Sum Of Pairs Research Articles

TPMA: A two pointers meta-alignment tool to ensemble different multiple nucleic acid sequence alignments.

Accurate multiple sequence alignment (MSA) is imperative for the comprehensive analysis of biological sequences. However, a notable challenge arises as no single MSA tool consistently outperforms its counterparts across diverse datasets. Users often have to try multiple MSA tools to achieve optimal alignment results, which can be time-consuming and memory-intensive. While the overall accuracy of certain MSA results may be lower, there could be local regions with the highest alignment scores, prompting researchers to seek a tool capable of merging these locally optimal results from multiple initial alignments into a globally optimal alignment. In this study, we introduce Two Pointers Meta-Alignment (TPMA), a novel tool designed for the integration of nucleic acid sequence alignments. TPMA employs two pointers to partition the initial alignments into blocks containing identical sequence fragments. It selects blocks with the high sum of pairs (SP) scores to concatenate them into an alignment with an overall SP score superior to that of the initial alignments. Through tests on simulated and real datasets, the experimental results consistently demonstrate that TPMA outperforms M-Coffee in terms of aSP, Q, and total column (TC) scores across most datasets. Even in cases where TPMA's scores are comparable to M-Coffee, TPMA exhibits significantly lower running time and memory consumption. Furthermore, we comprehensively assessed all the MSA tools used in the experiments, considering accuracy, time, and memory consumption. We propose accurate and fast combination strategies for small and large datasets, which streamline the user tool selection process and facilitate large-scale dataset integration. The dataset and source code of TPMA are available on GitHub (https://github.com/malabz/TPMA).

Enhanced Genetic Method for Optimizing Multiple Sequence Alignment

In the realm of bioinformatics, Multiple Sequence Alignment (MSA) is a pivotal technique used to optimize the alignment of multiple biological sequences, guided by specific scoring criteria. Existing approaches addressing the MSA challenge tend to specialize in distinct biological features, leading to variability in alignment outcomes for the same set of sequences. Consequently, this paper proposes an enhanced evolutionary-based approach that simplifies the sequence alignment problem without considering the sequences in the non-dominated solution. Our method employs a multi-objective optimization technique that uniquely excludes non-dominated solution sets, effectively mitigating computational complexities. Utilizing the Sum of Pairs and the Total Conserved Column as primary objective functions, our approach offers a novel perspective. We adopt an integer coding approach to enhance the computational efficiency, representing chromosomes with sets of integers during the alignment process. Using the SABmark and BAliBASE datasets, extensive experimentation is conducted to compare our method with existing ones. The results affirm the superior solution quality achieved by our approach compared to its predecessors. Furthermore, via the Wilcoxon signed-rank test, a statistical analysis underscores the statistical significance of our model’s improvement (p < 0.05). This comprehensive approach holds promise for advancing Multiple Sequence Alignment in bioinformatics.

Balanced of Countries Development Determinants: Barycentric Model

The authors investigate the issue of modelling the balance of countries development determinants based on determining the center of mass. They have identified the most relevant factors characterizing countries' social, economic, political spheres, digital capability and cybersecurity. The research has been carried based on empirical values of the selected 17 indicators for 127 world countries in 2018. As a result, the four-pole barycentric models were built as quadrangles, the vertices of which are composite targets formed by the determinants of the four spheres. The models' calculations were carried out taking into account three components: the values of the composite targets (as a geometric mean), the level of pairs balance (as the sum of opposite pairs of quadrilateral angles), and all four targets (as the distance between the actual and standard value of the center of mass). According to the analysis result of the first component, developed countries have the most effective targets (top five - Switzerland, Denmark, Norway, Finland, the Netherlands). Research of the results of the second component has revealed an imbalance in target pairs for most countries. Determinants of socio-political development are the most effective for developed countries. The economic sphere is most unbalanced for the least developed countries. Various determinants can cause an imbalance for developing and new industrial countries. The analysis of the center of mass distances revealed that not only developed countries could be balanced, but also developing, new industrial and the least developed, that indicates a balanced development of their determinants, which is pretty slow. New Zealand, Mauritius, South Africa and Mali were the most balanced in each group of countries economic growth.

