Numerical Matrices Research Articles

Pattern recognition in data as a diagnosis tool

Medical data often appear in the form of numerical matrices or sequences. We develop mathematical tools for automatic screening of such data in two medical contexts: diagnosis of systemic lupus erythematosus (SLE) patients and identification of cardiac abnormalities. The idea is first to implement adequate data normalizations and then identify suitable hyperparameters and distances to classify relevant patterns. To this purpose, we discuss the applicability of Plackett-Luce models for rankings to hyperparameter and distance selection. Our tests suggest that, while Hamming distances seem to be well adapted to the study of patterns in matrices representing data from laboratory tests, dynamic time warping distances provide robust tools for the study of cardiac signals. The techniques developed here may set a basis for automatic screening of medical information based on pattern comparison.

Bidirectional Long Short-Term Memory Network for Taxonomic Classification

Identifying and classifying Deoxyribonucleic Acid (DNA) sequences and their functions have been considered as the main challenges in bioinformatics. Advances in machine learning and Deep Learning (DL) techniques are expected to improve DNA sequence classification. Since the DNA sequence classification depends on analyzing textual data, Bidirectional Long Short-Term Memory (BLSTM) algorithms are suitable for tackling this task. Generally, classifiers depend on the patterns to be processed and the pre-processing method. This paper is concerned with a new proposed classification framework based on Frequency Chaos Game Representation (FCGR) followed by Discrete Wavelet Transform (DWT) and BLSTM. Firstly, DNA strings are transformed into numerical matrices by FCGR. Then, the DWT is used instead of the pooling layer as a tool of data compression. The benefit of using the DWT is two-fold. It preserves the useful information only that enables the following BLSTM training, effectively. Besides, DWT adds more important details to the encoded sequences due to finding effective features in the DNA fragments. Finally, the BLSTM model is trained to classify the DNA sequences. Evaluation metrics such as F1 score and accuracy show that the proposed framework outperforms the state-of-the-art algorithms. Hence, it can be used in DNA classification applications.

Triangular Regions Representations for Matching Images With Viewpoint Changes

This paper proposes triangular region representations based on keypoints detected in images with viewpoint changes. The strongest keypoints in the reference and query images are allocated individually using a previously published contourlet-based approach to determine the keypoints. These selected keypoints serve as vertices of the triangular regions to be transformed into rectangular representations as simple numeric matrices. The suggested representation methods used to form rectangular matrices are full triangle representation (FTR) and a lighter representation called triangle medians and sides representation (TMSR). For the former, the intensity values along the lines connecting the anchor keypoint to the points between the other two triangular vertices form the rows of the representation matrix. These two triangle vertices are located in an allotted window around the anchor keypoint from the nearby keypoints. For the latter, the intensity values on the six triangular lines, medians, and sides formed the resulting rectangular matrix. The proposed representations are validated for image-matching applications using a descriptor-less matching method. Moreover, the performances of these algorithms are compared with those of traditional algorithms. The results confirmed the superiority of the proposed method over these algorithms.

Solution of a Linear Nondegenerate Matrix Equation Based on the Zero Divisor

New formulas were obtained to solve the linear non-degenerate matrix equations based on zero divisors of numerical matrices. Two theorems were formulated, and a proof to one of them is provided. It is noted that the proof of the second theorem is similar to the proof of the first one. The proved theorem substantiates new formula in solving the equation equivalent in the sense of the solution uniqueness to the known formulas. Its fundamental difference lies in the following: any explicit matrix inversion or determinant calculation is missing; solution is "based" not on the left, but on the right side of the matrix equation; zero divisor method is used (it was never used in classical formulas for solving a matrix equation); zero divisor calculation is reduced to simple operations of permutating the vector elements on the right-hand side of the matrix equation. Examples are provided of applying the proposed method for solving a nondegenerate matrix equation to the numerical matrix equations. High accuracy of the proposed formulas for solving the matrix equations is demonstrated in comparison with standard solvers used in the MATLAB environment. Similar problems arise in the synthesis of fast and ultrafast iterative solvers of linear matrix equations, as well as in nonparametric identification of abnormal (emergency) modes in complex technical systems, for example, in the power systems

KerNet: A Novel Deep Learning Approach for Keratoconus and Sub-Clinical Keratoconus Detection Based on Raw Data of the Pentacam HR System

