GPU libraries speed performance analysis for RCWA simulation matrix operations

Rigorous Coupled Wave Analysis (RCWA) method is highly efficient for the simulation of diffraction efficiency and field distribution patterns in periodic structures and textured optoelectronic devices. GPU has been increasingly used in complex scientific problems such as climate simulation and the latest Covid-19 spread model. In this paper, we break down the RCWA simulation problem to key computational steps (eigensystem solution, matrix inversion/multiplication) and investigate speed performance provided by optimized linear algebra GPU libraries in comparison to multithreaded Intel MKL CPU library running on IRIDIS 5 supercomputer (1 NVIDIA v100 GPU and 40 Intel Xeon Gold 6138 cores CPU). Our work shows that GPU outperforms CPU significantly for all required steps. Eigensystem solution becomes 60% faster, Matrix inversion improves with size achieving 8x faster for large matrixes. Most significantly, matrix multiplication becomes 40x faster for small and 5x faster for large matrix sizes. © 2023 SPIE.

Automated Detection of Covid-19 from X-ray Using SVM

Earlier discovery of COVID-19 through precise diagnosis, particularly in instances with no evident symptoms, may reduce the mortality rate of patients. Chest X-ray images are the primary diagnostic tool for this condition. Patients exhibiting COVID-19 symptoms are causing hospitals to become overcrowded, which is becoming a big concern. The contribution that machine learning has made to big data medical research has been very helpful, opening up new ways to diagnose diseases. This study has developed a machine vision method to identify COVID-19 using X-ray images. The preprocessing stage has been applied to resize images and enhance the quality of X-ray images. The Gray-level co-occurrence matrix (GLCM) and Gray-Level Run Length Matrix (GLRLM) are then used to extract features from the X-ray images, and these features are combined to develop the performance classification via training by Support Vector Machine (SVM). The testing phase evaluated the model's performance using generalized data. This developed feature combination utilizing the GLCM and GLRLM algorithms assured a satisfactory evaluation performance based on COVID-19 detection compared to the immediate, single feature with a testing accuracy of 96.65%, a specificity of 99.54%, and a sensitivity of 97.98%. © 2022 IEEE.

Micromodel and Analysis of COVID-19 Based on Hypergraph

In view of the fact that the existing propagation models ignore the influence of different fields and different virus variants on individual infection, and the classical propagation models only describe the macroscopic situation of virus transmission, which cannot be specific to individual cases, this paper proposes 67ya microscopic virus propagation model based on hypergraph (HC-SIRS). Firstly, the concept of hypergraph is used to divide different fields of individuals into corresponding hyperedges. Based on different contact probabilities of each hyperedge, the contact probability matrix is formed to relate the contact between individuals. The individual infection probability of micro-virus propagation model based on hypergraph is deduced, and the corresponding differential equation is established. Secondly, the basic regeneration number and its characteristics of the model are derived. The upper bound of the basic regeneration number of the model is less than or equal to that of the classical SIRS model, indicating that the virus is more difficult to spread in this model. In fact, the different fields people live in and the different personal constitutions have a certain impact on the spread of the virus. The model is more comprehensive, so it is more suitable for simulating the spread of the virus in theory. Finally, the COVID-19 data of Diamond Princess and two cities in China are used for simulation experiments, and the mean absolute error(MAE) is used as the evaluation standard. The results showed that HC-SIRS could well simulate the spread of COVID-19. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

A Predictive Model of COVID-19 mRNA Vaccine Reactivity based on Dual Attention for Federated Learning Scenarios

The base reactivity of the mRNA sequence has a significant impact on the effectiveness of the mRNA vaccine in fighting against the pandemic of COVID-19. The annotation of mRNA sequence reactivity value is a time-consuming and labor-intensive work, which belongs to the private digital assets of each medical institution. It is not practical to train a predictive model by pooling private data from various parties. Fortunately, federated learning techniques can serve to collaboratively train a predictive model among medical institutions while preserving respective digital assets. However, due to the scarcity of data from each participant, conventional sequential prediction mod-els often fail to perform well. To overcome such a challenge, we propose a reactivity value prediction model based on both the self-attention and the convolutional attention mechanisms only requiring a small dataset of labeled samples. Inspired by BERT, we first train a self-attention feature extraction model through self-supervision using both labeled and unlabeled mRNA samples. In this way, the information of mRNA in the semantic space is deeply mined. Then, a convolutional attention block follows the self-attention block, to extract the attention matrix from the base-pair probability matrix and adjacency matrix. By doing so, the attention matrix can compensate for the insensitivity of the self-attention mechanism to the spatial information of mRNA. By using the Open Vaccine RNA database, experiments show that our prediction model for unseen mRNA has a better performance than other state-of-the-art deep learning models that are used to process gene sequences. Further ablation experiments demonstrate that the existence of the dual attention mechanism reduces the risk of overfitting, resulting in an excellent generalization capability of our model. © 2022 IEEE.

