Multiple Matrices Research Articles

A design of fuzzy sliding mode control for Markovian jumping system with different input matrices

In this paper, by means of sliding mode control (SMC), the problem resulted by local input matrices is investigated for fuzzy markovian jumping system. The stability of the considered fuzzy Markovian system with multiple sub-input matrices can be fulfilled using the method in this paper. First, the state equation of the considered system is transformed according to the input matrices. Second, according to the state equation, sliding mode surface is constructed. This surface contains several sub-surfaces. It can deal with this kind of fuzzy Markovian system with multiple sub-input matrices and uncertainties. And another characteristic is that there is not the process of reaching the sliding mode surface; It can settle the problem resulted by Markovian jumping and sliding mode method together. Third, by use of the Cramer's rule, a criterion is provided to judge the existence of sliding mode dynamics equation. A controller containing several sub-controllers components is designed. And these sub-controllers should keep the considered system on the several sub-surfaces and not leave it. At last, simulations are provided to illustrate the validity of the method in this paper.

Robust Multi-View Clustering Through Partition Integration on Stiefel Manifold

Multi-view clustering aims at integrating information from different views to improve clustering performance. Recent methods integrate multiple view-specific partition matrices to seek a consensus one and have demonstrated promising clustering performance in various applications. However, the clustering performance of such methods heavily relies on the consensus partition matrix estimated by the arithmetic mean in Euclidean space and thus is highly susceptible to noise corruption. To this end, this paper proposes to learn a consensus partition matrix through the geometric mean on the manifold to achieve robust clustering. Specifically, the multiple view-specific partition matrices can be regarded as points residing in the Stiefel manifold and enable a manifold-based integration. Consequently, the view-specific partition matrices are integrated by estimating a consensus partition matrix as the center point on the Stiefel manifold. Such a partition integration boils down to the Fréchet mean problem on a manifold, which is solved by the intrinsic manifold-based optimization and proves effective in providing a more robust estimation against noise. Experimental results on seven benchmark datasets demonstrate the effectiveness and noise-robustness of our proposed method in comparison to eight competitive methods.

Joint Network Topology Inference via Structural Fusion Regularization

Joint network topology inference represents a canonical problem of jointly learning multiple graph Laplacian matrices from heterogeneous graph signals. In such a problem, a widely employed assumption is that of a simple common component shared among multiple graphs. However, in practice, a more intricate topological pattern, comprising simultaneously of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">homogeneous</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">heterogeneous</i> components, would exhibit in multiple graphs. In this paper, we propose a general graph estimator based on a novel structural fusion regularization that enables us to jointly learn multiple graphs with such complex topological patterns, and enjoys rigorous theoretical guarantees. Specifically, in the proposed regularization term, the structural similarity among graphs is characterized by a Gram matrix, which enables us to flexibly model different types of network structural similarities through different Gram matrix choices. Algorithmically, the regularization term, coupling the parameters together, makes the formulated optimization problem intractable, and thus, we develop an implementable algorithm based on the alternating direction method of multipliers (ADMM) to solve it. Theoretically, non-asymptotic statistical analysis is provided, which precisely characterizes the minimum sample size required for the consistency of the graph estimator. This analysis also provides high-probability bounds on the estimation error as a function of graph structural similarities and other key problem parameters. Finally, the superior performance of the proposed method is demonstrated through simulated and real data examples.

