Complicated Mathematical Equations Research Articles

Stacking-ac4C: an ensemble model using mixed features for identifying n4-acetylcytidine in mRNA.

N4-acetylcytidine (ac4C) is a modification of cytidine at the nitrogen-4 position, playing a significant role in the translation process of mRNA. However, the precise mechanism and details of how ac4C modifies translated mRNA remain unclear. Since identifying ac4C sites using conventional experimental methods is both labor-intensive and time-consuming, there is an urgent need for a method that can promptly recognize ac4C sites. In this paper, we propose a comprehensive ensemble learning model, the Stacking-based heterogeneous integrated ac4C model, engineered explicitly to identify ac4C sites. This innovative model integrates three distinct feature extraction methodologies: Kmer, electron-ion interaction pseudo-potential values (PseEIIP), and pseudo-K-tuple nucleotide composition (PseKNC). The model also incorporates the robust Cluster Centroids algorithm to enhance its performance in dealing with imbalanced data and alleviate underfitting issues. Our independent testing experiments indicate that our proposed model improves the Mcc by 15.61% and the ROC by 5.97% compared to existing models. To test our model's adaptability, we also utilized a balanced dataset assembled by the authors of iRNA-ac4C. Our model showed an increase in Sn of 4.1%, an increase in Acc of nearly 1%, and ROC improvement of 0.35% on this balanced dataset. The code for our model is freely accessible at https://github.com/louliliang/ST-ac4C.git, allowing users to quickly build their model without dealing with complicated mathematical equations.

Going Back to the Basic of Green Economy： Special Reference to Economic Interpretation and Policies

It is no doubt that promoting green economy is the only option for the sustainable development. This paper provides a fundamental framework for economic studies on designing green policies that have many links with green technologies and environmental ethics. It also proposes a new theory of “pollution abatement stages model” in order to interpret how to improve environmental quality in a more efficient and effective way. For an intuitive understanding, we use more graphs instead of complicated mathematical equations to demonstrate ideas and the new theory. Key Words: green technologies, environmental ethics, green policies, pollution abatement stages model

Square Waveguide Cavity for Complex Permittivity and Permeability Measurement by Perturbation Method Without Repositioning

This article presents a novel configuration for the simultaneous complex permittivity and permeability determination with only a single sample placement inside the resonant cavity. The proposed structure incorporates two waveguide orthomode transducers (OMTs) and a square cavity. The square cavity is designed to overcome the limitation of permeability measurement by the rectangular cavity perturbation method. These components allow the product of two orthogonal transverse electric (TE) resonant modes (TE10L and TE01L) with the same cutoff frequencies. Based on Maxwell equations and perturbation theory, new relations are developed to characterize the complex permeability of specimens at TE01L modes. The proposed structure eliminates the main drawbacks of previous studies such as depolarization effect of partial-height samples, radiation of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H}$ </tex-math></inline-formula> -plane sample hole, need to apply the sample holder and precision positioner, multistate positioning, iterative calculations, extra calibration process, and employing complicated mathematical equations. The proposed configuration was designed using CST Microwave Studio (MWS) and ANSYS high-frequency structural simulator (HFSS) and then manufactured and measured. The operating frequency has been selected from 7.5 to 12.5 GHz. Good agreement is achieved between measurement and simulation. The performance of the developed structure was verified by measuring the material characteristics of bar-shaped dielectric and magneto-dielectric specimens and compared with other studies.

Visualisasi Algoritma sebagai Sarana Pembelajaran K-Means Clustering

Algorithm Visualization (AV) is often used in computer science to represents how an algorithm works. Educators believe that visualization can help students to learn difficult algorithms. In this paper, we put our interest in visualizing one of Machine Learning (ML) algorithms. ML algorithms are used in various fields. Some of the algorithms are used to classify, predict, or cluster data. Unfortunately, many students find that ML algorithms are hard to learn since some of these algorithms include complicated mathematical equations. We hope this research can help computer science students to understand K-Means Clustering in an easier way.