The Security Algorithm ES-BR22-001 Used to Secure the Health Data

The data age information is considerably more significant in open life, since individuals' well-being information just concluded regardless of whether COVID-19 impacted, and furthermore connected with all medical problems information. These information used to examine and anticipate the medical problems information by Machine Learning Algorithm, and afterward anticipated information need greater security. In this way, we applied the current strategy ChaCha technique and that strategy zeroed in as it were "encryption execution” so security is less. In this paper, to apply the new ES-BR22-001 strategy, this technique has 7 stages. The 1st stage is finding the K value. The 2nd stage is applying the K value in Eq. (1). The 3rd stage is finding the Sk values by using Eq. (1). The 4th stage is applying the Sk values in the sparse matrix. The 5th stage is sparse matrix values are converted into single line. The 6th stage is pairing all the values. The final stage is all paired values will be applied in the matrix. The new ES-BR22-001 method provides security and performance is good while compared to ChaCha method. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

A Matrix Factorization-Based Drug-Virus Link Prediction Method for SARS-CoV-2 Drug Prioritization

Matrix factorization (MF) has been widely used in drug discovery for link prediction, which aims to reveal new drug-target links by integrating drug-drug and target-target similarity information with a drug-target interaction matrix. The MF method is based on the assumption that similar drugs share similar targets and vice versa. However, one major disadvantage is that only one similarity metric is used in MF models, which is not enough to represent the similarity between drugs or targets. In this work, we develop a similarity fusion enhanced MF model to incorporate different types of similarity for novel drug-target link prediction. We apply the proposed model on a drug-virus association dataset for anti-COVID drug prioritization, and compare the performance with other existing MF models developed for COVID. The results show that the similarity fusion method can provide more useful information for drug-drug and virus-virus similarity and hence improve the performance of MF models. The top 10 drugs as prioritized by our model are provided, together with supporting evidence from literature. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

A Static Machine Learning Based Evaluation Method for Usability and Security Analysis in E-Commerce website

Measurement of e-commerce usability based on static quantities variable is state-of-the-art because of the adoption of sequential tracing of the next phase in the categorical data. An offline static model is trained. A static model is trained offline. In other words, we train the model once and then use it for a set period of time. The global COVID-19 outbreak has completely disrupted society and drastically altered daily life. The concept refers to an electronic commerce network that appears with thorough, understandable conviction, demand, and rapid confirmation as a replacement for the economic market’s "brick-and-mortar" model, which replaces how we do everything, including business strategy, and provides a better understanding with the interpretation of e-commerce features. This study was supervised to analyses usability assessments using statistical methods, as well as security assessments using online e-commerce security scanner tools, in order to investigate e-business standards that take into account the caliber of e-services in e-commerce websites across Asian nations. The method was developed to optimize complex systems based on multiple criteria. The initial (supplied) weights are used to determine the compromise ranking list and compromise solution. This paper examines the usability of e-commerce in rural areas using a new data set from the Jharkhand region. On the e-commerce websites of Jharkhand, India, usability is commonly considered in conjunction with learnability, memorability, effectiveness, engagement, efficiency, and completeness. Using a user-oriented questionnaire testing method, this survey attempts to close the gaps mentioned above. Then, across each column, divide each value by the column-wise sum that is created using their corresponding value, whichever produces a new matrix B. Finally, determine the row-wise sum of matrix B that represents the (3 X 1) matrix. Using model trees and bagging, this study addresses classification-related issues. This regression technique is useful for problems involving classification. The model is trained using secondary data from the MBTI 16 personality factors affecting personality category. Author

Informative Initialization and Kernel Selection Improves t-SNE for Biological Sequences