Keratoconus is one of the most severe corneal diseases, which is difficult to detect at the early stage (i.e., sub-clinical keratoconus) and possibly results in vision loss. In this paper, we propose a novel end-to-end deep learning approach, called KerNet, which processes the raw data of the Pentacam HR system (consisting of five numerical matrices) to detect keratoconus and sub-clinical keratoconus. Specifically, we propose a novel convolutional neural network, called KerNet, containing five branches as the backbone with a multi-level fusion architecture. The five branches receive five matrices separately and capture effectively the features of different matrices by several cascaded residual blocks. The multi-level fusion architecture (i.e., low-level fusion and high-level fusion) moderately takes into account the correlation among five slices and fuses the extracted features for better prediction. Experimental results show that: (1) our novel approach outperforms state-of-the-art methods on an in-house dataset, by ~1% for keratoconus detection accuracy and ~4 for sub-clinical keratoconus detection accuracy; (2) the attention maps visualized by Grad-CAM show that our KerNet places more attention on the inferior temporal part for sub-clinical keratoconus, which has been proved as the identifying regions for ophthalmologists to detect sub-clinical keratoconus in previous clinical studies. To our best knowledge, we are the first to propose an end-to-end deep learning approach utilizing raw data obtained by the Pentacam HR system for keratoconus and subclinical keratoconus detection. Further, the prediction performance and the clinical significance of our KerNet are well evaluated and proved by two clinical experts. Our code is available at https://github.com/upzheng/Keratoconus.

Novel technique of development of human derived acellular dermal matrix.

Reconstructive surgery techniques have evolved exponentially in last decades. From regional flaps to free tissue transfer, tissue movilization has become the gold standart treatment in many reconstructive procedures. Main disadvantage from these techniques lies in the possibility of sequels in donor zone. Furthermore, raising comorbidities in general population and growing indications for reconstructive surgery in elder people, have triggered the development of new biomaterials which can offer support in the reconstruction while elicit donor zone morbidity. Advances in tissue decellularization techniques have brought numerous matrices which have shown effectivity in many reconstructive procedures. Use of acellular dermal matrices may become an eligible solution for many reconstructive procedures. From breast reconstruction assisted by matrices to complex wound coverage passing throught tendon repair techniques, acellular dermal matrices have shown effectiveness in last studies. Local production of this biomaterial leads to cost minimization derived from harvesting and manufacturing matrices in our centre and avoid out-of-stock and storage issues. Current original protocol proposed by our group include all steps from harvesting samples from cadaveric donors till matrix storage after decellularization proccess. The result is a high valued biomaterial in terms of biocompatibility and security profile available.

BERT-m7G: A Transformer Architecture Based on BERT and Stacking Ensemble to Identify RNA N7-Methylguanosine Sites from Sequence Information

As one of the most prevalent posttranscriptional modifications of RNA, N7-methylguanosine (m7G) plays an essential role in the regulation of gene expression. Accurate identification of m7G sites in the transcriptome is invaluable for better revealing their potential functional mechanisms. Although high-throughput experimental methods can locate m7G sites precisely, they are overpriced and time-consuming. Hence, it is imperative to design an efficient computational method that can accurately identify the m7G sites. In this study, we propose a novel method via incorporating BERT-based multilingual model in bioinformatics to represent the information of RNA sequences. Firstly, we treat RNA sequences as natural sentences and then employ bidirectional encoder representations from transformers (BERT) model to transform them into fixed-length numerical matrices. Secondly, a feature selection scheme based on the elastic net method is constructed to eliminate redundant features and retain important features. Finally, the selected feature subset is input into a stacking ensemble classifier to predict m7G sites, and the hyperparameters of the classifier are tuned with tree-structured Parzen estimator (TPE) approach. By 10-fold cross-validation, the performance of BERT-m7G is measured with an ACC of 95.48% and an MCC of 0.9100. The experimental results indicate that the proposed method significantly outperforms state-of-the-art prediction methods in the identification of m7G modifications.

Abel inversion method using Chebyshev wavelets for tomographic reconstruction of an axisymmetric medium.

We describe an Abel inversion method for tomographic reconstruction of an axisymmetric medium. The essence of this method is the approximation of data by Chebyshev wavelets. A numerical method and operational matrices are proposed. The accuracy of the method is tested in terms of the noise coefficient. The studied method is compared with the Legendre wavelets method. The results show that the proposed method is less sensitive to noise. We also demonstrate the efficiency of the developed method by obtaining good and expected results for the inversion of interferometric data.

