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In this paper, we present a novel four-dimensional (4D) parameter estimation method to localize the mixed far-field (FF) and near-field (NF) targets using bistatic MIMO arrays and higher-order singular value decomposition (HOSVD). The estimated four parameters include the angle-of-departure (AOD), angle-of-arrival (AOA), range-of-departure (ROD), and range-of-arrival (ROA). In the method, we store array data in a tensor form to preserve the inherent multidimensional properties of the array data. First, the observation data are arranged into a third-order tensor and its covariance tensor is calculated. Then, the HOSVD of the covariance tensor is performed. From the left singular vector matrices of the corresponding module expansion of the covariance tensor, the subspaces with respect to transmit and receive arrays are obtained, respectively. The AOD and AOA of the mixed FF and NF targets are estimated with signal-subspace, and the ROD and ROA of the NF targets are achieved using noise-subspace. Finally, the estimated four parameters are matched via a pairing method. The Cramér–Rao lower bound (CRLB) of the mixed target parameters is also derived. The numerical simulations demonstrate the superiority of the tensor-based method.

Estimation of the number of components (or order) of a finite mixture model is a long standing and challenging problem in statistics. We propose the Group-Sort-Fuse (GSF) procedure—a new penalized likelihood approach for simultaneous estimation of the order and mixing measure in multidimensional finite mixture models. Unlike methods which fit and compare mixtures with varying orders using criteria involving model complexity, our approach directly penalizes a continuous function of the model parameters. More specifically, given a conservative upper bound on the order, the GSF groups and sorts mixture component parameters to fuse those which are redundant. For a wide range of finite mixture models, we show that the GSF is consistent in estimating the true mixture order and achieves the n−1/2 convergence rate for parameter estimation up to polylogarithmic factors. The GSF is implemented for several univariate and multivariate mixture models in the R package GroupSortFuse. Its finite sample performance is supported by a thorough simulation study, and its application is illustrated on two real data examples.

Frequency diverse array multiple-input multiple-output (FDA-MIMO) radar is an emerging technology to offer range-angle-dependent beampattern. Polarimetric FDA-MIMO radar can sense additional polarization information to improve target identification capability. In this article, we investigate the problem of joint range, angle and polarization parameter estimation in a monostatic polarimetric FDA-MIMO radar with an FDA at transmitter and a cross-dipole array at receiver. Unlike the conventional methods in which the multidimensional data structure is rearranged into vectors or matrices by stacking operation, we propose a Tucker tensor decomposition-based scheme, which can reserve the original data structure and avoid spoiling the inherent characteristics of interest, especially when the number of snapshots is small. The third-order tensor model of the observed data is constructed. Two approaches named as Tucker covariance reconstruction and Tucker signal subspace are presented using the fourth-order covariance tensor decomposition. The Cramér–Rao bound for range, angle and polarization estimation is also provided. Numerical experiments demonstrate the superiorities of the proposed approaches. Specifically, two targets with identical range and close angles are effectively distinguished.

Information reconciliation is a significant stage in continuous-variable quantum key distribution (CV-QKD) systems as it directly affects the performance of the CV-QKD systems including secret key rate and secure transmission distance. This paper proposes a multidimensional reconciliation scheme using deep learning in CV-QKD systems. Firstly, different neural networks are constructed to obtain the norm information. Secondly, a multidimensional reconciliation scheme with deep learning assisted norm information is proposed which no longer needs to transmit the norm information through the authenticated classical public channel. Finally, simulation results and performance analysis show that, compared with the traditional multidimensional reconciliation scheme, the multidimensional reconciliation scheme with deep learning assisted norm information can decrease the communication traffic to a certain extent.

A high tumor mutation burden (TMB) is known to drive the response to immune checkpoint inhibitors (ICI) and is associated with favorable prognoses. However, because it is a one-dimensional numerical representation of non-synonymous genetic alterations, TMB suffers from clinical challenges due to its equal quantification. Since not all mutations elicit the same antitumor rejection, the effect on immunity of neoantigens encoded by different types or locations of somatic mutations may vary. In addition, other typical genomic features, including complex structural variants, are not captured by the conventional TMB metric. Given the diversity of cancer subtypes and the complexity of treatment regimens, this paper proposes that tumor mutations capable of causing various degrees of immunogenicity should be calculated separately. TMB should therefore, be segmented into more exact, higher dimensional feature vectors to exhaustively measure the foreignness of tumors. We systematically reviewed patients’ multifaceted efficacy based on a refined TMB metric, investigated the association between multidimensional mutations and integrative immunotherapy outcomes, and developed a convergent categorical decision-making framework, TMBserval (Statistical Explainable machine learning with Regression-based VALidation). TMBserval integrates a multiple-instance learning concept with statistics to create a statistically interpretable model that addresses the broad interdependencies between multidimensional mutation burdens and decision endpoints. TMBserval is a pan-cancer-oriented many-to-many nonlinear regression model with discrimination and calibration power. Simulations and experimental analyses using data from 137 actual patients both demonstrated that our method could discriminate between patient groups in a high-dimensional feature space, thereby rationally expanding the beneficiary population of immunotherapy.