The t-distributed stochastic neighbor embedding (t-SNE) is a method for interpreting high dimensional (HD) data by mapping each point to a low dimensional (LD) space (usually two-dimensional). It seeks to retain the structure of the data. An important component of the t-SNE algorithm is the initialization procedure, which begins with the random initialization of an LD vector. Points in this initial vector are then updated to minimize the loss function (the KL divergence) iteratively using gradient descent. This leads comparable points to attract one another while pushing dissimilar points apart. We believe that, by default, these algorithms should employ some form of informative initialization. Another essential component of the t-SNE is using a kernel matrix, a similarity matrix comprising the pairwise distances among the sequences. For t-SNE-based visualization, the Gaussian kernel is employed by default in the literature. However, we show that kernel selection can also play a crucial role in the performance of t-SNE.In this work, we assess the performance of t-SNE with various alternative initialization methods and kernels, using four different sets, out of which three are biological sequences (nucleotide, protein, etc.) datasets obtained from various sources, such as the well-known GISAID database for sequences of the SARS-CoV-2 virus. We perform subjective and objective assessments of these alternatives. We use the resulting t-SNE plots and k-ary neighborhood agreement (k-ANA) to evaluate and compare the proposed methods with the baselines. We show that by using different techniques, such as informed initialization and kernel matrix selection, that t-SNE performs significantly better. Moreover, we show that t-SNE also takes fewer iterations to converge faster with more intelligent initialization. © 2022 IEEE.

The Security Algorithm BR22-01 Used to Secure the COVID'19 Health Data

The current generation data is most valuable in people's life, because data only decided people's health affected in COVID'19 or not, and not only COVID'19 all related to health issues data. To analyze and predict the health issue data by using Machine Learning Algorithm. This prediction issues data has most confidential data and need more security. So, applying the previous method is ChaCha method. This method focusing only performance not fully security. The new method is BR22-01. This method has five stages. The 1st stage is finding the secret key x & y value. The 2nd stage is applying key in Eq. (1). The 3rd stage is merge all values into single row then pair from left and swap the values in the HS matrix. The 4th stage is applying key in Eq. (2). The 5th stage is merge all values into single line then pair from left and swap the values in the HC matrix but reverse. The new method has provide good security as well as performance while compared to ChaCha method. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Extracting Self-Reported COVID-19 Symptom Tweets and Twitter Movement Mobility Origin/Destination Matrices to Inform Disease Models

The emergence of the novel coronavirus (COVID-19) generated a need to quickly and accurately assemble up-to-date information related to its spread. In this research article, we propose two methods in which Twitter is useful when modelling the spread of COVID-19: (1) machine learning algorithms trained in English, Spanish, German, Portuguese and Italian are used to identify symptomatic individuals derived from Twitter. Using the geo-location attached to each tweet, we map users to a geographic location to produce a time-series of potential symptomatic individuals. We calibrate an extended SEIRD epidemiological model with combinations of low-latency data feeds, including the symptomatic tweets, with death data and infer the parameters of the model. We then evaluate the usefulness of the data feeds when making predictions of daily deaths in 50 US States, 16 Latin American countries, 2 European countries and 7 NHS (National Health Service) regions in the UK. We show that using symptomatic tweets can result in a 6% and 17% increase in mean squared error accuracy, on average, when predicting COVID-19 deaths in US States and the rest of the world, respectively, compared to using solely death data. (2) Origin/destination (O/D) matrices, for movements between seven NHS regions, are constructed by determining when a user has tweeted twice in a 24 h period in two different locations. We show that increasing and decreasing a social connectivity parameter within an SIR model affects the rate of spread of a disease. © 2023 by the authors.

Mathematical modeling of vaccination as a control measure of stress to fight COVID-19 infections

The world experienced the life-threatening COVID-19 disease worldwide since its inversion. The whole world experienced difficult moments during the COVID-19 period, whereby most individual lives were affected by the disease socially and economically. The disease caused millions of illnesses and hundreds of thousands of deaths worldwide. To fight and control the COVID-19 disease intensity, mathematical modeling was an essential tool used to determine the potentiality and seriousness of the disease. Due to the effects of the COVID-19 disease, scientists observed that vaccination was the main option to fight against the disease for the betterment of human lives and the world economy. Unvaccinated individuals are more stressed with the disease, hence their body's immune system are affected by the disease. In this study, the SVEIHR deterministic model of COVID-19 with six compartments was proposed and analyzed. Analytically, the next-generation matrix method was used to determine the basic reproduction number (R0). Detailed stability analysis of the no-disease equilibrium (E0) of the proposed model to observe the dynamics of the system was carried out and the results showed that E0 is stable if R0<1 and unstable when R0>1. The Bayesian Markov Chain Monte Carlo (MCMC) method for the parameter identifiability was discussed. Moreover, the sensitivity analysis of R0 showed that vaccination was an essential method to control the disease. With the presence of a vaccine in our SVEIHR model, the results showed that R0=0.208, which means COVID-19 is fading out of the community and hence minimizes the transmission. Moreover, in the absence of a vaccine in our model, R0=1.7214, which means the disease is in the community and spread very fast. The numerical simulations demonstrated the importance of the proposed model because the numerical results agree with the sensitivity results of the system. The numerical simulations also focused on preventing the disease to spread in the community. © 2022 The Authors