C2IMUFS: Complementary and Consensus Learning-Based Incomplete Multi-View Unsupervised Feature Selection

Multi-view unsupervised feature selection (MUFS) has been demonstrated as an effective technique to reduce the dimensionality of multi-view unlabeled data. The existing methods assume that all of views are complete. However, multi-view data are usually incomplete, i.e., a part of instances are presented on some views but not all views. Besides, learning the complete similarity graph, as an important promising technology in existing MUFS methods, cannot achieve due to the missing views. In this paper, we propose a complementary and consensus learning-based incomplete multi-view unsupervised feature selection method (C <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula> IMUFS) to address the aforementioned issues. Concretely, C <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula> IMUFS integrates feature selection into an extended weighted non-negative matrix factorization model equipped with adaptive learning of view-weights and a sparse <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{2,p}$</tex-math></inline-formula> -norm, which can offer better adaptability and flexibility. By the sparse linear combinations of multiple similarity matrices derived from different views, a complementary learning-guided similarity matrix reconstruction model is presented to obtain the complete similarity graph in each view. Furthermore, C <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula> IMUFS learns a consensus clustering indicator matrix across different views and embeds it into a spectral graph term to preserve the local geometric structure. Comprehensive experimental results on real-world datasets demonstrate the effectiveness of C <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula> IMUFS compared with state-of-the-art methods.

Slepian Transform Based Detectors for HF Skywave Massive MIMO-OFDM Systems

In this paper, we investigate signal detection for high frequency (HF) skywave massive multiple-input multiple-output (MIMO) systems with orthogonal frequency division multiplexing (OFDM) modulation. We first introduce the beam based channel model for HF skywave massive MIMO-OFDM channels and show the relationship of sparse supports between the beam domain channel and the Fourier spectrum of the space domain channel. Based on the sparse beam domain channel, we propose a separate Slepian transform (SST) based detector, where a set of modulated Slepian sequences are designed independently for user terminals (UTs). Before the minimum mean-squared error (MMSE) detection, the Slepian transform is performed for each UT to reduce the dimension of the observation vector and the channel matrix, thus avoiding high dimensional matrices multiplications and inversions. Due to the sparsity of the beam domain channel, the Slepian transform of channel vectors can be efficiently implemented by low-dimensional matrix-vector multiplications. To further reduce the computational complexity, we propose a joint Slepian transform (JST) based detector, where a fixed set of modulated Slepian sequences are designed. As a result, Slepian transforms of the observation vector can be efficiently implemented using low-dimensional fast Fourier transform (FFT). Simulation results demonstrate the advantages of high performance and low complexity of proposed detectors.

A broad-based probe-free qPCR assay for detection and discrimination of three human herpes viruses

Primary infection or reactivation of latent human cytomegalovirus (HCMV) or herpes simplex viruses (HSV) 1 or 2 during pregnancy can transmit the virus in utero or during natural childbirth to the fetus. The majority of these infections are asymptomatic at birth but may present later with potentially lethal disseminated infection or meningitis (HSV), or long-term neurodevelopmental sequelae including sensorineural hearing loss or neurodevelopmental impairments (HCMV). Unfortunately, early signs and symptoms of disseminated viral infections may be misdiagnosed as bacterial sepsis. Therefore, immediate testing for viral etiologies may not be ordered or even considered by skilled clinicians. In asymptomatic HCMV infections, early detection is necessary to monitor for and treat future neurologic sequelae. In acutely ill-appearing infants, specific detection of viruses against other disease-causing agents is vital to inform correct patient management, including early administration of the correct antimicrobial(s). An ideal test should be rapid, inexpensive, require low sample volumes, and demonstrate efficacy in multiple tissue matrices to aid in timely clinical decision-making for neonatal infections. This work discusses the development of a rapid probe-free qPCR assay for HSV and HCMV that enables early and specific detection of these viruses in neonates. The assay’s probe free chemistry would allow easier extension to a broad-based multiplexed pathogenic panel as compared to assays utilizing sequence-specific probes or nested PCR.

