11,685 research outputs found
Time Discrete Approximation of Weak Solutions for Stochastic Equations of Geophysical Fluid Dynamics and Applications
As a first step towards the numerical analysis of the stochastic primitive
equations of the atmosphere and oceans, we study their time discretization by
an implicit Euler scheme. From deterministic viewpoint the 3D Primitive
Equations are studied with physically realistic boundary conditions. From
probabilistic viewpoint we consider a wide class of nonlinear, state dependent,
white noise forcings. The proof of convergence of the Euler scheme covers the
equations for the oceans, atmosphere, coupled oceanic-atmospheric system and
other geophysical equations. We obtain the existence of solutions weak in PDE
and probabilistic sense, a result which is new by itself to the best of our
knowledge
MIDI-VAE: Modeling Dynamics and Instrumentation of Music with Applications to Style Transfer
We introduce MIDI-VAE, a neural network model based on Variational
Autoencoders that is capable of handling polyphonic music with multiple
instrument tracks, as well as modeling the dynamics of music by incorporating
note durations and velocities. We show that MIDI-VAE can perform style transfer
on symbolic music by automatically changing pitches, dynamics and instruments
of a music piece from, e.g., a Classical to a Jazz style. We evaluate the
efficacy of the style transfer by training separate style validation
classifiers. Our model can also interpolate between short pieces of music,
produce medleys and create mixtures of entire songs. The interpolations
smoothly change pitches, dynamics and instrumentation to create a harmonic
bridge between two music pieces. To the best of our knowledge, this work
represents the first successful attempt at applying neural style transfer to
complete musical compositions.Comment: Paper accepted at the 19th International Society for Music
Information Retrieval Conference, ISMIR 2018, Paris, Franc
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