Canonical correlations in agricultural research: Method of interpretation used leads to greater reliability of results

Canonical correlations analyzes are being used in the agrarian sciences and constitute an important tool in the interpretation of results. This analysis is performed by complicated mathematical equations and it is only possible to use it thanks to the development of computational software, which allow different interpretations of results, and it is up to the researcher to choose according to his knowledge. Canonical correlations can be interpreted using canonical weights, canonical loadings, or canonical cross-loadings. In Brazil, most of the works that use these analyzes interpret the canonical weights. Therefore, this study aims to show, through an analysis of canonical correlations, the best way to interpret the results, so that they are presented in the most reliable way possible. Data from an experiment with two cultivars of biquinho pepper seeded in 5 light spectrums were performed. The variables were root length and volume, plant height, number of leaves, fresh shoot and root mass, shoot dry mass. Two groups of variables were organized, the multicollinearity was determined through the condition number and the inflation factor of the variance. Canonical correlations analysis was carried out, and weights, loadings, and canonical cross-loadings were estimated for the interpretation of the results. After the interpretations, it was defined that the canonical cross-loadings should be preferred for the interpretation of the canonical correlations. Weights or canonical coefficients provide dubious results of relationships between groups of characters and should be avoided.

Model Calibration of Stochastic Process and Computer Experiment for MVO Analysis of Multi-Low-Frequency Electromagnetic Data

An electromagnetic (EM) technique is employed in seabed logging (SBL) to detect offshore hydrocarbon-saturated reservoirs. In risk analysis for hydrocarbon exploration, computer simulation for subsurface modelling is a crucial task. It can be expensive and time-consuming due to its complicated mathematical equations, and only a few realizations of input-output pairs can be generated after a very lengthy computational time. Understanding the unknown functions without any uncertainty measurement could be very challenging as well. We proposed model calibration between a stochastic process and computer experiment for magnitude versus offset (MVO) analysis. Two-dimensional (2D) Gaussian process (GP) models were developed for low-frequencies of 0.0625–0.5 Hz at different hydrocarbon depths to estimate EM responses at untried observations with less time consumption. The calculated error measurements revealed that the estimates were well-matched with the computer simulation technology (CST) outputs. Then, GP was fitted in the MVO plots to provide uncertainty quantification. Based on the confidence intervals, hydrocarbons were difficult to determine especially when their depth was 3000 m from the seabed. The normalized magnitudes for other frequencies also agreed with the resulting predictive variance. Thus, the model resolution for EM data decreases as the hydrocarbon depth increases even though multi-low frequencies were exercised in the SBL application.

Graphical user interface based model for transmission line performance implementation in power system

&lt;span&gt;Transmission line is one of the important elements in the process of power transfer from the source of generation to the consumer. In order to analyze the performance of a transmission line, it has to be represented by an equivalent model with suitable circuit parameters at a per phase basis. The line models are used to measure voltages, currents and the amount of power flow depending on the line length. Transmission line performance is determined by the voltage regulation and its efficiency under their normal operating conditions. In this study, a systematic approach was developed in order to assists the lecturers in teaching this important topic to the students despite so many complicated mathematical equations involved in the calculation. With the aid of Graphical User Interface (GUI), the performance of transmission line can be determined and monitored due to the change of line parameters. The results obtained could assist the lecturers in delivering the concept of engineering in a more systematic approach. On top of that, it could also assist the power system utility in planning the transmission line that needed to be installed in the system.&lt;/span&gt;

IAI-DSAE: A Computational Method for Adenosine to Inosine Editing Site Prediction