Joint time domain nonlinear post-distortion scheme for reconstruction of distorted signals

Reconstruction of distorted signals (RODS), initially proposed in the frequency domain (FD), has been proved to be with high efficiency in depressing the distortion caused by the nonlinear power amplifier (PA). However, multiple high-dimensional transformation matrices are needed to reconstruct the FD distortion matrix, so high complexity is required. In this paper, we propose a new unified time domain (TD) nonlinear post-distortion scheme based on RODS, where a joint distortion matrix containing both PA and multipath channel coefficients is presented. When carrying out the least square inverse operation, the nonlinearity as well as channel fading effect can be eliminated simultaneously. By adjusting the elements in the distortion matrix according to the characteristics of PA and multipath channels, the proposed TD-RODS can also be suitable for flat fading with memoryless or memory nonlinear PAs. Further, the equivalence between the TD- and FD-RODS is presented, and then computer simulations are adopted to verify our analysis. In the proposed TD-RODS, the nonlinear distortion matrix is constructed more straightforward in a more cost-efficiency way, thus the overall computations is effectively reduced.

A Novel Complex-Valued Blind Source Separation and Its Applications in Integrated Reception

The separation of time–frequency mixing signals composed of radar, communication, and jamming is the first step in integrated reception processing, which requires higher accuracy for complex blind source separation (CVBSS). However, traditional CVBSS methods have limitations such as low separation accuracy, a slow convergence speed, and poor robustness in low signal-to-noise ratio (SNR) and high jamming-to-signal ratio (JSR) scenarios. To address the above issues, this paper firstly establishes a time delay mixing mathematical model. A robust whitening algorithm is proposed by using the time delay correlation matrix of the observed signal, which is insensitive to noise. Secondly, the joint diagonalized F-parametrization is used as the objective function, and the separation matrix is constructed based on the multiple complex-valued Givens matrices. The complex-valued Givens matrix not only ensures orthogonality in the separation matrix but also effectively reduces the number of parameters to be calculated. This approach guarantees accuracy and simplifies the complexity of the separation process. Finally, the nonlinear chaotic grey wolf optimizer is utilized to search for the optimal rotation angle. The simulation results demonstrate that this algorithm offers higher separation accuracy and requires fewer iterations compared to the traditional algorithm. Additionally, it enhances the accuracy of direction of arrival (DOA) estimation, reduces the communication bit error rate, and enables the joint estimation of the target distance and velocity even in the presence of powerful jamming and a low SNR.

Cache Optimization and Performance Modeling of Batched, Small, and Rectangular Matrix Multiplication on Intel, AMD, and Fujitsu Processors

Factorization and multiplication of dense matrices and tensors are critical, yet extremely expensive pieces of the scientific toolbox. Careful use of low rank approximation can drastically reduce the computation and memory requirements of these operations. In addition to a lower arithmetic complexity, such methods can, by their structure, be designed to efficiently exploit modern hardware architectures. The majority of existing work relies on batched BLAS libraries to handle the computation of many small dense matrices. We show that through careful analysis of the cache utilization, register accumulation using SIMD registers and a redesign of the implementation, one can achieve significantly higher throughput for these types of batched low-rank matrices across a large range of block and batch sizes. We test our algorithm on three CPUs using diverse ISAs – the Fujitsu A64FX using ARM SVE, the Intel Xeon 6148 using AVX-512, and AMD EPYC 7502 using AVX-2, and show that our new batching methodology is able to obtain more than twice the throughput of vendor optimized libraries for all CPU architectures and problem sizes.

Microplastics in the Lung Tissues Associated with Blood Test Index.

Microplastics (MPs) have received a lot of attention and have been detected in multiple environmental matrices as a new environmental hazard, but studies on human internal exposure to MPs are limited. Here, we collected lung tissue samples from 12 nonsmoking patients to evaluate the characteristics of MPs in human lung tissues using an Agilent 8700 laser infrared imaging spectrometer and scanning electron microscopy. We detected 108 MPs covering 12 types in the lung tissue samples, with a median concentration of 2.19 particles/g. Most of the MPs (88.89%) were sized between 20 to 100 μm. Polypropylene accounts for 34.26% of the MPs in the lung tissues, followed by polyethylene terephthalate (21.30%) and polystyrene (8.33%). Compared with males and those living far from a major road (≥300 m), females and those living near the main road (<300 m) had higher levels of MPs in lung tissues, which positively correlated with platelet (PLT), thrombocytocrit, fibrinogen (FIB), and negatively related with direct bilirubin (DB). These findings help confirm the presence in the respiratory system and suggest the potential sources and health effects of inhaled MPs.

