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Dmitri B. Chklovskii

Publications and source records attributed to Dmitri B. Chklovskii.

50 records · Page 3Linked to original sources
arXiv2012

Online computation of sparse representations of time varying stimuli using a biologically motivated neural network

Natural stimuli are highly redundant, possessing significant spatial and temporal correlations. While sparse coding has been proposed as an efficient strategy employed by neural systems to encode sensory stimuli, the underlying mechanisms are still not well understood. Most previous approaches model the neural dynamics by the sparse representation dictionary itself and compute the representation coefficients offline. In reality, faced with the challenge of constantly changing stimuli, neurons must compute the sparse representations dynamically in an online fashion. Here, we describe a leaky linearized Bregman iteration (LLBI) algorithm which computes the time varying sparse representations using a biologically motivated network of leaky rectifying neurons. Compared to previous attempt of dynamic sparse coding, LLBI exploits the temporal correlation of stimuli and demonstrate better performance both in representation error and the smoothness of temporal evolution of sparse coefficients.

q-bio.NC↗
arXiv2012

A network of spiking neurons for computing sparse representations in an energy efficient way

Computing sparse redundant representations is an important problem both in applied mathematics and neuroscience. In many applications, this problem must be solved in an energy efficient way. Here, we propose a hybrid distributed algorithm (HDA), which solves this problem on a network of simple nodes communicating via low-bandwidth channels. HDA nodes perform both gradient-descent-like steps on analog internal variables and coordinate-descent-like steps via quantized external variables communicated to each other. Interestingly, such operation is equivalent to a network of integrate-and-fire neurons, suggesting that HDA may serve as a model of neural computation. We show that the numerical performance of HDA is on par with existing algorithms. In the asymptotic regime the representation error of HDA decays with time, t, as 1/t. HDA is stable against time-varying noise, specifically, the representation error decays as 1/sqrt(t) for Gaussian white noise.

cs.NE↗
arXiv2012

Reconstruction of Sparse Circuits Using Multi-neuronal Excitation (RESCUME)

One of the central problems in neuroscience is reconstructing synaptic connectivity in neural circuits. Synapses onto a neuron can be probed by sequentially stimulating potentially pre-synaptic neurons while monitoring the membrane voltage of the post-synaptic neuron. Reconstructing a large neural circuit using such a "brute force" approach is rather time-consuming and inefficient because the connectivity in neural circuits is sparse. Instead, we propose to measure a post-synaptic neuron's voltage while stimulating sequentially random subsets of multiple potentially pre-synaptic neurons. To reconstruct these synaptic connections from the recorded voltage we apply a decoding algorithm recently developed for compressive sensing. Compared to the brute force approach, our method promises significant time savings that grow with the size of the circuit. We use computer simulations to find optimal stimulation parameters and explore the feasibility of our reconstruction method under realistic experimental conditions including noise and non-linear synaptic integration. Multineuronal stimulation allows reconstructing synaptic connectivity just from the spiking activity of post-synaptic neurons, even when sub-threshold voltage is unavailable. By using calcium indicators, voltage-sensitive dyes, or multi-electrode arrays one could monitor activity of multiple postsynaptic neurons simultaneously, thus mapping their synaptic inputs in parallel, potentially reconstructing a complete neural circuit.

q-bio.NC↗
arXiv2012

Sparse LMS via Online Linearized Bregman Iteration

We propose a version of least-mean-square (LMS) algorithm for sparse system identification. Our algorithm called online linearized Bregman iteration (OLBI) is derived from minimizing the cumulative prediction error squared along with an l1-l2 norm regularizer. By systematically treating the non-differentiable regularizer we arrive at a simple two-step iteration. We demonstrate that OLBI is bias free and compare its operation with existing sparse LMS algorithms by rederiving them in the online convex optimization framework. We perform convergence analysis of OLBI for white input signals and derive theoretical expressions for both the steady state and instantaneous mean square deviations (MSD). We demonstrate numerically that OLBI improves the performance of LMS type algorithms for signals generated from sparse tap weights.

cs.IT↗
arXiv2010

Structural Properties of the Caenorhabditis elegans Neuronal Network

Despite recent interest in reconstructing neuronal networks, complete wiring diagrams on the level of individual synapses remain scarce and the insights into function they can provide remain unclear. Even for Caenorhabditis elegans, whose neuronal network is relatively small and stereotypical from animal to animal, published wiring diagrams are neither accurate nor complete and self-consistent. Using materials from White et al. and new electron micrographs we assemble whole, self-consistent gap junction and chemical synapse networks of hermaphrodite C. elegans. We propose a method to visualize the wiring diagram, which reflects network signal flow. We calculate statistical and topological properties of the network, such as degree distributions, synaptic multiplicities, and small-world properties, that help in understanding network signal propagation. We identify neurons that may play central roles in information processing and network motifs that could serve as functional modules of the network. We explore propagation of neuronal activity in response to sensory or artificial stimulation using linear systems theory and find several activity patterns that could serve as substrates of previously described behaviors. Finally, we analyze the interaction between the gap junction and the chemical synapse networks. Since several statistical properties of the C. elegans network, such as multiplicity and motif distributions are similar to those found in mammalian neocortex, they likely point to general principles of neuronal networks. The wiring diagram reported here can help in understanding the mechanistic basis of behavior by generating predictions about future experiments involving genetic perturbations, laser ablations, or monitoring propagation of neuronal activity in response to stimulation.

