157,350 research outputs found

    Dendrites and conformal symmetry

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    Progress toward characterization of structural and biophysical properties of neural dendrites together with recent findings emphasizing their role in neural computation, has propelled growing interest in refining existing theoretical models of electrical propagation in dendrites while advocating novel analytic tools. In this paper we focus on the cable equation describing electric propagation in dendrites with different geometry. When the geometry is cylindrical we show that the cable equation is invariant under the Schr\"odinger group and by using the dendrite parameters, a representation of the Schr\"odinger algebra is provided. Furthermore, when the geometry profile is parabolic we show that the cable equation is equivalent to the Schr\"odinger equation for the 1-dimensional free particle, which is invariant under the Schr\"odinger group. Moreover, we show that there is a family of dendrite geometries for which the cable equation is equivalent to the Schr\"odinger equation for the 1-dimensional conformal quantum mechanics.Comment: 19 page

    The three dimensional motion and stability of a rotating space station-cable - Counterweight configuration

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    The three dimensional equations of motion for a cable connected space station - counterweight system are developed using a Lagrangian formulation. The system model employed allows for cable and end body damping and restoring effects. The equations are then linearized about the equilibrium motion and nondimensionalized. To first degree, the out-of-plane equations uncouple from the in-plane equations. Therefore, the characteristic polynomials for the in-plane and out-of-plane equations are developed and treated separately. From the general in-plane characteristic equation, necessary conditions for stability are obtained. The Routh-Hurwitz necessary and sufficient conditions for stability are derived for the general out-of-plane characteristic equation. Special cases of the in-plane and out-of-plane equations (such as identical end masses, and when the cable is attached to the centers of mass of the two end bodies) are then examined for stability criteria

    The three dimensional motion and stability of a rotating space station: Cable-counterweight configuration

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    The three dimensional equations of motion for a cable connected space station--counterweight system are developed using a Lagrangian formulation. The system model employed allows for cable and end body damping and restoring effects. The equations are then linearized about the equilibrium motion and nondimensionalized. To first degree, the out-of-plane equations uncouple from the inplane equations. Therefore, the characteristic polynomials for the in-plane and out-of-plane equations are developed and treated separately. From the general in-plane characteristic equation, necessary conditions for stability are obtained. The Routh-Hurwitz necessary and sufficient conditions for stability are derived for the general out-of-plane characteristic equation. Special cases of the in-plane and out-of-plane equations (such as identical end masses, and when the cable is attached to the centers of mass of the two end bodies) are then examined for stability criteria

    Generalized cable formalism to calculate the magnetic field of single neurons and neuronal populations

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    Neurons generate magnetic fields which can be recorded with macroscopic techniques such as magneto-encephalography. The theory that accounts for the genesis of neuronal magnetic fields involves dendritic cable structures in homogeneous resistive extracellular media. Here, we generalize this model by considering dendritic cables in extracellular media with arbitrarily complex electric properties. This method is based on a multi-scale mean-field theory where the neuron is considered in interaction with a "mean" extracellular medium (characterized by a specific impedance). We first show that, as expected, the generalized cable equation and the standard cable generate magnetic fields that mostly depend on the axial current in the cable, with a moderate contribution of extracellular currents. Less expected, we also show that the nature of the extracellular and intracellular media influence the axial current, and thus also influence neuronal magnetic fields. We illustrate these properties by numerical simulations and suggest experiments to test these findings.Comment: Physical Review E (in press); 24 pages, 16 figure

    AC loss in a stack of flat superconducting cables

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    An equation has been derived which describes the current distribution in a flat cable subjected to a time-dependent magnetic field directed perpendicular to the cable wide face. Solutions of this equation obtained in the case when all parameters are uniform along the cable allow us to obtain the time constant spectrum, magnetic moment of the cable and A.C. loss. For a stack of cables with height much larger than the cable width, the contribution of the self-screening is calculated analytically. Numerical examples are provided based on geometrical characteristics and interstrand contact resistance of a typical LHC cable and the inductance of the LHC dipole

    Time Fractional Cable Equation And Applications in Neurophysiology

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    We propose an extension of the cable equation by introducing a Caputo time fractional derivative. The fundamental solutions of the most common boundary problems are derived analitically via Laplace Transform, and result be written in terms of known special functions. This generalization could be useful to describe anomalous diffusion phenomena with leakage as signal conduction in spiny dendrites. The presented solutions are computed in Matlab and plotted.Comment: 10 figures. arXiv admin note: substantial text overlap with arXiv:1702.0532

    Dendritic cable with active spines: a modeling study in the spike-diffuse-spike framework

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    The spike-diffuse-spike (SDS) model describes a passive dendritic tree with active dendritic spines. Spine-head dynamics is modelled with a simple integrate-and-fire process, whilst communication between spines is mediated by the cable equation. Here we develop a computational framework that allows the study of multiple spiking events in a network of such spines embedded in a simple one-dimensional cable. This system is shown to support saltatory waves as a result of the discrete distribution of spines. Moreover, we demonstrate one of the ways to incorporate noise into the spine-head whilst retaining computational tractability of the model. The SDS model sustains a variety of propagating patterns
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