Enhanced DOA Estimation With Co-Prime Array in the Scenario of Impulsive Noise: A Pseudo Snapshot Augmentation Perspective

Co-prime array configuration is popular in the recent development of array signal processing by exploiting the sparse arrangement of arrays and the co-prime feature of the number of subarray elements. However, the assumption of Gaussian noise in most co-prime array processing research might lead to model mismatch in practical scenarios of impulsive noise, and therefore have an adverse impact on the estimation of direction of arrival (DOA). Moreover, co-prime array builds an enlarged virtual array by vectorizing the covariance matrix of the received signals, where the equivalent received signals of the virtual array have only a single snapshot. In this paper, we propose an enhanced fractional low-order method (EFLOM) for co-prime array configuration in scenarios of impulsive noise, from the perspective of pseudo snapshot increment. Since impulsive noise does not have finite second-order statistics or high-order cumulant, we construct a series of equivalent covariance matrices by using phased fractional low-order moments with different orders of the received signals. Then, the vectorization of multiple equivalent covariance matrices can be formed as the equivalent received signals of the virtual array with multiple snapshots. Since the reformed observations of the equivalent received signals are from the same sources, additional spatial smoothing preprocessing operations are still needed for decorrelation. While in this paper, we propose an improved spatial smoothing (ISS) technique by applying the information of both autocorrelation and cross subarray correlation of the covariance matrix. Afterwards, the classical multiple signal classification (MUSIC) is applied for the estimation of DOAs. The performance of the proposed method is theoretically verified and simulations are also provided to show its effectiveness in terms of the generalized signal to noise ratio (GSNR), parameter of impulsive noise, and angle separation.

A Diversified Attention Model for Interpretable Multiple Clusterings

Multiple clusterings can explore the same set of data from different perspectives by discovering different and meaningful clusterings. However, most, if not all, of the existing approaches overwhelmingly focus on the diversity between clustering subspaces, and pay much less attention on the salience of the subspaces. As a consequence, the quality of the produced clusterings is an understudied aspect of the problem. Furthermore, existing methods cannot explain the unique internal subspace structure of each clustering, and cannot incorporate multi-facet knowledge to generate different clusterings. In this paper, we propose a solution named <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">iMClusts</b> ( <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</u> nterpretable <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</u> ultiple <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Clust</u> ering <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</u> by diversified attention). iMClusts makes use of the expressive representational power of deep autoencoders and multi-head attention to generate multiple salient embedding matrices, and multiple clusterings therein. In addition, it leverages multi-facet knowledge and enhances the diversity between heads to boost the quality and diversity of multiple clusterings. Experimental results on benchmark datasets show that iMClusts can generate multiple clusterings with quality, interpretability, and diversity.

Dirac: A command-line γ-matrix calculator

A software for simplification of Dirac matrix polynomials that arise in particle physics problems is implemented. Program summaryProgram Title: DiracCPC Library link to program files:https://doi.org/10.17632/s5w3zyhy58.1Developer's repository link:https://github.com/skutnii/diracLicensing provisions: MITProgramming language: C++20Nature of problem: Particle physics computations require simplification of Dirac matrix polynomials. Non-commutativity and tensorial nature of Dirac matrices makes the task nontrivial. Complexity of the expressions grows quickly with the number of factors making manual computations beyond a few simplest cases unfeasible and highly error-prone. Existing software solutions are either proprietary and highly expensive or have poor if any support for Dirac matrix algebra.Solution method: The problem is solved by considering a representation of Dirac matrix algebra with 5×5pseudo-matrices - matrices made of the algebra's structure constants. In this representation, multiplication of the original matrices corresponds to multiplication of pseudo-matrices and Lorentz index contraction. The problem then gets reduced to simplification of polynomials in Minkowski metric, Kronecker, and Levi-Civita symbols.Additional comments including restrictions and unusual features: The input and output have ▪-like syntax with single-expression command line input and interactive shell modes. Scripting can be used for batched input processing and advanced ▪ formatting of the results. Example scripts demonstrate this feature and provide automated correctness tests. The software supports both rational and floating-point arithmetic.