As an important post-transcriptional modification, adenosine-to-inosine RNA editing generally occurs in both coding and noncoding RNA transcripts in which adenosines are converted to inosines. Accordingly, the diversification of the transcriptome can be resulted in by this modification. It is significant to accurately identify adenosine-to-inosine editing sites for further understanding their biological functions. Currently, the adenosine-to-inosine editing sites would be determined by experimental methods, unfortunately, it may be costly and time consuming. Furthermore, there are only a few existing computational prediction models in this field. Therefore, the work in this study is starting to develop other computational methods to address these problems. Given an uncharacterized RNA sequence that contains many adenosine resides, can we identify which one of them can be converted to inosine, and which one cannot? To deal with this problem, a novel predictor called iAI-DSAE is proposed in the current study. In fact, there are two key issues to address: one is ‘what feature extraction methods should be adopted to formulate the given sample sequence?’ The other is ‘what classification algorithms should be used to construct the classification model?’ For the former, a 540-dimensional feature vector is extracted to formulate the sample sequence by dinucleotide-based auto-cross covariance, pseudo dinucleotide composition, and nucleotide density methods. For the latter, we use the present more popular method i.e. deep spare autoencoder to construct the classification model. Generally, ACC and MCC are considered as the two of the most important performance indicators of a predictor. In this study, in comparison with those of predictor PAI, they are up 2.46% and 4.14%, respectively. The two other indicators, Sn and Sp, rise at certain degree also. This indicates that our predictor can be as an important complementary tool to identify adenosine-toinosine RNA editing sites. For the convenience of most experimental scientists, an easy-to-use web-server for identifying adenosine-to-inosine editing sites has been established at: http://www.jci-bioinfo.cn/iAI-DSAE, by which users can easily obtain their desired results without the need to go through the complicated mathematical equations involved. It is important to identify adenosine-to-inosine editing sites in RNA sequences for the intensive study on RNA function and the development of new medicine. In current study, a novel predictor, called iAI-DSAE, was proposed by using three feature extraction methods including dinucleotidebased auto-cross covariance, pseudo dinucleotide composition and nucleotide density. The jackknife test results of the iAI-DSAE predictor based on deep spare auto-encoder model show that our predictor is more stable and reliable. It has not escaped our notice that the methods proposed in the current paper can be used to solve many other problems in genome analysis.

Prediction of hydrocarbon depth for seabed logging (SBL) application using Gaussian process

Seabed Logging (SBL) is an application of marine Controlled-Source Electromagnetic (CSEM) technique to characterize hydrocarbon-filled layers underneath the seabed remotely in deep water regions. This technique maps structure of subsurface electrical resistivity in the offshore environment. Basically, exploration of offshore hydrocarbon is based on the contrast of electrical resistivity between hydrocarbon reservoir and its surrounding sea sediments. Modelling offshore hydrocarbon is a core analysis and time consuming task. Current numerical modelling techniques used in SBL application involve meshes and complicated mathematical equations. Thus, a simple supervised learning method which is Gaussian Process (GP) is proposed to process synthetic SBL data which are generated through Computer Simulation Technology (CST) software to predict the depth of hydrocarbon. This statistical model is able to provide additional hydrocarbon information by utilizing the prior information. 1-dimensional (1-D) forward GP models have successfully been developed to predict the presence of hydrocarbon and as the continuation work, 2-dimensional (2-D) forward GP model is then developed to be used as the standard profile in order to predict the depth of hydrocarbon. This shall give indication that GP can be used as the methodology to predict the depth of hydrocarbon reservoir underneath the seabed.

New matrix solution of the phase-correlation technique in a Brillouin dynamic grating sensor

In the phase-correlation measurement technique of Brillouin dynamic grating sensors, two counterpropagating pump waves are modulated by a pseudo-random bit sequence (PRBS) that applies a random phase shift of either 0 or π with a specified period. In order to define the sensing length and spatial resolution, the shape of the correlation peak has to be found. So far, many methods have been used to demonstrate the phase correlation, but they often require several lengthy and sometimes complicated mathematical assumptions and equations. One of the techniques that has the best reported spatial resolution is called the time gated phase-correlation technique. We introduce a novel method based on a matrix solution to show the phase modulation in the phase-correlation technique. It is a straightforward and intuitive pattern to visualize the phase modulation of the pumps and to attain the shape of the phase-correlation peaks. Finally, the results of the matrix method are completely consistent with the previous results.

