7,272 research outputs found
Compact convex sets of the plane and probability theory
The Gauss-Minkowski correspondence in states the existence of
a homeomorphism between the probability measures on such that
and the compact convex sets (CCS) of the plane
with perimeter~1. In this article, we bring out explicit formulas relating the
border of a CCS to its probability measure. As a consequence, we show that some
natural operations on CCS -- for example, the Minkowski sum -- have natural
translations in terms of probability measure operations, and reciprocally, the
convolution of measures translates into a new notion of convolution of CCS.
Additionally, we give a proof that a polygonal curve associated with a sample
of random variables (satisfying ) converges
to a CCS associated with at speed , a result much similar to
the convergence of the empirical process in statistics. Finally, we employ this
correspondence to present models of smooth random CCS and simulations
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
Linear elastic fracture mechanics predicts the propagation distance of frictional slip
When a frictional interface is subject to a localized shear load, it is often
(experimentally) observed that local slip events initiate at the stress
concentration and propagate over parts of the interface by arresting naturally
before reaching the edge. We develop a theoretical model based on linear
elastic fracture mechanics to describe the propagation of such precursory slip.
The model's prediction of precursor lengths as a function of external load is
in good quantitative agreement with laboratory experiments as well as with
dynamic simulations, and provides thereby evidence to recognize frictional slip
as a fracture phenomenon. We show that predicted precursor lengths depend,
within given uncertainty ranges, mainly on the kinetic friction coefficient,
and only weakly on other interface and material parameters. By simplifying the
fracture mechanics model we also reveal sources for the observed non-linearity
in the growth of precursor lengths as a function of the applied force. The
discrete nature of precursors as well as the shear tractions caused by
frustrated Poisson's expansion are found to be the dominant factors. Finally,
we apply our model to a different, symmetric set-up and provide a prediction of
the propagation distance of frictional slip for future experiments
Toward a 2D multiphysic code with solid-solid & fluid interactions for industrial related problems
In the present study, applications of the SPH method to industrial related issues are considered by starting from an existing open source 2D SPH code, namely the SPHYSICS code, which offers an effective ground for numerical developments, which are performed in order to bring an answer to industrial problems, such as simulations of solid/fluid coupling in a free surface flow context. The purpose of the present paper is therefore to expose the numerical developments which yield an enhanced version (referred to as "SPHYSIC2") of the initial code. Firstly, the different features added to obtain the operational code needed for engineering applications are described, and so are the problems raised on this way, offering a kind of review of SPH methods for engineers. Secondly, the validation of the proposed code is partially presented with two well known but difficult test cases, namely the classical "dam break" and "wedge entry"problems. Thirdly, principles of a method to solve solid/solid contacts, frequently present in realistic configuration, are exposed and applied to achieve more complex simulations. Finally, perspectives for new features of the SPHYSIC2 code are exposed and discussed
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