Efficient Predefined-Time Adaptive Neural Networks for Computing Time-Varying Tensor Moore-Penrose Inverse.

This article proposes predefined-time adaptive neural network (PTANN) and event-triggered PTANN (ET-PTANN) models to efficiently compute the time-varying tensor Moore-Penrose (MP) inverse. The PTANN model incorporates a novel adaptive parameter and activation function, enabling it to achieve strongly predefined-time convergence. Unlike traditional time-varying parameters that increase over time, the adaptive parameter is proportional to the error norm, thereby better allocating computational resources and improving efficiency. To further enhance efficiency, the ET-PTANN model combines an event trigger with the evolution formula, resulting in the adjustment of step size and reduction of computation frequency compared to the PTANN model. By conducting mathematical derivations, the article derives the upper bound of convergence time for the proposed neural network models and determines the minimum execution interval for the event trigger. A simulation example demonstrates that the PTANN and ET-PTANN models outperform other related neural network models in terms of computational efficiency and convergence rate. Finally, the practicality of the PTANN and ET-PTANN models is demonstrated through their application for mobile sound source localization.

Predefined-Time Zeroing Neural Networks With Independent Prior Parameter for Solving Time-Varying Plural Lyapunov Tensor Equation.

As an extension of the Lyapunov equation, the time-varying plural Lyapunov tensor equation (TV-PLTE) can carry multidimensional data, which can be solved by zeroing neural network (ZNN) models effectively. However, existing ZNN models only focus on time-varying equations in field of real number. Besides, the upper bound of the settling time depends on the value of ZNN model parameters, which is a conservative estimation for existing ZNN models. Therefore, this article proposes a novel design formula for converting the upper bound of the settling time into an independent and directly modifiable prior parameter. On this basis, we design two new ZNN models called strong predefined-time convergence ZNN (SPTC-ZNN) and fast predefined (FP)-time convergence ZNN (FPTC-ZNN) models. The SPTC-ZNN model has a nonconservative upper bound of the settling time, and the FPTC-ZNN model has excellent convergence performance. The upper bound of the settling time and robustness of the SPTC-ZNN and FPTC-ZNN models are verified by theoretical analyses. Then, the effect of noise on the upper bound of settling time is discussed. The simulation results show that the SPTC-ZNN and FPTC-ZNN models have better comprehensive performance than existing ZNN models.

A TDF-WNSP-WLFM algorithm for product recommendation based on multiple types of implicit user behavior.

E-commerce platforms usually train their recommender system models to achieve personalized recommendations based on user behavior data. User behavior can be categorized into implicit and explicit feedback. Explicit feedback data have been well studied. However, the implicit feedback data still have many issues, such as the multiple types of behavior data, lack of negative feedback, and lack of the ability to express the real user preference. Targeting these problems of implicit feedback, we propose a TDF-WNSP-WLFM (time decay factor-weight of negative sample possibility-weighted latent factor model) based on the latent factor model for product recommendation. Our method mainly focuses on reconstructing the implicit rating matrix to enable the algorithm to perform better. The TDF-WNSP-WLFM algorithm is tested on two public user behavior datasets from Taobao and REES46, two big e-commerce platforms. Our algorithm compares favorably with other known collaborative filtering methods.

Novel Protein Sequence Comparison Method Based on Transition Probability Graph and Information Entropy.

AIM AND OBJECTIVE: Aim and Objective: Sequence analysis is one of the foundations in bioinformatics. It is widely used to find out the feature metrics hidden in the sequence. Otherwise, the graphical representation of the biologic sequence is an important tool for sequencing analysis. This study is undertaken to find out a new graphical representation of biosequences. MATERIALS AND METHODS: The transition probability is used to describe amino acid combinations of protein sequences. The combinations are composed of amino acids directly adjacent to each other or separated by multiple amino acids. The transition probability graph is built up by the transition probabilities of amino acid combinations. Next, a map is defined as a representation from the transition probability graph to transition probability vector by the k-order transition probability graph. Transition entropy vectors are developed by the transition probability vector and information entropy. Finally, the proposed method is applied to two separate applications, 499 HA genes of H1N1, and 95 coronaviruses. RESULTS: By constructing a phylogenetic tree, it was found that the results of each application are consistent with other studies. CONCLUSION: The graphical representation proposed in this article is a practical and correct method.

Recent Advances on Prediction of Human Papillomaviruses Risk Types.