The barycentric model of determining the sustainable growth determinants

The authors investigate the issue of modelling the balance of sustainable growth determinants based on determining the center of mass. They have identified the most relevant factors that characterize countries' social, economic, and political spheres, digital capability, and cybersecurity to determine sustainable development and growth. The research has been carried out based on empirical values of the selected 17 indicators for 127 world countries in 2018. As a result, the four–pole barycentric models were built as quadrangles, the vertices of which are composite targets formed by the determinants of the four spheres. The models' calculations were carried out taking into account three components: the values of the composite targets (as a geometric mean), the level of pairs balance (as the sum of opposite pairs of quadrilateral angles), and all four targets (as the distance between the actual and standard value of the center of mass). According to the analysis result of the first component, developed countries have the most effective targets (top five – Switzerland, Denmark, Norway, Finland, and the Netherlands). Research of the results of the second component has revealed an imbalance in target pairs for most countries. Determinants of socio–political development are the most effective for developed countries. The economic sphere is most unbalanced for the least developed countries. Various determinants can cause an imbalance for developing and new industrial countries. The analysis of the center of mass distances revealed that not only developed countries could be balanced, but also developing, new industrial and the least developed, which indicates a balanced development of their determinants, which is pretty slow. New Zealand, Mauritius, South Africa and Mali were the most balanced in each country's sustainable growth group.

Multiple Sequence Alignment based on deep Q network with negative feedback policy

Background and objective:Multiple Sequence Alignment (MSA) is an essential procedure in the sequence analysis of biological macromolecules, which can obtain the potential information between multiple sequences, such as functional and structural information. At present, the main challenge of MSA is an NP-complete problem; the algorithm’s complexity increases exponentially with the increase of the number of sequences. Some methods are constantly approaching the results towards the optimal ratio and easy to fall into the local optimization, so the accuracy of these methods is still greatly improved. Methods:Here, we propose a new method based on deep reinforcement learning (DRL) for MSA. Specifically, inspired by biofeedback, we leverage the Negative Feedback Policy (NFP) to enhance the performance and accelerate the convergence of the model. Furthermore, we developed a new profile algorithm to compute the sequence from aligned sequences for the next profile-sequence alignment to facilitate the experiment. Results:Compared to six state-of-the-art methods, three different genetic algorithms, Q-learning, ClustalW, and MAFFT, our method exceeds these methods in terms of Sum-of-Pairs (SP) score and Column Score(CS) scores on most datasets in which the increased range of SP score is from 2 to 1056. Conclusion:Extensive experiments based on several datasets validate the effectiveness of our method for achieving a better alignment, and the results have higher accuracy and stability. The source code can be found at https://github.com/MrZhang176/DNPMSA.

Joint optimization of flight and train timetables for air and high-speed railway integration services with maximum accessibility

One important benefit of air and high-speed railway (AH) integration services is increasing the number of destinations within passengers’ reach, which means intermodal services can facilitate passengers from cities that are linked to nearby airports by railway, to travel to or from more locations. However, certain origin-destination (OD) pairs are not accessible when the flight and train timetables are not well coordinated, which will lead to a reduction in the overall benefit. Given the original timetables, a joint optimization model for flight and train timetables is proposed, to improve the intermodal service accessibility in an AH transfer hub with a railway link. The objectives are to maximize the weighted sum of accessible OD pairs and minimize the time shifts compared with the original timetables. A real-world case study in China is performed to demonstrate the applicability of the model. The results illustrate that the model can effectively improve the accessibility.

