating one of the mica surfaces with an oppositely charged polyelectrolyte.

cond-mat.soft↗
arXiv2006

Triangular lattice neurons may implement an advanced numeral system to precisely encode rat position over large ranges

We argue by observation of the neural data that neurons in area dMEC of rats, which fire whenever the rat is on any vertex of a regular triangular lattice that tiles 2-d space, may be using an advanced numeral system to reversibly encode rat position. We interpret measured dMEC properties within the framework of a residue number system (RNS), and describe how RNS encoding -- which breaks the non-periodic variable of rat position into a set of narrowly distributed periodic variables -- allows a small set of cells to compactly represent and efficiently update rat position with high resolution over a large range. We show that the uniquely useful properties of RNS encoding still hold when the encoded and encoding quantities are relaxed to be real numbers with built-in uncertainties, and provide a numerical and functional estimate of the range and resolution of rat positions that can be uniquely encoded in dMEC. The use of a compact, `arithmetic-friendly' numeral system to encode a metric variable, as we propose is happening in dMEC, is qualitatively different from all previously identified examples of coding in the brain. We discuss the numerous neurobiological implications and predictions of our hypothesis.

q-bio.NC↗
arXiv2005

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.

cond-mat.soft↗
arXiv2004

Competition between condensation of monovalent and multivalent ions in DNA aggregation

We discuss the distribution of ions around highly charged PEs when there is competition between monovalent and multivalent ions, pointing out that in this case the number of condensed ions is sensitive to short-range interactions, salt, and model-dependent approximations. This sensitivity is discussed in the context of recent experiments on DNA aggregation, induced by multivalent counterions such as spermine and spermidine.

cond-mat.soft↗
arXiv2000

Hydration interactions: aqueous solvent effects in electric double layers

A model for ionic solutions with an attractive short-range pair interaction between the ions is presented. The short-range interaction is accounted for by adding a quadratic non-local term to the Poisson-Boltzmann free energy. The model is used to study solvent effects in a planar electric double layer. The counter-ion density is found to increase near the charged surface, as compared with the Poisson-Boltzmann theory, and to decrease at larger distances. The ion density profile is studied analytically in the case where the ion distribution near the plate is dominated only by counter-ions. Further away from the plate the density distribution can be described using a Poisson-Boltzmann theory with an effective surface charge that is smaller than the actual one.

cond-mat.soft↗
arXiv2000

Discrete aqueous solvent effects and possible attractive forces

We study discrete solvent effects on the interaction of two parallel charged surfaces in ionic aqueous solution. These effects are taken into account by adding a bilinear non-local term to the free energy of Poisson-Boltzmann theory. We study numerically the density profile of ions between the two plates, and the resulting inter-plate pressure. At large plate separations the two plates are decoupled and the ion distribution can be characterized by an effective Poisson-Boltzmann charge that is smaller than the nominal charge. The pressure is thus reduced relative to Poisson-Boltzmann predictions. At plate separations below ~2 nm the pressure is modified considerably, due to the solvent mediated short-range attraction between ions in the the system. For high surface charges this contribution can overcome the mean-field repulsion giving rise to a net attraction between the plates.

cond-mat.soft↗