Multi-label Emotion Classification of COVID-19 Tweets with Deep Learning and Topic Modelling

The COVID-19 pandemic has become one of the severe diseases in recent years. As it majorly affects the common livelihood of people across the universe, it is essential for administrators and healthcare professionals to be aware of the views of the community so as to monitor the severity of the spread of the outbreak. The public opinions are been shared enormously in microblogging media like twitter and is considered as one of the popular sources to collect public opinions in any topic like politics, sports, entertainment etc., This work presents a combination of Intensity Based Emotion Classification Convolution Neural Network (IBEC-CNN) model and Non-negative Matrix Factorization (NMF) for detecting and analyzing the different topics discussed in the COVID-19 tweets as well the intensity of the emotional content of those tweets. The topics were identified using NMF and the emotions are classified using pretrained IBEC-CNN, based on predefined intensity scores. The research aimed at identifying the emotions in the Indian tweets related to COVID-19 and producing a list of topics discussed by the users during the COVID-19 pandemic. Using the Twitter Application Programming Interface (Twitter API), huge numbers of COVID-19 tweets are retrieved during January and July 2020. The extracted tweets are analyzed for emotions fear, joy, sadness and trust with proposed Intensity Based Emotion Classification Convolution Neural Network (IBEC-CNN) model which is pretrained. The classified tweets are given an intensity score varies from 1 to 3, with 1 being low intensity for the emotion, 2 being the moderate and 3 being the high intensity. To identify the topics in the tweets and the themes of those topics, Non-negative Matrix Factorization (NMF) has been employed. Analysis of emotions of COVID-19 tweets has identified, that the count of positive tweets is more than that of count of negative tweets during the period considered and the negative tweets related to COVID-19 is less than 5%. Also, more than 75% negative tweets expressed sadness, fear are of low intensity. A qualitative analysis has also been conducted and the topics detected are grouped into themes such as economic impacts, case reports, treatments, entertainment and vaccination. The results of analysis show that the issues related to the pandemic are expressed different emotions in twitter which helps in interpreting the public insights during the pandemic and these results are beneficial for planning the dissemination of factual health statistics to build the trust of the people. The performance comparison shows that the proposed IBEC-CNN model outperforms the conventional models and achieved 83.71% accuracy. The % of COVID-19 tweets that discussed the different topics vary from 7.45% to 26.43% on topics economy, Statistics on cases, Government/Politics, Entertainment, Lockdown, Treatments and Virtual Events. The least number of tweets discussed on politics/government on the other hand the tweets discussed most about treatments. © 2023 CRL Publishing. All rights reserved.

Improved Gentry–Halevi's fully homomorphic encryption-based lightweight privacy preserving scheme for securing medical Internet of Things

Internet of Medical Things (IoMT) solutions have proliferated rapidly in the COVID-19 pandemic era. The smart medical sensors capture real-time data from remote patients and communicate it to medical servers in a secure and privacy-preserving manner. It is a herculean challenge to guarantee security and privacy in Medical IoT applications. Hence, an improved Gentry–Halevi's fully homomorphic encryption-based (IGHFHE) lightweight privacy preserving user authentication scheme is proposed in this work. The scheme is proposed with an integer matrix computation strategy for securing data computation with privacy protection. It adopts the translation process of Gentry–Halevi's fully homomorphic encryption process for performing homomorphic addition and multiplication, then encrypt an integer matrix modulo that represents a positive integer. Extensive informal investigation and simulation of the proposed IGHFHE scheme shows that it is more resistant to well-known attacks for preventing authentication breaches. Also, the proposed IGHFHE scheme reduced computational and storage overhead by 4.98% and 5.78% respectively on average in comparison to other prevailing schemes. © 2023 John Wiley & Sons Ltd.

