Dendrites and conformal symmetry

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

Suppression of zinc dendrites in zinc electrode power cells

Addition of various tetraalkyl quarternary ammonium salts, to alkaline zincate electrolyte of cell, prevents formation of zinc dendrites during charging of zinc electrode. Electrode capacity is not impaired and elimination of dendrites prolongs cell life

Understanding the formation of twinned dendrites (‘feather’ grains)

The phenomenon of feather grain growth is interesting from both a theoretical and commercial point of view. Here we report the results of phase-field simulations aimed at understanding the formation of twinned dendrites. We show that, while a competition between oppositely directed capillary and kinetic anisotropies with a simple four-fold symmetry can produce low anisotropy structures such as dendritic seaweed, there is no indication that this can give rise to twinned dendrites. In contrast, adding small components of an anisotropy, with higher order harmonics, can produce features reminiscent of twinned dendrites and may also be able to stabilise the grooved tip morphology

Computing threshold functions using dendrites

Neurons, modeled as linear threshold unit (LTU), can in theory compute all thresh- old functions. In practice, however, some of these functions require synaptic weights of arbitrary large precision. We show here that dendrites can alleviate this requirement. We introduce here the non-Linear Threshold Unit (nLTU) that integrates synaptic input sub-linearly within distinct subunits to take into account local saturation in dendrites. We systematically search parameter space of the nTLU and TLU to compare them. Firstly, this shows that the nLTU can compute all threshold functions with smaller precision weights than the LTU. Secondly, we show that a nLTU can compute significantly more functions than a LTU when an input can only make a single synapse. This work paves the way for a new generation of network made of nLTU with binary synapses.Comment: 5 pages 3 figure

Mechanisms of Dendrites Occurrence during Crystallization: Features of the Ice Crystals Formation

Dendrites formation in the course of crystallization presents very general phenomenon, which is analyzed in details via the example of ice crystals growth in deionized water. Neutral molecules of water on the surface are combined into the double electric layer (DEL) of oriented dipoles; its field reorients approaching dipoles with observable radio-emission in the range of 150 kHz. The predominant attraction of oriented dipoles to points of gradients of this field induces dendrites growth from them, e.g. formation of characteristic form of snowflakes at free movement of clusters through saturated vapor in atmosphere. The constant electric field strengthens DELs' field and the growth of dendrites. Described phenomena should appear at crystallization of various substances with dipole molecules, features of radio-emission can allow the monitoring of certain processes in atmosphere and in technological processes. Crystallization of particles without constant moments can be stimulated by DELs of another nature with attraction of virtual moments of particles to gradients of fields and corresponding dendrites formation.Comment: 6 page

Ray optics in flux avalanche propagation in superconducting films

Experimental evidence of wave properties of dendritic flux avalanches in superconducting films is reported. Using magneto-optical imaging the propagation of dendrites across boundaries between a bare NbN film and areas coated by a Cu-layer was visualized, and it was found that the propagation is refracted in full quantitative agreement with Snell's law. For the studied film of 170 nm thickness and a 0.9 mkm thick metal layer, the refractive index was close to n=1.4. The origin of the refraction is believed to be caused by the dendrites propagating as an electromagnetic shock wave, similar to damped modes considered previously for normal metals. The analogy is justified by the large dissipation during the avalanches raising the local temperature significantly. Additional time-resolved measurements of voltage pulses generated by segments of the dendrites traversing an electrode confirm the consistency of the adapted physical picture.Comment: 4 pages, 4 figure

Tbr1 instructs laminar patterning of retinal ganglion cell dendrites.

Visual information is delivered to the brain by >40 types of retinal ganglion cells (RGCs). Diversity in this representation arises within the inner plexiform layer (IPL), where dendrites of each RGC type are restricted to specific sublaminae, limiting the interneuronal types that can innervate them. How such dendritic restriction arises is unclear. We show that the transcription factor Tbr1 is expressed by four mouse RGC types with dendrites in the outer IPL and is required for their laminar specification. Loss of Tbr1 results in elaboration of dendrites within the inner IPL, while misexpression in other cells retargets their neurites to the outer IPL. Two transmembrane molecules, Sorcs3 and Cdh8, act as effectors of the Tbr1-controlled lamination program. However, they are expressed in just one Tbr1+ RGC type, supporting a model in which a single transcription factor implements similar laminar choices in distinct cell types by recruiting partially non-overlapping effectors