853 research outputs found
Super approximation for
Let be finite
symmetric and assume generates a group which is Zariski-dense in
. We prove that the Cayley graphs form a family of
expanders
Sum-product phenomenon in quotients of rings of algebraic integers
We obtain a bounded generation theorem over , where
is the ring of integers of a number field and a
general ideal of . This addresses a conjecture of Salehi-Golsefidy.
Along the way, we obtain nontrivial bounds for additive character sums over
for a prime ideal with the aid of
certain sum-product estimates
Fast Diffusion GAN Model for Symbolic Music Generation Controlled by Emotions
Diffusion models have shown promising results for a wide range of generative
tasks with continuous data, such as image and audio synthesis. However, little
progress has been made on using diffusion models to generate discrete symbolic
music because this new class of generative models are not well suited for
discrete data while its iterative sampling process is computationally
expensive. In this work, we propose a diffusion model combined with a
Generative Adversarial Network, aiming to (i) alleviate one of the remaining
challenges in algorithmic music generation which is the control of generation
towards a target emotion, and (ii) mitigate the slow sampling drawback of
diffusion models applied to symbolic music generation. We first used a trained
Variational Autoencoder to obtain embeddings of a symbolic music dataset with
emotion labels and then used those to train a diffusion model. Our results
demonstrate the successful control of our diffusion model to generate symbolic
music with a desired emotion. Our model achieves several orders of magnitude
improvement in computational cost, requiring merely four time steps to denoise
while the steps required by current state-of-the-art diffusion models for
symbolic music generation is in the order of thousands
Data-driven structural control of monopile wind turbine towers based on machine learning
This paper studies the data-driven structural control of monopile wind turbine towers based on machine learning approach, by using an active tuned mass damper (TMD) located in the nacelle. The adaptive dynamic programming (ADP) approach is employed to obtain the optimal controller which is derived on the modern large-scale machine learning platform Tensorflow. The proposed network structure includes three simple three-layer neural networks (NNs), i.e. a plant network, a critic network, and an action network. The plant network is used to capture the fully nonlinear dynamics of the structural system while the action network is used to approximate the optimal controller. Their training requires the gradient information flowing through the whole network. The automatic differentiation is used in this paper for all the gradient derivations, which greatly improves the employed ADP algorithm’s ability in solving complex practical problems. The simulation results of structural control of monopile turbine towers show that on average the active TMD achieves 15% performance improvement on tower fatigue load reduction over a passive TMD, with small active power consumption (less than 0.24% of the turbine’s nominal power production). Besides, the controller design considers the trade-off between control performance and power consumption
Long-distance and high-impact wind farm wake effects revealed by SAR: a global-scale study
Wind, as a clean and sustainable source of energy, has witnessed significant
growth in recent years. However, with a growing number of wind farms
authorised, constructed and commissioned, the wake effect (the reduced wind
speed caused by upstream wind farms) is emerging as a pressing concern for both
farm owners and policymakers. Here, to systematically and comprehensively
investigate the wake effects in real-world wind farms, we analyse the wind
speed retrieved from 7122 Sentinel 1A/B SAR images spanning over three years,
encompassing more than 60 large-scale wind farms across Europe and Asia. Our
study reveals that long-distance wakes can propagate more than 100 km.
Additionally, we identify that wake effects lead to, on average, a 1.204 m/s
(or 12.4%) speed reduction for downstream wake-affected areas. We envisage that
our quantitative findings can provide vital support to wake-related planning
and legislation for future wind energy projects where wind power plants are
expected to be in close proximity
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