This paper proposes solutions to three issues pertaining to the estimation of finite mixture models with an unknown number of components: the non-identifiability induced by overfitting the number of components, the mixing limitations of standard Markov Chain Monte Carlo (MCMC) sampling techniques, and the related label switching problem. An overfitting approach is used to estimate the number of components in a finite mixture model via a Zmix algorithm. Zmix provides a bridge between multidimensional samplers and test based estimation methods, whereby priors are chosen to encourage extra groups to have weights approaching zero. MCMC sampling is made possible by the implementation of prior parallel tempering, an extension of parallel tempering. Zmix can accurately estimate the number of components, posterior parameter estimates and allocation probabilities given a sufficiently large sample size. The results will reflect uncertainty in the final model and will report the range of possible candidate models and their respective estimated probabilities from a single run. Label switching is resolved with a computationally light-weight method, Zswitch, developed for overfitted mixtures by exploiting the intuitiveness of allocation-based relabelling algorithms and the precision of label-invariant loss functions. Four simulation studies are included to illustrate Zmix and Zswitch, as well as three case studies from the literature. All methods are available as part of the R package Zmix, which can currently be applied to univariate Gaussian mixture models.

Multidimensional item response theory (MIRT) models have generated increasing interest in the psychometrics literature. Efficient approaches for estimating MIRT models with dichotomous responses have been developed, but constructing an equally efficient and robust algorithm for polytomous models has received limited attention. To address this gap, this paper presents a novel Gaussian variational estimation algorithm for the multidimensional generalized partial credit model. The proposed algorithm demonstrates both fast and accurate performance, as illustrated through a series of simulation studies and two real data analyses.

Due to the intricate chaotic environments encountered in distributed sensor applications, such as sea monitoring, machinery fault diagnosis, and EEG weak signal detection, neural networks often face insufficient data to effectively carry out detection tasks. In contrast to traditional machine learning models, a statistical approach employing multidimensional nonlinear correlation (MNC) exhibits an unparalleled signal pattern prediction capability and possesses a streamlined yet robust framework for signal processing. However, the direct application of MNC to weak pulse signal detection remains constrained. To surmount these challenges and achieve high‐precision signal detection, we explore a novel MNC approach, integrating phase reconstruction and manifold broad learning, specifically tailored for distributed sensor fusion detection amidst chaotic noise. Initially, the distributed observational data undergoes phase space reconstruction, transforming it into fixed‐size arrays. These reconstructed tuples are then processed through the high‐dimensional sequence of manifold broad learning, serving as inputs for the nonlinear correlation module to extract spatiotemporal features. Subsequently, a MNC system augmented with a QRS detector layer is devised to predict and classify the presence of a weak pulse signal. This integrated MNC approach, combining phase reconstruction and broad learning, operates within an enhanced feature space of the source domain, realizing detection fusion across distributed sensors through a majority voting principle. Simulation studies and experiments conducted on sea clutter datasets demonstrate the efficacy and robustness of the proposed MNC method, leveraging phase reconstruction and manifold broad learning strategies, for distributed sensor weak pulse signal fusion detection within chaotic backgrounds.

Refrigeration systems are complex, non-linear, multi-modal, and multi-dimensional. However, traditional methods are based on a trial and error process to optimize these systems, and a global optimum operating point cannot be guaranteed. Therefore, this work aims to study a two-stage vapor compression refrigeration system (VCRS) through a novel and robust hybrid multi-objective grey wolf optimizer (HMOGWO) algorithm. The system is modeled using response surface methods (RSM) to investigate the impacts of design variables on the set responses. Firstly, the interaction between the system components and their cycle behavior is analyzed by building four surrogate models using RSM. The model fit statistics indicate that they are statistically significant and agree with the design data. Three conflicting scenarios in bi-objective optimization are built focusing on the overall system following the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) decision-making methods. The optimal solutions indicate that for the first to third scenarios, the exergetic efficiency (EE) and capital expenditure (CAPEX) are optimized by 33.4% and 7.5%, and the EE and operational expenditure (OPEX) are improved by 27.4% and 19.0%. The EE and global warming potential (GWP) are also optimized by 27.2% and 19.1%, where the proposed HMOGWO outperforms the MOGWO and NSGA-II. Finally, the K-means clustering technique is applied for Pareto characterization. Based on the research outcomes, the combined RSM and HMOGWO techniques have proved an excellent solution to simulate and optimize two-stage VCRS.

The quaternion windowed linear canonical transform is a tool for processing multidimensional data and enhancing the quality and efficiency of signal and image processing; however, it has disadvantages due to the noncommutativity of quaternion multiplication. In contrast, reduced biquaternions, as a special case of four-dimensional algebra, possess unique advantages in computation because they satisfy the multiplicative exchange rule. This paper proposes the reduced biquaternion windowed linear canonical transform (RBWLCT) by combining the reduced biquaternion signal and the windowed linear canonical transform that has computational efficiency thanks to the commutative property. Firstly, we introduce the concept of a RBWLCT, which can extract the time local features of an image and has the advantages of both time-frequency analysis and feature extraction; moreover, we also provide some fundamental properties. Secondly, we propose convolution and correlation operations for RBWLCT along with their corresponding generalized convolution, correlation, and product theorems. Thirdly, we present a fast algorithm for RBWLCT and analyze its computational complexity based on two dimensional Fourier transform (2D FTs). Finally, simulations and examples are provided to demonstrate that the proposed transform effectively captures the local RBWLCT-frequency components with enhanced degrees of freedom and exhibits significant concentrations.