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As the counterpart of electromagnetic and acoustic metamaterials, elastic metamaterials, artificial periodic composite materials, also offer the ultimate possibility to manipulate elastic wave propagation in the subwavelength scale through different mechanisms. Aiming at the promising superlensing for the medical ultrasonic and detection, the double-negative metamaterials which possess the negative mass density and elastic modulus simultaneously can be acted as the ideal superlens for breaking the diffraction limit. In this paper, we use topology optimization to design the two-dimensional single-phase anisotropic elastic metamaterials with broadband double-negative indices and numerically demonstrate the superlensing at the deep-subwavelength scale. We also discuss the impact of several parameters adopted in the objective function and constraints on the optimized results. Unlike all previous reported mechanisms, our optimized structures exhibit the new quadrupolar or multipolar resonances for the negative mass density, negative longitudinal and shear moduli. In addition, we observe the negative refraction of transverse waves in a single-phase material. Most structures can serve as the anisotropic zero-index metamaterials for the longitudinal or transverse wave at a certain frequency. The cloaking effect is demonstrated for both the longitudinal and transverse waves. Moreover, with the particular constraints in optimization, we design a super-anisotropic metamaterial exhibiting the double-negative and hyperbolic dispersions along two principal directions, respectively. Our optimization work provides a robust computational approach to negative index engineering in elastic metamaterials and guides design of other kinds of metamaterials, including the electromagnetic and acoustic metamaterials. The unusual properties of our optimized structures are likely to inspire new ideas and novel applications including the low-frequency vibration attenuation, flat lens and ultrasonography for elastic waves in the future.

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/.