Firefly algorithm-based LSTM model for Guzheng tunes switching with big data analysis.

Guzheng tune progression involves intricately harmonizing melodic motif transitions. Effectively navigating this vast creative possibility space to expose musically consistent elaborations presents challenges. We develop a specialized large long short-term memory (LSTM) model for generating musically consistent Guzheng tune transitions. First, we propose novel firefly algorithm (FA) enhancements, e.g., adaptive diversity preservation and adaptive swim parameters, to boost exploration effectiveness for navigating the vast creative combinatorics when generating Guzheng tune transitions. Then, we develop a specialized stacked LSTM architecture incorporating residual connections and conditioned embedding vectors that can leverage long-range temporal dependencies in Guzheng music patterns, including unsupervised learning of concise Guzheng-specific melody embedding vectors via a variational autoencoder, encapsulating unique harmonic signatures from performance descriptors to provide style guidance. Finally, we use LSTM networks to develop adversarial generative large models that enable realistic synthesis and evaluation of Guzheng tunes switching. We gather an extensive 10+ hour corpus of solo Guzheng recordings spanning 230 musical pieces, 130 distinguished performing artists, and 600+ audio tracks. Simultaneously, we conduct thorough Guzheng data analysis. Comparative assessments against strong baselines over systematic musical metrics and professional listeners validate significant generation fidelity improvements. Our model achieves a 63 % reduction in reconstruction error compared to the standard FA optimization after 1000 iterations. It also outperforms baselines in capturing characteristic motifs, maintaining modality coherence with under 2 % dissonant pitch errors, and retaining desired rhythmic cadences. User studies further confirm the superior naturalness, novelty, and stylistic faithfulness of the generated tune transitions, with ratings close to real data.

Laguerre Wavelet Approach for a Two-Dimensional Time-Space Fractional Schrödinger Equation.

This article is devoted to the determination of numerical solutions for the two-dimensional time-spacefractional Schrödinger equation. To do this, the unknown parameters are obtained using the Laguerre wavelet approach. We discretize the problem by using this technique. Then, we solve the discretized nonlinear problem by means of a collocation method. The method was proven to give very accurate results. The given numerical examples support this claim.

Optimal Control of Time-Delay Fractional Equations via a Joint Application of Radial Basis Functions and Collocation Method.

A novel approach to solve optimal control problems dealing simultaneously with fractional differential equations and time delay is proposed in this work. More precisely, a set of global radial basis functions are firstly used to approximate the states and control variables in the problem. Then, a collocation method is applied to convert the time-delay fractional optimal control problem to a nonlinear programming one. By solving the resulting challenge, the unknown coefficients of the original one will be finally obtained. In this way, the proposed strategy introduces a very tunable framework for direct trajectory optimization, according to the discretization procedure and the range of arbitrary nodes. The algorithm's performance has been analyzed for several non-trivial examples, and the obtained results have shown that this scheme is more accurate, robust, and efficient than most previous methods.