Assessment of Wind Power Integrated to the Power Systems Using Probabilistic Load Flow Based on PFV with LS

Power flow analysis (PFA) is one of the most important issues of power system analysis and design. This paper aims at developing and applying a high-speed sampling method to produce large-capacity sample set based on pattern feature vector with layer structure (PFV with LS) of IEEE 14-bus system data analytical methods. In this study, sampling based pattern vectors are constructed in three layers. The first and second layer vectors are very low dimensional, and the sampling of the third layer is in parallel for each local area. Samples generated by this sampling method can be applied to the calculation of probabilistic load flow (PLF) and probabilistic static security assessment. Simulation results show that the proposed method can improve efficiency of PLF analysis and probabilistic static security assessment. The advantages of using PLF based on PFV with LS as the power flow limit can minimize the complicated mathematical equations. Furthermore, the algorithm is very simple and accurate, especially when the system connected to the wind power.

IDNA6mA-PseKNC: Identifying DNA N6-methyladenosine sites by incorporating nucleotide physicochemical properties into PseKNC

N6-methyladenine (6mA) is one kind of post-replication modification (PTM or PTRM) occurring in a wide range of DNA sequences. Accurate identification of its sites will be very helpful for revealing the biological functions of 6mA, but it is time-consuming and expensive to determine them by experiments alone. Unfortunately, so far, no bioinformatics tool is available to do so. To fill in such an empty area, we have proposed a novel predictor called iDNA6mA-PseKNC that is established by incorporating nucleotide physicochemical properties into Pseudo K-tuple Nucleotide Composition (PseKNC). It has been observed via rigorous cross-validations that the predictor's sensitivity (Sn), specificity (Sp), accuracy (Acc), and stability (MCC) are 93%, 100%, 96%, and 0.93, respectively. For the convenience of most experimental scientists, a user-friendly web server for iDNA6mA-PseKNC has been established at http://lin-group.cn/server/iDNA6mA-PseKNC, by which users can easily obtain their desired results without the need to go through the complicated mathematical equations involved.

Back Propagation Neural Network (BPNN) Based Recognition Of Handwritten Mathematical Equations

The recognition of handwritten mathematical symbols and equations are the critical and challenging issue in the field of pattern recognition. It is the need to recognize complicated handwritten mathematical equations viz. law of gravity, convolution integral etc. The issues like overwriting of symbols, characters etc. are identified and solved it by selecting best classifier to improve recognition rate. The machine learning approach with enhanced multi layer precentor feed forward back propagation neural network algorithm with an offline mode of recognition has been used to improve throughput, accuracy and overall efficiency of mathematical equations recognition. The hybrid features extracted viz. centroid, boundary box, zoning density, line segment etc. and gradient descent with momentum training algorithm has been used. Adaptive learning is used to carry out the experiment on numerous kinds of equations. Through experimental result, the system is evaluated and illustrated which shows the significant improvement 93.5 % accuracy in recognition of simple as well as complicated mathematical equations. In future current methodology will be the key factor to initiate paperless work and digital world.

A review of multi-objective optimization: Methods and its applications

Several reviews have been made regarding the methods and application of multi-objective optimization (MOO). There are two methods of MOO that do not require complicated mathematical equations, so the problem becomes simple. These two methods are the Pareto and scalarization. In the Pareto method, there is a dominated solution and a non-dominated solution obtained by a continuously updated algorithm. Meanwhile, the scalarization method creates multi-objective functions made into a single solution using weights. There are three types of weights in scalarization which are equal weights, rank order centroid weights, and rank-sum weights. Next, the solution using the Pareto method is a performance indicators component that forms MOO a separate and produces a compromise solution and can be displayed in the form of Pareto optimal front, while the solution using the scalarization method is a performance indicators component that forms a scalar function which is incorporated in the fitness function.