Multi-Output Learning Based on Multimodal GCN and Co-Attention for Image Aesthetics and Emotion Analysis

With the development of social networks and intelligent terminals, it is becoming more convenient to share and acquire images. The massive growth of the number of social images makes people have higher demands for automatic image processing, especially in the aesthetic and emotional perspective. Both aesthetics assessment and emotion recognition require a higher ability for the computer to simulate high-level visual perception understanding, which belongs to the field of image processing and pattern recognition. However, existing methods often ignore the prior knowledge of images and intrinsic relationships between aesthetic and emotional perspectives. Recently, machine learning and deep learning have become powerful methods for researchers to solve mathematical problems in computing, such as image processing and pattern recognition. Both images and abstract concepts can be converted into numerical matrices and then establish the mapping relations using mathematics on computers. In this work, we propose an end-to-end multi-output deep learning model based on multimodal Graph Convolutional Network (GCN) and co-attention for aesthetic and emotion conjoint analysis. In our model, a stacked multimodal GCN network is proposed to encode the features under the guidance of the correlation matrix, and a co-attention module is designed to help the aesthetics and emotion feature representation learn from each other interactively. Experimental results indicate that our proposed model achieves competitive performance on the IAE dataset. Progressive results on the AVA and ArtPhoto datasets also prove the generalization ability of our model.

A Bayesian Model to Forecast the Time Series Kinetic Energy Data for a Power System

Withthe massive penetration of electronic power converter (EPC)-based technologies, numerous issues are being noticed in the modern power system that may directly affect system dynamics and operational security. The estimation of system performance parameters is especially important for transmission system operators (TSOs) in order to operate a power system securely. This paper presents a Bayesian model to forecast short-term kinetic energy time series data for a power system, which can thus help TSOs to operate a respective power system securely. A Markov chain Monte Carlo (MCMC) method used as a No-U-Turn sampler and Stan’s limited-memory Broyden–Fletcher–Goldfarb–Shanno (LM-BFGS) algorithm is used as the optimization method here. The concept of decomposable time series modeling is adopted to analyze the seasonal characteristics of datasets, and numerous performance measurement matrices are used for model validation. Besides, an autoregressive integrated moving average (ARIMA) model is used to compare the results of the presented model. At last, the optimal size of the training dataset is identified, which is required to forecast the 30-min values of the kinetic energy with a low error. In this study, one-year univariate data (1-min resolution) for the integrated Nordic power system (INPS) are used to forecast the kinetic energy for sequences of 30 min (i.e., short-term sequences). Performance evaluation metrics such as the root-mean-square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and mean absolute scaled error (MASE) of the proposed model are calculated here to be 4.67, 3.865, 0.048, and 8.15, respectively. In addition, the performance matrices can be improved by up to 3.28, 2.67, 0.034, and 5.62, respectively, by increasing MCMC sampling. Similarly, 180.5 h of historic data is sufficient to forecast short-term results for the case study here with an accuracy of 1.54504 for the RMSE.

Functional Properties of a Purified Reconstituted Bilayer Matrix Design Support Natural Wound Healing Activities.

Background:Biomaterial engineering has produced numerous matrices for use in tissue repair, utilizing various materials and processing methods, which can impact the ability of the products to encourage wound healing. Recently, we observed favorable clinical outcomes, using a novel purified reconstituted bilayer matrix (PRBM; Geistlich Derma-Gide) to treat chronic diabetic foot ulcers.Methods:Evaluations of the structural and functional characteristics of PRBM in vitro were performed to assess how this biomaterial may affect the favorable clinical results observed by influencing the wound environment and key physiologic mechanisms necessary for the healing process. Investigations included scanning electron microscopy, cell culture analyses, gene expression assays, matrix metalloproteinase activity assessment, and pH measurement.Results:Cross-sectional scanning electron microscopy demonstrated a distinct bilayer structure with porous and compact layers. The PRBM structure allowed cell types involved in wound healing to bind and proliferate. Expression analysis of growth factor-responsive genes demonstrated binding and preservation of bioactive growth factors TGF-β1, bFGF, and VEGF by PRBM. Boyden chamber migration assays revealed increased cellular migration compared with controls. In the presence of PRBM, the activity of MMP-1, MMP-2, and MMP-9 was significantly lower compared with control samples. pH of the PRBM in solution was slightly acidic.Conclusions:Based on in vitro evaluations, it appears that the PRBM processing without deleterious chemical crosslinking results in a suitable ECM possessing characteristics to aid natural wound healing, including cell attachment, migration, proliferation, differentiation, and angiogenesis. These in vitro data support the promising healing rate observed clinically when chronic DFUs are treated with PRBM.

