In this paper, a distributed algorithm for reaching average consensus is proposed for multi-agent systems with tree communication graph, when the edge weight distribution is unbalanced. First, the problem is introduced as a key topic of core algorithms for several modern scenarios. Then, the relative solution is proposed as a finite-time algorithm, which can be included in any application as a preliminary setup routine, and it is well-suited to be integrated with other adaptive setup routines, thus making the proposed solution useful in several practical applications. A special focus is devoted to the integration of the proposed method with a recent Laplacian eigenvalue allocation algorithm, and the implementation of the overall approach in a wireless sensor network framework. Finally, a worked example is provided, showing the significance of this approach for reaching a more precise average consensus in uncertain scenarios.

The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic 2ⁿ-dimensional extensions in modeling some genetic and cultural phenomena. Mathematical properties of hyperbolic numbers and their bisymmetric matrix representations are described in a connection with their application to analyze the following structures: alphabets of DNA nucleobases; inherited phyllotaxis phenomena; Punnett squares in Mendelian genetics; the psychophysical Weber-Fechner law; long literary Russian texts (in their special binary representations). New methods of algebraic analysis of the harmony of musical works are proposed, taking into account the innate predisposition of people to music. The hypothesis is put forward that sets of eigenvectors of matrix representations of basis units of 2ⁿ-dimensional hyperbolic numbers play an important role in transmitting biological information. A general hyperbolic rule regarding the oligomer cooperative organization of different genomes is described jointly with its quantum-information model. Besides, the hypothesis about some analog of the Weber-Fechner law for sequences of spikes in single nerve fibers is formulated. The proposed algebraic approach is connected with the theme of the grammar of biology and applications of bisymmetric doubly stochastic matrices. Applications of hyperbolic numbers reveal hidden interrelations between structures of different biological and physical phenomena. They lead to new approaches in mathematical modeling genetic phenomena and innate biological structures.

Deep learning-based handwriting personality prediction uses neural networks (CNNs) to consider and predict personality characters from handwritten text to improve applications such as adaptive technology and automated data access. This method requires high computational resources and widely classified data, and its accuracy may suffer from signature variation and overfitting. This study introduces a novel optimizeddeep learning for Hand Written Personality Prediction. First the input data is collected from givendataset and an enhanced Gaussian filter is used in pre-processing to improve image quality by reducing noise and increasing contrast.After pre-processing, features are extracted by PCA-based normalized GIST, which standardizes the features to improve image representation.These extracted features are generated using an adaptive horse herd optimization algorithm to select the most important features. Based on selected features Improved Generative Adversarial Networks with artificial hummingbird optimization (IGAN_AHb) enables fast and efficient convergence of GANs. This reduce the mode collapse and ensures training with consistently fine-tuned parameters.The selected features are considered by characters such as openness, conscientiousness, extroversion, agreeableness and neuroticism, and finally classified using the IGAN_AHb classifier. In the result section, the proposed model is compared with various models with the matrix precision, recall, F1-score. The proposed model attained the value of 97.3% of precision and a recall rate of 96%, respectively. By comparing with other models, the proposed model attained highest values.

This paper explores innovative approaches to determining eigenvalues and eigenvectors through the combination of neural networks and traditional numerical methods. Traditional methods like the Newton-Raphson and Durand-Kerner algorithms are proven effective but often require good initial approximations and can be sensitive to the choice of starting points. In this study, we propose a hybrid approach that uses neural networks to generate better initial approximations, which are then iteratively refined using traditional methods. By combining the pattern recognition power of neural networks with the adaptability of traditional numerical methods, we demonstrate faster convergence and higher accuracy in determining eigenvalues and eigenvectors. Experimental results on various polynomials of different degrees and characteristics show that our hybrid approach outperforms individual methods, providing a more robust and efficient solution.