How Big Data Analytics Mitigates Supply Chain Vulnerability? An Interpretive Structural Modeling

The COVID-19 pandemic and trade frictions impact the continuity of supply chain (SC) operations. In the volatile environment, big data analytics (BDA), a key technology for storing data and predictive analytics, has become an important tool for mitigating SC vulnerability. Based on the literature review, this paper identifies six influencing factors and four vulnerability drivers for mitigating vulnerability, and employs Interpretive Structural Modeling (ISM) and Cross-Impact Matrix Multiplication Applied to a Classification (MICMAC) to explore the influence pathways that BDA mitigates SC vulnerability. The findings show that BDA can influence knowledge acquisition and strategy formulation by improving the forecasting capability of enterprises, which facilitates strategy implementation and ultimately mitigates vulnerability. Furthermore, with the support of BDA, resource redundancy addresses vulnerability from supply-side, higher production level and efficiency reduce vulnerability from demand-side, and rational SC design alleviates vulnerability from operation-side. © 2022 IEEE.

Towards Privacy-Preserving Computation on Gene: Construct Covid-19 Phylogenetic Tree using Homomorphic Encryption

Constructing a phylogenetic tree is an essential method of analyzing the evolution of the covid-19 virus. In the case of multiple entities holding different coronavirus genetic data, it is simple to aggregate all data into one entity and then calculate the phylogenetic tree. However, such a method is challenging to carry out. Genetic data is susceptible and has high economic value, and it is usually impossible to copy between different entities directly. Also, the direct sharing of genetic data can lead to data leaks or even legal problems. In this paper, we propose a homomorphic-encryption-based solution to tackle this problem, where two participants, A and B, both hold a part of covid-19 genetic data and compute the gene distance matrix calculation of the overall dataset without revealing the genetic data held by both parties. After the computation, participant A can decrypt the final distance matrix from the encrypted result and then use the plain-text result to construct the covid-19 phylogenetic tree. Experiment results show that the proposed method can process the genetic data accurately in a short time, and the phylogenetic tree generated by the proposed solution has no loss of accuracy compared to plain-text calculation. In terms of engineering optimization, we propose an optimized encryption method, which can further shorten the encryption time of the entire dataset without reducing the security level. © 2022 IEEE.

Analysis of the spread of COVID-19 in Ukraine using Google Trends tools

The paper is devoted to the analysis of the spread of the COVID-19 pandemic in Ukraine based on finding the correlation between search terms in Google search engine and laboratory-confirmed cases. Statistics were obtained from open sources. The analysis was performed on matrices based on the Pearson correlation coefficient. To do this, we analyzed 25 typical search phrases, and after grouping them-7 remained. The data were reduced to the same discreteness. Correlation matrices were calculated for each wave of the pandemic and for altogether. As a result, the correlation between search phrases and laboratory-confirmed cases was observed only in the second and third waves of the pandemic. Moreover, in the first wave, the preconditions for its occurrence were found;in the second-Pearson's correlation coefficient was 0.74, and in the third wave, it decreased to 0.57. Other correlations that are specific to each pandemic wave are also analyzed. Additionally, it was proved that polynomials of the 6th degree most effectively restore lost data. © 2022 IEEE.

Recommendations in E-Commerce Systems Based on Deep Matrix Factorization

E-commerce systems (including online shopping, entertainment, etc.) play an increasingly important role and have become popular in digital life. These systems have also become one of the cores, and vital issues for many businesses, especially from the recent COVID-19 pandemic, the importance of online e-commerce systems are very necessary. Techniques in recommendation systems are widely used to support users in finding suitable products/items in online systems. This work proposes using deep matrix factorization for recommendation in online e-commerce systems. We provide a detailed architecture of a deep matrix factorization as well as make a comparison with the standard matrix factorization model. Experimental results on ten published data sets show that the deep matrix factorization model can work well for recommendations in online e-commerce systems. © 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

Implementation of Support Vector Machine with Lexicon Based for Sentiment Analysis on Twitter