Multiple sequence alignment quality comparison in T-Coffee, MUSCLE and M-Coffee based on different benchmarks

Multiple sequence alignment (MSA) is a fundamental process in the studies for determination of evolutionary, structural and functional relationships of biological sequences or organisms. There are various heuristic approaches comparing more than two sequences to generate MSA. However, each tool used for MSA is not suitable for every dataset. Considering the importance of MSA in wide range of relationship studies, we were interested in comparing the performance of different MSA tools for various datasets. In this study, we applied three different MSA tools, T-Coffee, MUSCLE and M-Coffee, on several datasets, BAliBase, SABmark, DIRMBASE, ProteinBali and DNABali. It was aimed to evaluate the differences in the performance of these tools based on the stated benchmarks regarding the % consistency, sum of pairs (SP) and column scores (CS) by using Suite MSA. We also calculated the average values of these scores for each tool to examine the results in comparative perspective. Eventually, we conclude that all three tools performed their best with the datasets from ProteinBali (average % consistency: 29.6, 32.3, 29.7; SP: 0.74, 0.73, 0.74; CS with gaps: 0.27, 0.27, 0.26 for T-Coffee, MUSCLE, M-Coffee, respectively), whereas the lowest performance was obtained in datasets from DIRMBASE (average % consistency: 1.8, 1.1, 4.3; SP: 0.05, 0.04, 0.04 CS with gaps: 0.01, 0, 0.008 for T-Coffee, MUSCLE, M-Coffee, respectively)

Evaluation of Gaussian process regression kernel functions for improving groundwater prediction

Systematic model error is caused by the unreasonable simplification of real groundwater system, which damages the reliability of groundwater model prediction. Gaussian process regression (GPR) is a popular data-driven method used to build a statistical complementary model to correct systematic prediction error and improve model prediction. Kernel function is a crucial component of GPR, it represents the assumptions on systematic prediction error that we want to learn. In order to evaluate the influence of GPR kernel on capturing systematic prediction error, we compared the performances of GPR with nine kernels in groundwater predictions. These kernels include three commonly used single kernels, i.e., squared exponential (SE), Matérn class (MT), and rational quadratic (RQ) kernels, and six new kernels formed by combining these single kernels as sum or product of pairs (SE_MT_s, SE_RQ_s, MT_RQ_s, SE_MT_p, SE_RQ_p, and MT_RQ_p). Moreover, three groundwater case studies, including two analytical cases and one real case, are used to test these kernels, and four metrics are applied to measure the performances of these kernels. The evaluation results show that kernel functions have apparent influence on the ability of the GPR-based complementary model to capture the systematic prediction error of groundwater model. The single kernel RQ-based GPR yields the best performance in improving groundwater predictions among the nine kernels for all case studies. The combined kernels MT_RQ_s, SE_RQ_s also perform well in groundwater predictions, and the commonly used SE kernel has mediocre performance in predicting groundwater observations.

A faster Fourier transform? Computing small-scale power spectra and bispectra for cosmological simulations in 𝒪(N2) time

ABSTRACT We present $\mathcal {O}(N^2)$ estimators for the small-scale power spectrum and bispectrum in cosmological simulations. In combination with traditional methods, these allow spectra to be efficiently computed across a vast range of scales, requiring orders of magnitude less computation time than Fast Fourier Transform based approaches alone. These methods are applicable to any tracer; simulation particles, haloes or galaxies, and take advantage of the simple geometry of the box and periodicity to remove almost all dependence on large random particle catalogues. By working in configuration-space, both power spectra and bispectra can be computed via a weighted sum of particle pairs up to some radius, which can be reduced at larger k, leading to algorithms with decreasing complexity on small scales. These do not suffer from aliasing or shot-noise, allowing spectra to be computed to arbitrarily large wavenumbers. The estimators are rigorously derived and tested against simulations, and their covariances discussed. The accompanying code, hipster, has been publicly released, incorporating these algorithms. Such estimators will be of great use in the analysis of large sets of high-resolution simulations.

Operational calculus for rows, columns, and blocks of linear relations

Columns and rows are operations for pairs of linear relations in Hilbert spaces, modelled on the corresponding notions of the componentwise sum and the usual sum of such pairs. The introduction of matrices whose entries are linear relations between underlying component spaces takes place via the row and column operations. The main purpose here is to offer an attempt to formalize the operational calculus for block matrices, whose entries are all linear relations. Each block relation generates a unique linear relation between the Cartesian products of initial and final Hilbert spaces that admits particular properties which will be characterized. Special attention is paid to the formal matrix multiplication of two blocks of linear relations and the connection to the usual product of the unique linear relations generated by them. In the present general setting these two products need not be connected to each other without some additional conditions.