BACKGROUND: Some studies have shown that Human Papillomavirus (HPV) is strongly associated with cervical cancer. As we all know, cervical cancer still remains the fourth most common cancer, affecting women worldwide. Thus, it is both challenging and essential to detect risk types of human papillomaviruses. METHODS: In order to discriminate whether HPV type is highly risky or not, many epidemiological and experimental methods have been proposed recently. For HPV risk type prediction, there also have been a few computational studies which are all based on Machine Learning (ML) techniques, but adopt different feature extraction methods. Therefore, we conclude and discuss several classical approaches which have got a better result for the risk type prediction of HPV. RESULTS: This review summarizes the common methods to detect human papillomavirus. The main methods are sequence- derived features, text-based classification, gap-kernel method, ensemble SVM, Word statistical model, position- specific statistical model and mismatch kernel method (SVM). Among these methods, position-specific statistical model get a relatively high accuracy rate (accuracy=97.18%). Word statistical model is also a novel approach, which extracted the information of HPV from the protein "sequence space" with word statistical model to predict high-risk types of HPVs (accuracy=95.59%). These methods could potentially be used to improve prediction of highrisk types of HPVs. CONCLUSION: From the prediction accuracy, we get that the classification results are more accurate by establishing mathematical models. Thus, adopting mathematical methods to predict risk type of HPV will be the main goal of research in the future.

Novel Method of 3-Dimensional Graphical Representation for Proteins and Its Application.

In this article, we propose a 3-dimensional graphical representation of protein sequences based on 10 physicochemical properties of 20 amino acids and the BLOSUM62 matrix. It contains evolutionary information and provides intuitive visualization. To further analyze the similarity of proteins, we extract a specific vector from the graphical representation curve. The vector is used to calculate the similarity distance between 2 protein sequences. To prove the effectiveness of our approach, we apply it to 3 real data sets. The results are consistent with the known evolution fact and show that our method is effective in phylogenetic analysis.

A protein mapping method based on physicochemical properties and dimension reduction.

BACKGROUND: The graphical mapping of a protein sequence is more difficult than the graphical mapping of a DNA sequence because of the twenty amino acids and their complicated physicochemical properties. However, the graphical mapping for protein sequences attracts many researchers to develop different mapping methods. Currently, researchers have proposed their mapping methods based on several physicochemical properties. In this article, a new mapping method for protein sequences is developed by considering additional physicochemical properties, which is a simple and effective approach. METHODS: Based on the 12 major physicochemical properties of amino acids and the PCA method, we propose a simple and intuitive 2D graphical mapping method for protein sequences. Next, we extract a 20D vector from the graphical mapping which is used to characterize a protein sequence. RESULTS: The proposed graphical mapping consists of three important properties, one-to-one, no circuit, and good visualization. This mapping contains more physicochemical information. Next, this proposed method is applied to two separate applications. The results illustrate the utility of the proposed method. DISCUSSION: To validate the proposed method, we first give a comparison of protein sequences, which consists of nine ND6 proteins. The similarity/dissimilarity matrix for the ssnine ND6 proteins correctly reveals their evolutionary relationship. Next, we give another application for the cluster analysis of HA genes of influenza A (H1N1) isolates. The results are consistent with the known evolution fact of the H1N1 virus. The separate applications further illustrate the utility of the proposed method.

Two-step camera calibration method based on the SPGD algorithm.

Given the rapid convergence characteristic of the stochastic parallel gradient descent (SPGD) algorithm, this study proposes a method that applies the algorithm to a two-step camera calibration method to resolve the frequent iteration and long calibration time deficiencies that exist under the traditional two-step camera calibration method, thereby achieving rapid calibration. The method first uses image coordinates obtained with subpixel positioning technology as initial values of control variables, in addition to positive disturbances produced on a two-dimensional plane, then uses two-step theory to calculate the average value of aberrations. Based on the same rationale, negative disturbances are then produced and the average value of the aberrations is calculated. Finally if, after assessing whether to continue with further iterations based on the difference in these values, continued iterations confirm new control variables based on the SPGD algorithm iteration formula, a new cycle is started until the results satisfy requirements. Theoretical analysis and experimental results show that the proposed rapid calibration method using the SPGD algorithm in the two-step camera calibration method is 3-4 times faster than the traditional two-step calibration method, and that it has significant potential value for use in certain time-constrained projects.

Gene comparison based on the repetition of single-nucleotide structure patterns.

According to the repetition structure patterns of single-nucleotides, we propose a novel digital representation method to characterize primary DNA sequences. Based on this representation we give a new RP-SP (repeat and space) vector to compute the distance of different sequences. The examination of similarities/dissimilarities among different sequences illustrates the utility of the proposed RP-SP vector distance. Then, we use the proposed RP-SP vector method to analyze two groups of genomes, 15 E. coli genomes and 31 mitochondrial genomes. For comparison, we also apply other alignment-free methods to the two groups of genomes. The results show that the proposed method can distinguish characteristics of different genomes and used to reconstruct the phylogenetic tree of different genomes.

Application of 2D graphic representation of protein sequence based on Huffman tree method.