q-bio.NC↗
arXiv2003

Ocular dominance patterns and the wire length minimization: a numerical study

We study a mathematical model for ocular dominance patterns (ODPs) in primary visual cortex. This model is based on the premise that ODP is an adaptation to minimize the length of intra-cortical wiring. Thus we attempt to understand the existing ODPs by solving a wire length minimization problem. We divide all the neurons into two classes: left- and right-eye dominated. We find that segregation of neurons into monocular regions reduces wire length if the number of connections to the neurons of the same class (intraocular) differs from the number of interocular connections. The shape of the regions depends on the relative fraction of neurons in the two classes. We find that if both classes are almost equally represented, the optimal ODP consists of interdigitating stripes. If one class is less numerous than the other, the optimal ODP consists of patches of the less abundant class surrounded by the neurons of the other class. We predict that the transition from stripes to patches occurs when the fraction of neurons dominated by the underrepresented eye is about 40%. This prediction agrees with the data in macaque and Cebus monkeys. We also study the dependence of the periodicity of ODP on the parameters of our model.

q-bio.NC↗
arXiv2003

Branching Law for Axons

What determines the caliber of axonal branches? We pursue the hypothesis that the axonal caliber has evolved to minimize signal propagation delays, while keeping arbor volume to a minimum. We show that for a general cost function the optimal diameters of mother ($d_0$) and daughter ($d_1$, $d_2$) branches at a bifurcation obey a branching law: $d_{0}^{ν+2}=d_{1}^{ν+2} + d_{2}^{ν+2}$. The derivation relies on the fact that the conduction speed scales with the axon diameter to the power $ν$ ($ν=1$ for myelinated axons and $ν=0.5$ for non-myelinated axons). We test the branching law on the available experimental data and find a reasonable agreement.

physics.bio-ph↗
arXiv1999

Optimal sizes of dendritic and axonal arbors in a topographic projection

I consider a topographic projection between two neuronal layers with different densities of neurons. Given the number of output neurons connected to each input neuron (divergence) and the number of input neurons synapsing on each output neuron (convergence) I determine the widths of axonal and dendritic arbors which minimize the total volume of axons and dendrites. Analytical results for one-dimensional and two-dimensional projections can be summarized qualitatively in the following rule: neurons of the sparser layer should have arbors wider than those of the denser layer. This agrees with the anatomical data from retinal and cerebellar neurons whose morphology and connectivity are known. The rule may be used to infer connectivity of neurons from their morphology.

cond-mat.dis-nn↗
arXiv1999

Binocular disparity can explain the orientation of ocular dominance stripes in primate V1

In the primate primary visual area (V1), the ocular dominance pattern consists of alternating monocular stripes. Stripe orientation follows systematic trends preserved across several species. I propose that these trends result from minimizing the length of intra-cortical wiring needed to recombine information from the two eyes in order to achieve the perception of depth. I argue that the stripe orientation at any point of V1 should follow the direction of binocular disparity in the corresponding point of the visual field. The optimal pattern of stripes determined from this argument agrees with the ocular dominance pattern of macaque and Cebus monkeys. This theory predicts that for any point in the visual field the limits of depth perception are greatest in the direction along the ocular dominance stripes at that point.

cond-mat.dis-nn↗
arXiv1999

Ocular dominance patterns in mammalian visual cortex: A wire length minimization approach

We propose a theory for ocular dominance (OD) patterns in mammalian primary visual cortex. This theory is based on the premise that OD pattern is an adaptation to minimize the length of intra-cortical wiring. Thus we can understand the existing OD patterns by solving a wire length minimization problem. We divide all the neurons into two classes: left-eye dominated and right-eye dominated. We find that segregation of neurons into monocular regions reduces wire length if the number of connections with the neurons of the same class differs from that with the other class. The shape of the regions depends on the relative fraction of neurons in the two classes. If the numbers are close we find that the optimal OD pattern consists of interdigitating stripes. If one class is less numerous than the other, the optimal OD pattern consists of patches of the first class neurons in the sea of the other class neurons. We predict the transition from stripes to patches when the fraction of neurons dominated by the ipsilateral eye is about 40%. This prediction agrees with the data in macaque and Cebus monkeys. This theory can be applied to other binary cortical systems.

cond-mat.soft↗
arXiv1996

Consequences of a possible adiabatic transition between ν=1/3 and ν=1 quantum Hall states in a narrow wire

We consider the possibility of creating an adiabatic transition through a narrow neck, or point contact, between two different quantized Hall states that have the same number of edge modes, such as ν=1 and ν=1/3. We apply both the composite fermion and the Luttinger liquid formalism to analyze the transition. We suggest that using such adiabatic junctions one could build a DC step-up transformer, where the output voltage is higher than the input. Difficulties standing in the way of an experimental implementation of the adiabatic junction are addressed.

cond-mat.mes-hall↗
arXiv1996

Comment on ``New Class of Resonances at the Edge of the Two-Dimensional Electron Gas.''

A reproducible resonance structure in the conductance through an incompressible strip in the quantized Hall regime was recently reported by Zhitenev {\it et al}. Although the authors disfavored the explanation of the conductance resonances based on resonant tunneling (RT) through an impurity state, I believe that it should not be dismissed and can explain a number of experimental observations very well. In particular, I point out a new characteristic signature of RT in the quantized Hall regime: the quantization of the slopes of the resonance tracks on the magnetic field-gate voltage plot.

cond-mat↗
arXiv1995

The Structure of Fractional Edge States: A Composite Fermion Approach

I study the structure of the two-dimensional electron gas edge in the quantum Hall regime using the composite fermion approach. The electron density distribution and the composite fermion energy spectrum are obtained numerically in Hartree approximation for bulk filling factors $ν=1,1/3,2/3,1/5$. For a very sharp edge of the $ν=1$ state the one-electron picture is valid. As the edge width $a$ is increased the density distribution shows features related to the fractional states and new fractional channels appear in pairs. For a very smooth edge I find quasiclassically the number of channels $p\sim\sqrt{a/l_H}$, where $l_H$ is the magnetic length.

cond-mat↗