IKcr-PseEns: Identify lysine crotonylation sites in histone proteins with pseudo components and ensemble classifier

Lysine crotonylation (Kcr) is an evolution-conserved histone posttranslational modification (PTM), occurring in both human somatic and mouse male germ cell genomes. It is important for male germ cell differentiation. Information of Kcr sites in proteins is very useful for both basic research and drug development. But it is time-consuming and expensive to determine them by experiments alone. Here, we report a novel predictor called iKcr-PseEns that is established by incorporating five tiers of amino acid pairwise couplings into the general pseudo amino acid composition. It has been observed via rigorous cross-validations that the new predictor's sensitivity (Sn), specificity (Sp), accuracy (Acc), and stability (MCC) are 90.53%, 95.27%, 94.49%, and 0.826, respectively. For the convenience of most experimental scientists, a user-friendly web-server for iKcr-PseEns has been established at http://www.jci-bioinfo.cn/iKcr-PseEns, by which users can easily obtain their desired results without the need to go through the complicated mathematical equations involved.

IRNA-2methyl: Identify RNA 2'-O-methylation Sites by Incorporating Sequence-Coupled Effects into General PseKNC and Ensemble Classifier.

Being a kind of post-transcriptional modification (PTCM) in RNA, the 2'-Omethylation modification occurs in the processes of life development and disease formation as well. Accordingly, from the angles of both basic research and drug development, we are facing a challenging problem: given an uncharacterized RNA sequence formed by many nucleotides of A (adenine), C (cytosine), G (guanine), and U (uracil), which one can be of 2-O'-methylation modification, and which one cannot? Unfortunately, so far no computational method whatsoever has been developed to address such a problem. To fill this empty area, we propose a predictor called iRNA-2methyl. It is formed by incorporating a series of sequence-coupled factors into the general PseKNC (pseudo nucleotide composition), followed by fusing 12 basic random forest classifier into four ensemble predictors, with each aimed to identify the cases of A, C, G, and U along the RNA sequence concerned, respectively. Rigorous jackknife cross-validations have indicated that the success rates are very high (>93%). For the convenience of most experimental scientists, a user-friendly web-server for iRNA-2methyl has been established at http://www.jci-bioinfo.cn/iRNA-2methyl, by which users can easily obtain their desired results without the need to go through the complicated mathematical equations involved. The proposed predictor iRNA-2methyl will become a very useful bioinformatics tool for medicinal chemistry, helping to design effective drugs against the diseases related to the 2'-Omethylation modification.

IPGK-PseAAC: Identify Lysine Phosphoglycerylation Sites in Proteins by Incorporating Four Different Tiers of Amino Acid Pairwise Coupling Information into the General PseAAC.

Occurring at Lys residues, the PGK (lysine phosphoglycerylation) is a special kind of post-translational modification (PTM). It may invert the charge potential of the modified residue and change the protein structures and functions, causing various diseases in liver, brain, and kidney. From the angles of both basic research and drug development, we are facing a critical challenging problem: for an uncharacterized protein sequence containing many Lys residues, which ones can be of phosphoglycerylation, and which ones cannot? To address this problem, we have developed a predictor called iPGK-PseAAC by incorporating into the general PseAAC (pseudo amino acid composition) with four different tiers of amino acid pairwise coupling information, where tiers 1, 2, 3, and 4 refer to the amino acid pairwise couplings between all the 1st, 2nd, 3rd, and 4th most contiguous residues along a protein segment, respectively. Rigorous cross-validations indicated that the proposed predictor remarkably outperformed its existing counterparts. The proposed predictor iPGK-PseAAC will become a very useful bioinformatics tool for medicinal chemistry. For the convenience of most experimental scientists, a user-friendly webserver for iGPK-PseAAC has been established at http://app.aporc.org/iPGK-PseAAC/, by which users can easily obtain their desired results without the need to go through the complicated mathematical equations involved.