Numerical Study of Stochastic Leontief-Type Model with Impulses

ABSTRACT In this article, a stochastic Leontief model with impulses has been studied, which is represented by a system of stochastic differential-algebraic equations, in both sides of the rectangular constant numerical matrices that form a singular pencil. The system has been considered in terms of the current velocity of the solution, which is a direct analog of the physical velocity of deterministic processes. The proposed approach in this work does not impose restrictions on the size and the form of the matrices included in the Leontief-type system. The Kroenke-Weierstrass transformation of the pencil was conducted by the coefficient matrices to the canonical form has been used to simplify the study of equations. This study also involves two methods: Firstly, using a stochastic differential equation, this was followed by using the so-called mean derivatives of Nelson random processes to describe the solutions of this equation. The distinguishing feature of the work proposed an approach based on the convergence of the theoretical results to the exact one. The findings show that explicit formulas for solutions and solvability conditions are obtained, and for a subsystem resolved with respect to the symmetric derivative. The theorem of existence of solutions for the system under consideration has been proved under certain conditions on the coefficients of the system. Conducting computational experiments on the model confirming the effectiveness of the proposed approach. Error, maximum and minimum of the singular values of matrices.

Oriented by Characteristic Roots Reduced Matrices in the Class of Semiscalarly Equivalent

A set of polynomial 3 × 3 -matrices of simple structure has been singled out, for which a so-called oriented by certain characteristic roots reduced matrix is established in the class of semiscalarly equivalent. The invariants of such reduced matrices and the conditions of their semiscalar equivalence are indicated. The obtained results will also be applied to the problem of similarity of sets of numerical matrices.

DESCRIPTION OF ALGORITHMS FOR BALANCING NUMERICAL MATRICES AND THEIR DIVISION INTO HIERARCHICAL LEVELS ACCORDING TO THEIR TYPE AND COMPLEXITY

This article describes a set of algorithms for so-called balancing of numerical matrices, which were developed by the author. Each section consists of several algorithms that are divided into different levels. The order of these levels depended on the chronology of the creation of certain algorithms. Chronology also affected the complexity of these balancing algorithms, so it can be argued that the algorithms are described in order from the simplest level to the most complex. It is important to emphasize that the purpose of the article is to describe the actions on matrices that determine the balancing algorithm of a certain level, and practical application will be the next step.

The prediction of vehicle vibration transmitted to the occupant using a modular transfer matrix

Industry is moving towards more data-oriented design and analyses to solve complex analytical problems. Solving complex and large finite element models is still challenging and requires high computational time and resources. Here, a modular method is presented to predict the transmission of vehicle body vibration to the occupants’ body by combining the numerical transfer matrices of the subsystems. The transfer matrices of the subsystems are presented in the form of data which is sourced from either physical tests or finite element models. The structural dynamics of the vehicle body is represented using a transfer matrix at each of the seat mounting points in three triaxial (X–Y–Z) orientations. The proposed method provides an accurate estimation of the transmission of the vehicle body vibration to the seat frame and the seated occupant. This method allows the combination of conventional finite element analytical model data and the experimental data of subsystems to accurately predict the dynamic performance of the complex structure. The numerical transfer matrices can also be the subject of machine learning for various applications such as for the prediction of the vibration discomfort of the occupant with different seat and foam designs and with different physical characteristics of the occupant body.

Encryption and Decryption of Images using GGH Algorithm: Proposed

Images are considered as important data used in many fields such as military operations, medical imaging, and astronomy researches. For sending images through an insecure network, it is necessary to develop a secure encryption algorithm when transmitting the images. Three main properties of security services (i.e., confidentiality, integrity, and availability), the confidentiality is the most essential feature for exchanging images. The Goldreich Goldwasser Halevi (GGH) algorithm can be a good method for encrypting images as both the algorithm and sensitive data are represented in numeric matrices. Additionally, the GGH algorithm does not increase the size of the image. However, one of the disadvantages of using the GGH algorithm is the attacking of GGH cryptosystem mainly relied on special properties of the lattice generated. This shortcoming of GGH algorithm has been taken to proposed lattice reduction algorithms. A lattice basis reduction algorithm to get a better basis which is used into encryption and decryption approach.

A transformer architecture based on BERT and 2D convolutional neural network to identify DNA enhancers from sequence information.

