72,057 research outputs found
Characteristics of optical multi-peak solitons induced by higher-order effects in an erbium-doped fiber system
We study multi-peak solitons \textit{on a plane-wave background} in an
erbium-doped fiber system with some higher-order effects, which is governed by
a coupled Hirota and Maxwel-Bloch (H-MB) model. The important characteristics
of multi-peak solitons induced by the higher-order effects, such as the
velocity changes, localization or periodicity attenuation, and state
transitions, are revealed in detail. In particular, our results demonstrate
explicitly that a multi-peak soliton can be converted to an anti-dark soliton
when the periodicity vanishes; on the other hand, a multi-peak soliton is
transformed to a periodic wave when the localization vanishes. Numerical
simulations are performed to confirm the propagation stability of multi-peak
solitons riding on a plane-wave background. Finally, we compare and discuss the
similarity and difference of multi-peak solitons in special degenerate cases of
the H-MB system with general existence conditions.Comment: 7 pages, 4 figure
Separable subgroups have bounded packing
In this note, we prove that separable subgroups have bounded packing in
ambient groups. The notion bounded packing was introduced by Hruska and Wise
and in particular, our result answers positively a question of theirs, asking
whether each subgroup of a virtually polycyclic group has the bounded packing
property.Comment: 2 pages, to appear Proc. Amer. Math. So
Universal Properties of Fermi Gases in One-dimension
In this Rapid Communication, we investigate the universal properties of a
spin-polarized two-component Fermi gas in one dimension (1D) using Bethe
ansatz. We discuss the quantum phases and phase transitions by obtaining exact
results for the equation of state, the contact, the magnetic susceptibility and
the contact susceptibility, giving a precise understanding of the 1D analogue
of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer crossover in
three dimension (3D) and the associated universal magnetic properties. In
particular, we obtain the exact form of the magnetic susceptibility at low temperatures, where is the
energy gap and is the temperature. Moreover, we establish exact upper and
lower bounds for the relation between polarization and the contact for
both repulsive and attractive Fermi gases. Our findings emphasize the role of
the pair fluctuations in strongly interacting 1D fermion systems that can shed
light on higher dimensions.Comment: 4 figures, the main pape
MuseGAN: Multi-track Sequential Generative Adversarial Networks for Symbolic Music Generation and Accompaniment
Generating music has a few notable differences from generating images and
videos. First, music is an art of time, necessitating a temporal model. Second,
music is usually composed of multiple instruments/tracks with their own
temporal dynamics, but collectively they unfold over time interdependently.
Lastly, musical notes are often grouped into chords, arpeggios or melodies in
polyphonic music, and thereby introducing a chronological ordering of notes is
not naturally suitable. In this paper, we propose three models for symbolic
multi-track music generation under the framework of generative adversarial
networks (GANs). The three models, which differ in the underlying assumptions
and accordingly the network architectures, are referred to as the jamming
model, the composer model and the hybrid model. We trained the proposed models
on a dataset of over one hundred thousand bars of rock music and applied them
to generate piano-rolls of five tracks: bass, drums, guitar, piano and strings.
A few intra-track and inter-track objective metrics are also proposed to
evaluate the generative results, in addition to a subjective user study. We
show that our models can generate coherent music of four bars right from
scratch (i.e. without human inputs). We also extend our models to human-AI
cooperative music generation: given a specific track composed by human, we can
generate four additional tracks to accompany it. All code, the dataset and the
rendered audio samples are available at https://salu133445.github.io/musegan/ .Comment: to appear at AAAI 201
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