Based on Huffman tree method, we propose a new 2D graphic representation of protein sequence. This representation can completely avoid loss of information in the transfer of data from a protein sequence to its graphic representation. The method consists of two parts. One is about the 0-1 codes of 20 amino acids by Huffman tree with amino acid frequency. The amino acid frequency is defined as the statistical number of an amino acid in the analyzed protein sequences. The other is about the 2D graphic representation of protein sequence based on the 0-1 codes. Then the applications of the method on ten ND5 genes and seven Escherichia coli strains are presented in detail. The results show that the proposed model may provide us with some new sights to understand the evolution patterns determined from protein sequences and complete genomes.

Using Huffman coding method to visualize and analyze DNA sequences.

On the basis of the Huffman coding method, we propose a new graphical representation of DNA sequence. The representation can avoid degeneracy and loss of information in the transfer of data from a DNA sequence to its graphical representation. Then a multicomponent vector from the representation is introduced to characterize quantitatively DNA sequences. The components of the vector are derived from the graphical representation of DNA primary sequence. The examination of similarities and dissimilarities among the complete coding sequences of ß-globin gene of 11 species and six ND6 proteins shows the utility of the scheme.

Self-similarity analysis of eubacteria genome based on weighted graph.

We introduce a weighted graph model to investigate the self-similarity characteristics of eubacteria genomes. The regular treating in similarity comparison about genome is to discover the evolution distance among different genomes. Few people focus their attention on the overall statistical characteristics of each gene compared with other genes in the same genome. In our model, each genome is attributed to a weighted graph, whose topology describes the similarity relationship among genes in the same genome. Based on the related weighted graph theory, we extract some quantified statistical variables from the topology, and give the distribution of some variables derived from the largest social structure in the topology. The 23 eubacteria recently studied by Sorimachi and Okayasu are markedly classified into two different groups by their double logarithmic point-plots describing the similarity relationship among genes of the largest social structure in genome. The results show that the proposed model may provide us with some new sights to understand the structures and evolution patterns determined from the complete genomes.

A combination dimensionality reduction approach to codon position patterns of eubacteria based on their complete genomes.

Graphical techniques have become powerful tools for the visualization and analysis of complicated biological systems. However, we cannot give such a graphical representation in a 2D/3D space when the dimensions of the represented data are more than three dimensions. The proposed method, a combination dimensionality reduction approach (CDR), consists of two parts: (i) principal component analysis (PCA) with a newly defined parameter ρ and (ii) locally linear embedding (LLE) with a proposed graphical selection for its optional parameter k. The CDR approach with ρ and k not only avoids loss of principal information, but also sufficiently well preserves the global high-dimensional structures in low-dimensional space such as 2D or 3D. The applications of the CDR on characteristic analysis at different codon positions in genome show that the method is a useful tool by which biologists could find useful biological knowledge.

New method for global alignment of 2 DNA sequences by the tree data structure.

We introduce a new approach to investigate problem of DNA sequence alignment. The method consists of three parts: (i) simple alignment algorithm, (ii) extension algorithm for largest common substring, (iii) graphical simple alignment tree (GSA tree). The approach firstly obtains a graphical representation of scores of DNA sequences by the scoring equation R(0)*R-S(0)*S-T(0)*(a+bk). Then a GSA tree is constructed to facilitate solving the problem for global alignment of 2 DNA sequences. Finally we give several practical examples to illustrate the utility and practicality of the approach.

Classification analysis of dual nucleotides using dimension reduction.

We introduce a new approach to investigate the dual nucleotides compositions of 11 Gram-positive and 12 Gram-negative eubacteria recently studied by Sorimachi and Okayasu. The approach firstly obtains a 16-dimension vector set of dual nucleotides by PN-curve from the complete genome of organism. Each vector of the set corresponds to a single gene of genome. Then we reduce the 16-dimension vector set to 2-dimension by principal components analysis (PCA). The reduction avoids possible loss of information averaging all 16-dimension vectors. Then we suggest a 2D graphical representation based on the 2-dimension vector to investigate the classification patters among different organisms.

Numerical characterization of DNA sequences based on digital signal method.

Based on digital signal method, we propose a new representation of DNA primary sequence. The representation can completely avoid loss of information in the transfer of data from a DNA sequence to its mathematical representation. Afterwards, we suggest one such approach to reach quantification of similarities based on digital signal similarity theory. The examination of similarities/dissimilarities among the coding sequences of the first exon of beta-globin gene of 11 species shows the utility of the scheme.

New 3D graphical representation of DNA sequence based on dual nucleotides.

We introduce a 3D graphical representation of DNA sequences based on the pairs of dual nucleotides (DNs). Based on this representation, we consider some mathematical invariants and construct two 16-component vectors associated with these invariants. The vectors are used to characterize and compare the complete coding sequence part of beta globin gene of nine different species. The examination of similarities/dissimilarities illustrates the utility of the approach.