Synchronization and control for directly coupled reaction–diffusion neural networks with multiweights and hybrid coupling

This paper mainly deals with the synchronization and pinning control for multiweighted, directly, and hybridly coupled reaction–diffusion neural networks (MDHCRDNNs). Different communication channels are expressed by multiple coupling matrices, while hybrid coupling means that state information combined with spatial diffusion information are employed jointly to attain synchronization. In comparison to previously published literature on multiweighted networks, outer matrices (OMs) in our paper can be directly coupled, with negative elements, and not even connected. One novel synchronization strategy is proposed to address directed networks with multiweights by integrating state matrices and spatial matrices into new union matrices. Then, for MDHCRDNNs, we obtain if the weighted groups of added OMs for each dimension are strongly connected, then synchronization and pinning synchronization criteria are derived. Furthermore, synchronization for adaptive coupling strength is solved as well. Finally, the effectiveness of these obtained results is verified through simulation examples.

Epilithic biofilms as a discriminating matrix for long-term and growing season pesticide contamination in the aquatic environment: Emphasis on glyphosate and metabolite AMPA

The indiscriminate use of pesticides represents high ecological risk in aquatic systems. Recently, the inclusion of epilithic biofilms as a reactive matrix has shown potential in diagnosing the health of water resources. The objective of this study was to use multiple matrices (water, suspended sediments, and biofilms) to discriminate contamination degrees in catchments with long and recent history of intensive pesticide use and to monitor growing season pesticides transfer to watercourses. Two catchments were monitored: one representative of “modern agriculture” in a subtropical environment, and another representative of recent agricultural expansion over the Pampa Biome in subtropical Brazil. Glyphosate and AMPA were accumulated in the biofilms and were detected at all sites and at all monitoring times, in concentrations ranging from 195 to 7673 μg kg−1 and from 225 to 4180 μg kg−1, respectively. Similarly, the fungicide tebuconazole has always been found in biofilms. The biofilms made it possible to discriminate the long-term history of pesticide use in the catchments and even to identify the influx pulses of pesticides immediately after their application to crops, which was not possible with active water sampling and even with suspended sediment monitoring. It is strongly recommended that, in regions with intensive cultivation of soybeans and other genetically modified crops, the presence of glyphosate and its metabolite AMPA be permanently monitored, a practice still very scarce in the literature.

Determination of furosemide and its glucuronide metabolite in plasma, plasma ultrafiltrate and urine by HPLC-MS/MS with application to secretion and metabolite formation clearances in non-pregnant and pregnant women

