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Abstract The frequency scaling exponent of low-frequency excitations in microscopically small glasses, which do not allow for the existence of waves (phonons), has been in the focus of the recent literature. The density of statesg(ω) of these modes obeys anω^sscaling, where the exponents, ranging between 2 and 5, depends on the quenching protocol. The orgin of these findings remains controversal. Here we show, using heterogeneous-elasticity theory, that in a marginally-stable glass sampleg(ω) follows a Debye-like scaling (s= 2), and the associated excitations (type-I) are of random-matrix type. Further, using a generalisation of the theory, we demonstrate that in more stable samples, other, (type-II) excitations prevail, which are non-irrotational oscillations, associated with local frozen-in stresses. The corresponding frequency scaling exponentsis governed by the statistics of small values of the stresses and, therefore, depends on the details of the interaction potential. 

The nematodeCaenorhabditis elegansis a widely used model organism for neuroscience. Although its nervous system has been fully reconstructed, the physiological bases of single-neuron functioning are still poorly explored. Recently, many efforts have been dedicated to measuring signals fromC.elegansneurons, revealing a rich repertoire of dynamics, including bistable responses, graded responses, and action potentials. Still, biophysical models able to reproduce such a broad range of electrical responses lack. Realistic electrophysiological descriptions started to be developed only recently, merging gene expression data with electrophysiological recordings, but with a large variety of cells yet to be modeled. In this work, we contribute to filling this gap by providing biophysically accurate models of six classes ofC.elegansneurons, the AIY, RIM, and AVA interneurons, and the VA, VB, and VD motor neurons. We test our models by comparing computational and experimental time series and simulate knockout neurons, to identify the biophysical mechanisms at the basis of inter and motor neuron functioning. Our models represent a step forward toward the modeling ofC.elegansneuronal networks and virtual experiments on the nematode nervous system.