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 four-category MRI-LRG system based on the areal analysis of RT-induced fibrosis and residual tumor was established. Univariate analysis was performed using the Kaplan-Meier method, and comparisons were conducted via the log-rank test. Multivariate analyses were conducted using Cox regression models to calculate the hazard ratios (HRs) with 95% confidence intervals (CIs) and adjusted P values. Survival curves were calculated using the Kaplan-Meier method and compared using the log-rank test. Results: The sum of MRI-LRG scores (LRG-sum) was an independent prognostic factor for progression-free survival (PFS) (HR 2.50, 95% CI: 1.28-4.90; P<0.001). LRG-sum ≤9 and >9 showed a poorer 5-year PFS rate than did LRG-sum ≤2 (66.1%, 42.9%, and 77.6%, respectively; P<0.001). A survival clustering analysis-based decision tree model showed more complex interactions among LRG-sum and pretreatment and post-RT Epstein-Barr virus (EBV) DNA, yielding four patient clusters with differentiated disease progression risks (5-year PFS rates of 89.5%, 76.4%, 57.6%, and 27.8%, respectively), which showed better risk stratification than did post-RT EBV DNA alone (P<0.001). Conclusions: The MRI-LRG system adds prognostic information and is a potentially reliable, noninvasive means to stratify treatment modalities for patients with NPC.

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

BACKGROUND. 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. OBJECTIVE. 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. METHODS. This retrospective study included 1752 patients (median age, 46 years; 1297 men, 455 women) with NPC treated by intensity-modulated radiotherapy (RT) from January 2010 to March 2014 from two hospitals; 438 patients underwent MRI 3-4 months after treatment. Two radiologists measured the minimal axial diameter (MAD) of the largest RLN for each patient using a consensus process. A third radiologist measured MAD in 260 randomly selected patients to assess interobserver agreement. Initial ROC and restricted cubic spline (RCS) analyses were used to derive an optimal MAD threshold for predicting progression-free survival (PFS). The threshold's predictive utility was assessed in multivariable Cox regression analyses, controlling for standard clinical predictors. The threshold's utility for predicting PFS and overall survival (OS) was compared with a 5-mm threshold using Kaplan-Meier curves and log-rank tests. RESULTS. The intraclass correlation coefficient for MAD was 0.943. ROC and RCS analyses yielded an optimal threshold of 6 mm. In multivariable analyses, MAD of 6 mm and greater independently predicted PFS in all patients (HR = 1.35, p = .02), patients with N0 or N1 disease (HR = 1.80, p = .008), and patients who underwent posttreatment MRI (HR = 1.68, p = .04). In patients with N1 disease without cervical lymph node involvement, 5-year PFS was worse for MAD greater than or equal to 6 mm than for MAD that was greater than or equal to 5 mm but less than 6 mm (77.2% vs 89.7%, p = .03). OS was significantly different in patients with stage I and stage II disease defined using a 6-mm threshold (p = .04), but not using a 5-mm threshold (p = .09). The 5-year PFS rate was associated with a post-RT MAD of 6 mm and greater (HR = 1.68, p = .04) but not a post-RT MAD greater than or equal to 5 mm (HR = 1.09, p = .71). CONCLUSION. The findings support a threshold MAD of 6 mm for determining RLN involvement in patients with NPC. CLINICAL IMPACT. Future AJCC staging updates should consider incorporation of the 6-mm threshold for N-category and tumor-stage determinations.

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. MATERIALS AND METHODS: We retrospectively enrolled 1207 patients diagnosed with non-metastatic advanced NPC from two centres, and divided into training (N = 544), internal testing (N = 367), and external testing (N = 296) cohorts. Machine learning algorithms including multivariate analysis, deep learning, Lasso, and Rulefit were used to establish corresponding prognostic models. The concordance indices (C- indices) of three clinical and six combined models with different algorithms for overall survival (OS) prediction were compared. Survival benefits of induction chemotherapy (IC) were calculated among risk groups stratified by different models. A website was established for individualised survival visualisation. RESULTS: Incorporating structured variables into Stage model significantly improved the prognostic prediction performance. Six prognostic rules with structured variables were identified by Rulefit. OS prediction of Rules model was comparable to Lasso model in internal testing cohort (C-index: 0.720 vs. 0.713, P = 0.100) and achieved the highest C-index of 0.711 in external testing cohort, indicating better generalisability. The Rules model stratified patients into risk groups with significant 5-year OS differences in each cohort, and revealed significant survival benefits from additional IC in high-risk group. CONCLUSION: The Rulefit-based Rules model, with the revelation of intrinsic associations behind structured variables, is promising in risk stratification and guiding individualised IC treatment for advanced NPC.

