63,177 research outputs found
An accurate, fast, mathematically robust, universal, non-iterative algorithm for computing multi-component diffusion velocities
Using accurate multi-component diffusion treatment in numerical combustion
studies remains formidable due to the computational cost associated with
solving for diffusion velocities. To obtain the diffusion velocities, for low
density gases, one needs to solve the Stefan-Maxwell equations along with the
zero diffusion flux criteria, which scales as , when solved
exactly. In this article, we propose an accurate, fast, direct and robust
algorithm to compute multi-component diffusion velocities. To our knowledge,
this is the first provably accurate algorithm (the solution can be obtained up
to an arbitrary degree of precision) scaling at a computational complexity of
in finite precision. The key idea involves leveraging the fact
that the matrix of the reciprocal of the binary diffusivities, , is low
rank, with its rank being independent of the number of species involved. The
low rank representation of matrix is computed in a fast manner at a
computational complexity of and the Sherman-Morrison-Woodbury
formula is used to solve for the diffusion velocities at a computational
complexity of . Rigorous proofs and numerical benchmarks
illustrate the low rank property of the matrix and scaling of the
algorithm.Comment: 16 pages, 7 figures, 1 table, 1 algorith
On Iterative Algorithms for Quantitative Photoacoustic Tomography in the Radiative Transport Regime
In this paper, we describe the numerical reconstruction method for
quantitative photoacoustic tomography (QPAT) based on the radiative transfer
equation (RTE), which models light propagation more accurately than diffusion
approximation (DA). We investigate the reconstruction of absorption coefficient
and/or scattering coefficient of biological tissues. Given the scattering
coefficient, an improved fixed-point iterative method is proposed to retrieve
the absorption coefficient for its cheap computational cost. And we prove the
convergence. To retrieve two coefficients simultaneously, Barzilai-Borwein (BB)
method is applied. Since the reconstruction of optical coefficients involves
the solution of original and adjoint RTEs in the framework of optimization, an
efficient solver with high accuracy is improved from~\cite{Gao}. Simulation
experiments illustrate that the improved fixed-point iterative method and the
BB method are the comparative methods for QPAT in two cases.Comment: 21 pages, 44 figure
Deep Learning Techniques for Music Generation -- A Survey
This paper is a survey and an analysis of different ways of using deep
learning (deep artificial neural networks) to generate musical content. We
propose a methodology based on five dimensions for our analysis:
Objective - What musical content is to be generated? Examples are: melody,
polyphony, accompaniment or counterpoint. - For what destination and for what
use? To be performed by a human(s) (in the case of a musical score), or by a
machine (in the case of an audio file).
Representation - What are the concepts to be manipulated? Examples are:
waveform, spectrogram, note, chord, meter and beat. - What format is to be
used? Examples are: MIDI, piano roll or text. - How will the representation be
encoded? Examples are: scalar, one-hot or many-hot.
Architecture - What type(s) of deep neural network is (are) to be used?
Examples are: feedforward network, recurrent network, autoencoder or generative
adversarial networks.
Challenge - What are the limitations and open challenges? Examples are:
variability, interactivity and creativity.
Strategy - How do we model and control the process of generation? Examples
are: single-step feedforward, iterative feedforward, sampling or input
manipulation.
For each dimension, we conduct a comparative analysis of various models and
techniques and we propose some tentative multidimensional typology. This
typology is bottom-up, based on the analysis of many existing deep-learning
based systems for music generation selected from the relevant literature. These
systems are described and are used to exemplify the various choices of
objective, representation, architecture, challenge and strategy. The last
section includes some discussion and some prospects.Comment: 209 pages. This paper is a simplified version of the book: J.-P.
Briot, G. Hadjeres and F.-D. Pachet, Deep Learning Techniques for Music
Generation, Computational Synthesis and Creative Systems, Springer, 201
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