Twitter is one of the social media that is widely used where Indonesia occupies the 6th largest Twitter user in the world. This research is a quantitative study on fine-grained sentiment analysis that extracts sentiment with the topic of the covid vaccine from Twitter with the aim of implementing the Support Vector Machine algorithm. The research flow uses the SEMMA method (Sample, Explore, Modify, Model, and Assess). The collection of data sets in the form of tweets crawled from Twitter by utilizing the Twitter API at the sample stage for further exploration of the attributes of the data set at the explore stage. The modify stage is text preprocessing so that the data set is more structured. After that is the model stage which applies the lexicon based method to assign sentiment classes to the data set. Data sets that have labels will be classified using the Naïve Bayes method and the Support Vector Machine. The final stage of the SEMMA method is to assess the method applied using confusion matrix and k-fold Cross Validation. The accuracy results from the Support Vector Machine method, the best parameter results using the CV Grid Search are the rbf kernel with C=100 and degree = 0.01 resulting in an accuracy of 85%. The accuracy of the implementation of the Support Vector Machine algorithm produces good scores for the Covid-19 vaccine topic, so that the algorithm can be applied to the classification of sentiment analysis on new data. © 2022 IEEE.

Time-Leveled Hypersoft Matrix, Level Cuts, Operators, and COVID-19 Collective Patient Health State Ranking Model

This article is the first step to formulate such higher dimensional mathematical structures in the extended fuzzy set theory that includes time as a fundamental source of variation. To deal with such higher dimensional information, some modern data processing structures had to be built. Classical matrices (connecting equations and variables through rows and columns) are a limited approach to organizing higher dimensional data, composed of scattered information in numerous forms and vague appearances that differ on time levels. To extend the approach of organizing and classifying the higher dimensional information in terms of specific time levels, this unique plithogenic crisp time-leveled hypersoft-matrix (PCTLHS matrix) model is introduced. This hypersoft matrix has multiple parallel layers that describe parallel universes/realities/information on some specific time levels as a combined view of events. Furthermore, a specific kind of view of the matrix is described as a top view. According to this view, i-level cuts, sublevel cuts, and sub-sublevel cuts are introduced. These level cuts sort the clusters of information initially, subject-wise then attribute-wise, and finally time-wise. These level cuts are such matrix layers that focus on one required piece of information while allowing the variation of others, which is like viewing higher dimensional images in lower dimensions as a single layer of the PCTLHS matrix. In addition, some local aggregation operators are designed to unify i-level cuts. These local operators serve the purpose of unifying the material bodies of the universe. This means that all elements of the universe are fused and represented as a single body of matter, reflecting multiple attributes on different time planes. This is how the concept of a unified global matter (something like dark matter) is visualized. Finally, to describe the model in detail, a numerical example is constructed to organize and classify the states of patients with COVID-19.

A Triangle Framework among Subgraph Isomorphism, Pharmacophore and Structure-function Relationship

Coronavirus disease 2019 (COVID-19) has gained utmost attention in the current time from academic research and industrial practices because it continues to rage in many countries. Pharmacophore models exploit molecule topological similarity as well as functional compound similarity so that they can be reliable via the application of the concept of bioisosterism. In this work, we analyze the targets for coronavirus protein and the structure of RNA virus variation, thereby complete the safety and pharmacodynamic action evaluation of small-molecule anti-coronavirus oral drugs. Common pharmacophore identifications could be converted into subgraph querying problems, due to chemical structures can also be converted to graphs, which is a knotty problem pressing for a solution. We adopt simplified representation pharmacophore graphs by reducing complete molecular structures to s to detect isomorphic topological patterns and further to improve the substructure retrieval efficiency. Our threefold architecture subgraph isomorphism-based method retrieves query subgraphs over large graphs. First, by means of extracting a sequence of subgraphs to be matched and then comparing the number of vertex and edge between the potential isomorphic subgraphs and the query graph, we lower the computational scaling markedly. Afterwards, the directed vertex and edge matrix recording vertex and edge positional relation, directional relation and distance relation has been created. Then, on the basis of permutation theorem, we calculate the row sum of vertex and edge adjacency matrix of query graph and potential sample. Finally, according to equinumerosity theorem, we check the eigenvalues of the vertex and edge adjacency matrices of the two graphs are equinumerous. The topological distance could be calculated based on the graph isomorphism and the subgraph isomorphism can be implemented after the combination of the subgraph. The proposed quantitative structure-function relationships (QSFR) approach can be effectively applied for pharmacophoric patterns identification. The framework of new drug development for covid-19 has been established based on this triangle. © 2022 ACM.