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 l1 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 l1 norm shrinks each entry of the sparse tensor S with the same strength. It has been shown that larger singular values generally correspond to prominent information of the data and should be less penalized. The same goes for large entries in S in terms of absolute values. In this paper, we propose a Double Auto-weighted TRPCA (DATRPCA) method. s Instead of using predefined and manually set weights merely for the low-rank tensor as previous works, DATRPCA automatically and adaptively assigns smaller weights and applies lighter penalization to significant singular values of the low-rank tensor and large entries of the sparse tensor simultaneously. We have further developed an efficient algorithm to implement DATRPCA based on the Alternating Direction Method of Multipliers (ADMM) framework. In addition, we have also established the convergence analysis of the proposed algorithm. The results on both synthetic and real-world data demonstrate the effectiveness of DATRPCA for low-rank tensor recovery, color image recovery and background modelling.

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. To accomplish the control objective, innovative nonlinear controllers and the Lyapunov functions are designed. Furthermore, some criteria of FXTSYN for UCQVMNNs are given using inequality techniques and the novel FXTSYN theory. And the accurate settling time is obtained explicitly. Finally, in order to show that the obtained theoretical results are accurate, useful, and applicable, numerical simulations are presented at the conclusion.

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. To this end, we propose a multi-agent system based on an augmented Lagrangian function and prove that it converges to a locally optimal solution to an optimization problem in the presence of nonconvexity. In addition, a collaborative neurodynamic optimization method is adopted to obtain a globally optimal solution. Three numerical examples are elaborated to illustrate the effectiveness of the main results.

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. Each Clifford-valued RNN minimizes a local objective function individually, with local interactions with others. The convergence of the neural system is rigorously proved based on the Lyapunov theory. Two illustrative examples are delineated to demonstrate the viability of the results in this article.

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. This can handle over-fitting or under-fitting problems neglected in this kind of research for quaternion representation (QR) in color image processing. That is how to treat redundancy caused by the extra scalar part when the vector part of a quaternion is used to represent a color pixel. We apply QSVND to quaternion principal component analysis (QPCA) for color face recognition (FR), which can deal with the phenomenon of under-fitting of vector part norm approximation. Comparisons with the competing approaches on AR, FERET, FEI, and KDEF&AKDEF databases consistently show the superiority of the proposed approach for color FR.

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. Furthermore, the nuclear norm of the quaternion matrix is replaced by the sum of the Frobenius norm of its two low-rank factor quaternion matrices. Based on the relationship between the quaternion matrix and its equivalent complex matrix, the problem eventually is converted from the quaternion number domain to the complex number domain. An alternating minimization method is applied to solve the model. Simulation results on color image recovery show the superior performance and efficiency of the proposed algorithm over some tensor-based and quaternion-based ones.

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. Another critical issue is that their performance may be severely hampered due to the data noise or outliers in practice. To tackle the problems above, in this work we propose a robust quaternion valued sparse representation (RQVSR) method in a fully quaternion valued setting. To handle the quaternion noises, we first define a new robust estimator referred as quaternion Welsch estimator to measure the quaternion residual error. Compared to the conventional quaternion mean square error, it can largely suppress the impact of large data corruption and outliers. To implement RQVSR, we have overcome the difficulties raised by the noncommutativity of quaternion multiplication and developed an effective algorithm by leveraging the half-quadratic theory and the alternating direction method of multipliers framework. The experimental results show the effectiveness and robustness of the proposed method for quaternion sparse signal recovery and color image reconstruction.

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. Finally, two illustrative examples demonstrate the effectiveness of proposed methods.

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=i2=j2=k2=-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. Combining with the generalized ∞-norm and Cauchy convergence property in the quaternion field, some sufficient conditions to guarantee the stability are established without using any Lyapunov-Krasovskii functional and linear matrix inequality. Finally, a numerical example is given to demonstrate the effectiveness of the results.

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. To remedy this limitation, in this paper, we propose two novel RC methods for color FR, namely, quaternion CRC (QCRC) and quaternion SRC (QSRC) using quaternion ℓ1 minimization. By modeling each color image as a quaternionic signal, they naturally preserve the color structures of both query and gallery color images while uniformly coding the query channel images in a holistic manner. Despite the empirical success of CRC and SRC on FR, a few theoretical results are developed to guarantee their effectiveness. Another purpose of this paper is to establish the theoretical guarantee for QCRC and QSRC under mild conditions. Comparisons with competing methods on benchmark real-world databases consistently show the superiority of the proposed methods for both color FR and reconstruction.