Furosemide (FUR) has been used in probe drugs cocktails for in vivo evaluation of the renal transporters OAT1 and OAT3 activities in studies of drug-drug interactions (generally using probenecid as an inhibitor) and drug-disease interactions. The objective of this study was to develop and validate methods for FUR and its glucuronide metabolite (FUR-GLU) analysis in plasma, plasma ultrafiltrate and urine for application in pharmacokinetics studies: a pilot drug-drug interaction study in pregnant women (n = 2), who received a single oral dose of FUR (40 mg) and in another occasion a single oral dose of probenecid (750 mg) before a single oral dose of FUR (40 mg), and in non-pregnant women participants (n = 12), who only received a single oral dose of FUR (40 mg). The samples preparation for FUR in 50 µL of plasma and plasma lysate were carried by acidified liquid-liquid extraction, while 50 µL of urine and 200 µL of plasma ultrafiltrate were simply diluted with the mobile phase. The methods presented linearities in the range of 0.50 – 2500 ng/mL of plasma and plasma lysate, 0.125 – 250 ng/mL of plasma ultrafiltrate, and 50 – 20,000 ng/mL of urine. FUR-GLU methods presented linearities in the range of 0.125 – 250 ng/mL of plasma ultrafiltrate and 50 – 20,000 ng/mL of urine. Precision and accuracy evaluations showed coefficients of variation and relative errors < 15%. In the pregnant women participants, the mean values of FUR CLrenal, CLsecretion, CLformation. FUR-GLU and CLnon-renal were all reduced when probenecid was administered with FUR (8.24 vs 2.89 L/h, 8.15 vs 2.80 L/h, 3.86 vs 1.75 L/h, 48.26 vs 22.10 L/h, respectively). Non-pregnant women presented similar values of FUR CLrenal, CLsecretion, CLformation. FUR-GLU to the pregnant women who received FUR only. Finally, FUR fraction unbound (fu) resulted in values of approximately 1% in pregnant women and to 0.22% in non-pregnant women. These developed and validated methods for FUR and FUR-GLU quantification in multiple matrices can allow the further investigation of UGT1A9/1A1 and the fu when FUR is administered as an OAT 1 and 3 in vivo probe.

Total variation regularized multi-matrices weighted Schatten p-norm minimization for image denoising

Motivated by the superior performance of nonconvex nonsmooth Lp (0<p<1) norm, this paper introduces a novel method that combines the weighted Schatten p-norm, Lp-norm, and total variation regularization based on the multiple matrices denoising framework. The weighted Schatten p-norm encodes the global low-rank to multiple matrices data, while the Lp-norm provides noise robustness. Total variation regularization is incorporated to promote structural smoothness and edge preservation in the image. To solve the nonconvex and nonsmooth model, an efficient alternating direction method of multipliers (ADMM) is designed. In addition, we discuss how the value of p in the three items affects the denoising performance in simulated images. Extensive experiments on face datasets, videos, and real-world noisy images demonstrate that the proposed method significantly improves denoising performance, particularly for removing large sparse noise.

Synthesis of conch-like layered carbon nanosheets by ball-milling assisted ultrasonic exfoliation for highly selective removal of Cd(II) from multiple water matrices

Development of carbonaceous materials from biomass have attracted tremendous research interest because of their intriguing physicochemical properties and promising applications. However, endowing them with precisely controlled morphologies remains a formidable challenge. Herein, oxygen-functionalized biomass-derived carbon-nanosheets (CNSs) framework was synthesized using ball-milling ultrasonic exfoliation for their application to remove cadmium Cd(II) from water matrices. The obtained CNSs showed remarkably higher surface area (368.9 m2/g), thickness-range (∼6–8 nm) and pore size (10.58 nm) than pristine carbon (PC) (10.126 m2/g, 1–2 µm and 2.13 nm, respectively). CNSs demonstrated higher adsorption capacity (545.76 mg g−1), superior reusability (removal efficiency maintained >91 % after 10 cycles) and excellent selectivity (Kd = 4.7 × 106 mL g−1). The adsorption isotherm and kinetics data were better fitted by Langmuir and pseudo-second order models. High adsorption selectivity of CNSs led to 97.7 % Cd(II) adsorption in presence of Cu(II), Zn(II), Pb(II) and Ni(II) ions. The strong efficiency of CNSs was also evident in complex water matrices including tap water, groundwater (Cd(II) removal of >99 %) and river water (98.97 %). The experimental analyses indicate that electrostatic attraction and surface complexation as the prominent adsorption mechanisms. Overall, this work illustrates an applicable strategy to develop carbon-nanosheets and their successful application to remove toxic metals from water matrices.

Local laws for multiplication of random matrices

Local laws for multiplication of random matrices

Optimizing consistency and consensus in group decision making based on relative projection between multiplicative reciprocal matrices

Optimizing consistency and consensus in group decision making based on relative projection between multiplicative reciprocal matrices