We study the propagation and attenuation of zero sound and first sound in thin, arbitrarily polarized Fermi-liquid films. Following Khalatnikov and Abrikosov, we solve Landau's linearized kinetic equation in the relaxation-time approximation for a complex speed of sound. Analytic solutions are obtained in the hydrodynamic and ballistic limits for arbitrary polarization. By solving the collision integral in two dimensions, we find the well-known result that quasiparticle-quasiparticle collisions contribute to the collision frequencies 1/τ σ , with a low-temperature term proportional to T 2 ln (T F σ /T ), where σ = ↑, ↓ is the spin state. If the films are adsorbed to a dynamic substrate, we find additional possible contributions to the collision frequency that come from quasiparticle-phonon interactions. We show, however, that for 3 He thin films, the mismatch between possible maximum values of the Fermi velocity and the substrate speed of sound freezes this contribution out at usual experimental temperatures. Thus, we can conclude that zero sound propagates at absolute zero in this type of adsorbed Fermi-liquid film. By utilizing previous results for the Landau parameters of an arbitrarily polarized 3 He film, we compute numerical solutions for the sound speeds and attenuation in the hydrodynamic and ballistic regimes, thereby studying the transition from first sound to zero sound as a function of temperature.

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We examine in detail the method introduced by Sanchez-Castro, Bedell, and Wiegers (SBW) to solve Landau's linearized kinetic equation, and compare it with the well-known standard method introduced by Abrikosov and Khalatnikov (AK). The SBW approach, hardly known, differs from AK in the way that moments are taken with respect to the angular functions of the Fourier transformed kinetic equation. We compare the SBW and AK solutions for zero-sound and firstsound propagation speeds and attenuation both analytically in the zero and full polarization limits, and numerically at arbitrary polarization using Landau parameters appropriate for thin 3 He films.We find that the lesser known method not only yields results in close agreement with the standard method, but in most cases does so with far less analytic and computational effort.

In this work, we explore whether it is possible to learn representations of endoscopic video frames to perform tasks such as identifying surgical tool presence without supervision. We use a maximum mean discrepancy (MMD) variational autoencoder (VAE) to learn lowdimensional latent representations of endoscopic videos and manipulate these representations to distinguish frames containing tools from those without tools. We use three different methods to manipulate these latent representations in order to predict tool presence in each frame. Our fully unsupervised methods can identify whether endoscopic video frames contain tools with average precision of 71.56, 73.93, and 76.18, respectively, comparable to supervised methods. Our code is available at https://github.com/zdavidli/tool-presence/.