IRNAm5C-PseDNC: identifying RNA 5-methylcytosine sites by incorporating physical-chemical properties into pseudo dinucleotide composition.

Occurring at cytosine (C) of RNA, 5-methylcytosine (m5C) is an important post-transcriptional modification (PTCM). The modification plays significant roles in biological processes by regulating RNA metabolism in both eukaryotes and prokaryotes. It may also, however, cause cancers and other major diseases. Given an uncharacterized RNA sequence that contains many C residues, can we identify which one of them can be of m5C modification, and which one cannot? It is no doubt a crucial problem, particularly with the explosive growth of RNA sequences in the postgenomic age. Unfortunately, so far no user-friendly web-server whatsoever has been developed to address such a problem. To meet the increasingly high demand from most experimental scientists working in the area of drug development, we have developed a new predictor called iRNAm5C-PseDNC by incorporating ten types of physical-chemical properties into pseudo dinucleotide composition via the auto/cross-covariance approach. Rigorous jackknife tests show that its anticipated accuracy is quite high. For most experimental scientists’ convenience, a user-friendly web-server for the predictor has been provided at http://www.jci-bioinfo.cn/iRNAm5C-PseDNC along with a step-by-step user guide, by which users can easily obtain their desired results without the need to go through the complicated mathematical equations involved. It has not escaped our notice that the approach presented here can also be used to deal with many other problems in genome analysis.

IATC-mHyb: a hybrid multi-label classifier for predicting the classification of anatomical therapeutic chemicals.

Recommended by the World Health Organization (WHO), drug compounds have been classified into 14 main ATC (Anatomical Therapeutic Chemical) classes according to their therapeutic and chemical characteristics. Given an uncharacterized compound, can we develop a computational method to fast identify which ATC class or classes it belongs to? The information thus obtained will timely help adjusting our focus and selection, significantly speeding up the drug development process. But this problem is by no means an easy one since some drug compounds may belong to two or more than two ATC classes. To address this problem, using the DO (Drug Ontology) approach based on the ChEBI (Chemical Entities of Biological Interest) database, we developed a predictor called iATC-mDO. Subsequently, hybridizing it with an existing drug ATC classifier, we constructed a predictor called iATC-mHyb. It has been demonstrated by the rigorous cross-validation and from five different measuring angles that iATC-mHyb is remarkably superior to the best existing predictor in identifying the ATC classes for drug compounds. To convenience most experimental scientists, a user-friendly web-server for iATC-mHyd has been established at http://www.jci-bioinfo.cn/iATC-mHyb, by which users can easily get their desired results without the need to go through the complicated mathematical equations involved.

IRSpot-EL: identify recombination spots with an ensemble learning approach.

Coexisting in a DNA system, meiosis and recombination are two indispensible aspects for cell reproduction and growth. With the avalanche of genome sequences emerging in the post-genomic age, it is an urgent challenge to acquire the information of DNA recombination spots because it can timely provide very useful insights into the mechanism of meiotic recombination and the process of genome evolution. To address such a challenge, we have developed a predictor, called IRSPOT-EL: , by fusing different modes of pseudo K-tuple nucleotide composition and mode of dinucleotide-based auto-cross covariance into an ensemble classifier of clustering approach. Five-fold cross tests on a widely used benchmark dataset have indicated that the new predictor remarkably outperforms its existing counterparts. Particularly, far beyond their reach, the new predictor can be easily used to conduct the genome-wide analysis and the results obtained are quite consistent with the experimental map. For the convenience of most experimental scientists, a user-friendly web-server for iRSpot-EL has been established at http://bioinformatics.hitsz.edu.cn/iRSpot-EL/, by which users can easily obtain their desired results without the need to go through the complicated mathematical equations involved. bliu@gordonlifescience.org or bliu@insun.hit.edu.cnSupplementary information: Supplementary data are available at Bioinformatics online.