Advancements in exponential synchronization and encryption techniques: Quaternion-Valued Artificial Neural Networks with two-sided coefficients.

This paper presents cutting-edge advancements in exponential synchronization and encryption techniques, focusing on Quaternion-Valued Artificial Neural Networks (QVANNs) that incorporate two-sided coefficients. The study introduces a novel approach that harnesses the Cayley-Dickson representation method to simplify the complex equations inherent in QVANNs, thereby enhancing computational efficiency by exploiting complex number properties. The study employs the Lyapunov theorem to craft a resilient control system, showcasing its exponential synchronization by skillfully regulating the Lyapunov function and its derivatives.

A neurodynamic optimization approach to distributed nonconvex optimization based on an HP augmented Lagrangian function.

This paper develops a neurodynamic model for distributed nonconvex-constrained optimization. In the distributed constrained optimization model, the objective function and inequality constraints do not need to be convex, and equality constraints do not need to be affine. A Hestenes-Powell augmented Lagrangian function for handling the nonconvexity is established, and a neurodynamic system is developed based on this.

A magnetic resonance imaging-based lymph node regression grading scheme for nasopharyngeal carcinoma after radiotherapy.

Background: Among patients with nasopharyngeal carcinoma (NPC), there is no established method to distinguish between patients with residual disease that may eventually progress and those who have achieved cured. We thus aimed to assess the prognostic value of magnetic resonance imaging (MRI)-based lymph node regression grade (LRG) in the risk stratification of patients with NPC following radiotherapy (RT).

Methods: This study retrospectively enrolled 387 patients newly diagnosed with NPC between January 2010 and January 2013.

A Rulefit-based prognostic analysis using structured MRI report to select potential beneficiaries from induction chemotherapy in advanced nasopharyngeal carcinoma: A dual-centre study.

Background And Purpose: Structured MRI report facilitate prognostic prediction for nasopharyngeal carcinoma (NPC). However, the intrinsic association among structured variables is not fully utilised. This study aimed to investigate the performance of a Rulefit-based model in feature integration behind structured MRI report and prognostic prediction in advanced NPC.

Optimal Size Threshold for MRI-Detected Retropharyngeal Lymph Nodes to Predict Outcomes in Nasopharyngeal Carcinoma: A Two-Center Study.

Retropharyngeal lymph node (RLN) metastases have profound prognostic implications in patients with nasopharyngeal carcinoma (NPC). However, the AJCC staging system does not specify a size threshold for determining RLN involvement, resulting in inconsistent thresholds in practice. The purpose of this article was to determine the optimal size threshold for determining the presence of metastatic RLNs on MRI in patients with NPC, in terms of outcome predictions.

Double Auto-Weighted Tensor Robust Principal Component Analysis.

Tensor Robust Principal Component Analysis (TRPCA), which aims to recover the low-rank and sparse components from their sum, has drawn intensive interest in recent years. Most existing TRPCA methods adopt the tensor nuclear norm (TNN) and the tensor l norm as the regularization terms for the low-rank and sparse components, respectively. However, TNN treats each singular value of the low-rank tensor L equally and the tensor l norm shrinks each entry of the sparse tensor S with the same strength.

Collaborative neurodynamic optimization for solving nonlinear equations.

A distributed optimization method for solving nonlinear equations with constraints is developed in this paper. The multiple constrained nonlinear equations are converted into an optimization problem and we solve it in a distributed manner. Due to the possible presence of nonconvexity, the converted optimization problem might be a nonconvex optimization problem.

Fixed-time synchronization for quaternion-valued memristor-based neural networks with mixed delays.

In this paper, the fixed-time synchronization (FXTSYN) of unilateral coefficients quaternion-valued memristor-based neural networks (UCQVMNNs) with mixed delays is investigated. A direct analytical approach is suggested to obtain FXTSYN of UCQVMNNs utilizing one-norm smoothness in place of decomposition. When dealing with drive-response system discontinuity issues, use the set-valued map and the differential inclusion theorem.

Quaternion Scalar and Vector Norm Decomposition: Quaternion PCA for Color Face Recognition.

This paper proposes a decomposition called quaternion scalar and vector norm decomposition (QSVND) for approximation problems in color image processing. Different from traditional quaternion norm approximations that are always the single objective models (SOM), QSVND is adopted to transform the SOM into the bi-objective model (BOM). Furthermore, regularization is used to solve the BOM problem as a common scalarization method, which converts the BOM into a more reasonable SOM.

Clifford-Valued Distributed Optimization Based on Recurrent Neural Networks.

In this paper, we address the Clifford-valued distributed optimization subject to linear equality and inequality constraints. The objective function of the optimization problems is composed of the sum of convex functions defined in the Clifford domain. Based on the generalized Clifford gradient, a system of multiple Clifford-valued recurrent neural networks (RNNs) is proposed for solving the distributed optimization problems.

Color Image Recovery Using Low-Rank Quaternion Matrix Completion Algorithm.

As a new color image representation tool, quaternion has achieved excellent results in color image processing problems. In this paper, we propose a novel low-rank quaternion matrix completion algorithm to recover missing data of a color image. Motivated by two kinds of low-rank approximation approaches (low-rank decomposition and nuclear norm minimization) in traditional matrix-based methods, we combine the two approaches in our quaternion matrix-based model.

Robust Sparse Representation in Quaternion Space.

Sparse representation has achieved great success across various fields including signal processing, machine learning and computer vision. However, most existing sparse representation methods are confined to the real valued data. This largely limit their applicability to the quaternion valued data, which has been widely used in numerous applications such as color image processing.

Event-Triggered Control for the Disturbance Decoupling Problem of Boolean Control Networks.

This paper investigates the disturbance decoupling problem (DDP) of Boolean control networks (BCNs) by event-triggered control. Using the semi-tensor product of matrices, algebraic forms of BCNs can be achieved, based on which, event-triggered controllers are designed to solve the DDP of BCNs. In addition, the DDP of Boolean partial control networks is also derived by event-triggered control.

Decomposition approach to the stability of recurrent neural networks with asynchronous time delays in quaternion field.

In this paper, the global exponential stability for recurrent neural networks (QVNNs) with asynchronous time delays is investigated in quaternion field. Due to the non-commutativity of quaternion multiplication resulting from Hamilton rules: ij=-ji=k, jk=-kj=i, ki=-ik=j, ijk=i=j=k=-1, the QVNN is decomposed into four real-valued systems, which are studied separately. The exponential convergence is proved directly accompanied with the existence and uniqueness of the equilibrium point to the consider systems.

Quaternion Collaborative and Sparse Representation With Application to Color Face Recognition.

Collaborative representation-based classification (CRC) and sparse RC (SRC) have recently achieved great success in face recognition (FR). Previous CRC and SRC are originally designed in the real setting for grayscale image-based FR. They separately represent the color channels of a query color image and ignore the structural correlation information among the color channels.