Recently, language representation models have drawn a lot of attention in the natural language processing field due to their remarkable results. Among them, bidirectional encoder representations from transformers (BERT) has proven to be a simple, yet powerful language model that achieved novel state-of-the-art performance. BERT adopted the concept of contextualized word embedding to capture the semantics and context of the words in which they appeared. In this study, we present a novel technique by incorporating BERT-based multilingual model in bioinformatics to represent the information of DNA sequences. We treated DNA sequences as natural sentences and then used BERT models to transform them into fixed-length numerical matrices. As a case study, we applied our method to DNA enhancer prediction, which is a well-known and challenging problem in this field. We then observed that our BERT-based features improved more than 5-10% in terms of sensitivity, specificity, accuracy and Matthews correlation coefficient compared to the current state-of-the-art features in bioinformatics. Moreover, advanced experiments show that deep learning (as represented by 2D convolutional neural networks; CNN) holds potential in learning BERT features better than other traditional machine learning techniques. In conclusion, we suggest that BERT and 2D CNNs could open a new avenue in biological modeling using sequence information.

Legacy and Emerging Per- and Polyfluoroalkyl Substances: Analytical Techniques, Environmental Fate, and Health Effects

Due to their unique chemical properties, per- and polyfluoroalkyl substances (PFAS) have been used extensively as industrial surfactants and processing aids. While several types of PFAS have been voluntarily phased out by their manufacturers, these chemicals continue to be of ecological and public health concern due to their persistence in the environment and their presence in living organisms. Moreover, while the compounds referred to as “legacy” PFAS remain in the environment, alternative compounds have emerged as replacements for their legacy predecessors and are now detected in numerous matrices. In this review, we discuss the historical uses of PFAS, recent advances in analytical techniques for analysis of these compounds, and the fate of PFAS in the environment. In addition, we evaluate current biomonitoring studies of human exposure to legacy and emerging PFAS and examine the associations of PFAS exposure with human health impacts, including cancer- and non-cancer-related outcomes. Special focus is given to short-chain perfluoroalkyl acids (PFAAs) and ether-substituted, polyfluoroalkyl alternatives including hexafluoropropylene oxide dimer acid (HFPO-DA; tradename GenX), 4,8-dioxa-3H-perfluorononanoic acid (DONA), and 6:2 chlorinated polyfluoroethersulfonic acid (6:2 Cl-PFESA; tradename F-53B).

Multiply accumulate operations in memristor crossbar arrays for analog computing

Memristors are now becoming a prominent candidate to serve as the building blocks of non-von Neumann in-memory computing architectures. By mapping analog numerical matrices into memristor crossbar arrays, efficient multiply accumulate operations can be performed in a massively parallel fashion using the physics mechanisms of Ohm’s law and Kirchhoff’s law. In this brief review, we present the recent progress in two niche applications: neural network accelerators and numerical computing units, mainly focusing on the advances in hardware demonstrations. The former one is regarded as soft computing since it can tolerant some degree of the device and array imperfections. The acceleration of multiple layer perceptrons, convolutional neural networks, generative adversarial networks, and long short-term memory neural networks are described. The latter one is hard computing because the solving of numerical problems requires high-precision devices. Several breakthroughs in memristive equation solvers with improved computation accuracies are highlighted. Besides, other nonvolatile devices with the capability of analog computing are also briefly introduced. Finally, we conclude the review with discussions on the challenges and opportunities for future research toward realizing memristive analog computing machines.

STANDARDIZATION, QUALITY CONTROL AND ANTIMICROBIAL STUDY OF ARKA TAILA: AN AYURVEDA FORMULATION

Herbal medicines have a huge therapeutic history for a long period of time and still serving many more health requirements in the worldwide. Although there is a still very huge challenge in its quality control and quality assurance; because of the high variability of chemical compounds present in it. Herbal drugs, singularly and in combinations, contain numerous complex matrices in which not a single active constituent is responsible for the overall efficacy. This creates a challenge in establishing quality control standards and standardization of finished herbal drugs. Many drugs in Ayurveda describe regarding treatment of vicharchika (Atopic dermatitis). Arka taila is one of them. In this study Arka taila was subjected to study organoleptic analysis, phytochemical analysis, and qualitative analysis to detect the presence of various functional groups, and thin layer chromatography (TLC) examination by optimizing the solvent systems. The investigation revealed the density, Refractive index, Saponification value, Rancidity, Total fatty matter and Iodine value mainly and also subjected to in vitro antibacterial assay against human pathogens MTCC No.39-Klebsiella aerogenes, MTCC No.10239- Escherichia coli, MTCC No.1034- Pseudomonas aeruginosa, MTCC No.6908- Staphylococcus aureus by Mueller hinton agar well diffusion method. The results of this study suggest that Arka taila can be used as an antibacterial agent against infections caused by Klebsiella aerogenes, Escherichia coli, Staphylococcus aureus.