Correlation Properties and Construction of Quadriphase Z-Complementary Pairs

Based on Gray mapping, the properties of the autocorrelation sum of quadriphase Z-complementary pairs (QZCPs) are investigated. It is proved that both the real and imaginary parts of the sum equal zero modulo 2. Additionally, a novel construction that transforms binary ZCPs (BZCPs) into QZCPs is presented. The proposed construction can produce QZCPs, which are different to the ones from existing constructions, with the same zero-correlation-zone (ZCZ) width-length ratios (ZWLRs) as the employed BZCPs.

THERMODYNAMIC PROPERTIES OF ORGANIC ACIDS AND SOME THEIR DERIVATIVES

The heats of vaporization, combustion, formation, entropy and the heat capacities in different phases of different carbonic acids and their derivatives: acetates, esters with fatty radicals, two-, three- and four-basic acids (52 compounds) were analysed in the framework of one-parametric mathematic equations. The experimental data of all chosen one-, two-, three- and four-basic acids were analyzed. It was determined, that all thermodynamic functions of these types of compounds depend on the number of valence electrons N, from which the sum of lone electron pairs g as represented in the equations Δvap,c,fH° = i ± f (N-g) and S°(Cp) = i ± f (N-g) is excluded. The coefficients f in the first equations is in the range of 104-113 kJ mol-1 electron-1, that corresponds to the same values f in the equations, which are mentioned in our earlier papers on the determination of the heats of combustion of organic acids. As concerned of coefficient i in the received equations, necessary to note that situation is not synonymous as with the coefficient f. The magnitudes of this coefficient are different in the equations of vaporization, combustion, formation also as in the equations of entropy and the heat of capacity. On the base of literary experimental data we calculated the 29 new equations, which can be used for the calculation of the same thermodynamic functions for other new organic acids and especially bioorganic substances with the useful properties. Necessary to add, that the received equations can serve as additional material for the calculation of the bond energies of fatty acids and their derivatives in gas phase.

Analysis of thermochemical data of fatty acids and acetates on their base

The heat of vaporization, combustion, formation, entropy in different phases and the heat of capacity of fatty carbonic acids and their acetates were analyzed and was determined that all functions of these types of compounds depend from the number of valence electrons N from which is excluded the sum of lone electron pairs g as represented in equations Δvap,f,cH° = i ± f (N – g) and S° (Cp) = i ± f (N – g). The coefficients f in the first equations is in the range 108 – 109 kJ⋅mol−1 electron−1, that corresponds to the same values f in the equations, which are related to combustion processes. Other coefficient i is different for each type of compounds. The received new seven equations can be used for the calculation of the same thermodynamic functions for other organic and especially bioorganic substances with fatty radicals.

Multiobjective artificial fish swarm algorithm for multiple sequence alignment

Multiple sequence alignment (MSA) represents a basic task for many bioinformatics applications. MSA allows finding common conserved regions among various sequences of proteins or DNA. However, to find the optimal multiple sequence alignment, it is necessary to design an efficient exploration approach that could explore a huge number of possible multiple sequence alignments. As well as, it is required to use a powerful evaluation method to assess the biological relevance of these multiple sequence alignment. To address these main problems, this article presents a multiobjective artificial fish swarm algorithm (MOAFS) to solve multiple sequence alignment. MOAFS uses the behaviors of artificial fish swarm algorithm such as the cooperation, decentralization and parallelism to ensure a good trade-off between the exploration and the exploitation of the search space of MSA problem. To preserve the quality and consistency of alignment, two fitness functions have been simultaneously used by the MOAFS algorithm: (i) Weighted Sum of Pairs to determine similar regions horizontally and (ii) Similarity function to determine vertically similar regions between the sequences of an alignment. Following the exploration of space search, the Pareto-optimal set is obtained by MOAFS which performs the optimal multiple sequence alignments for both fitness functions. The performance of MOAFS algorithm has been proved by comparing our algorithm with different progressive alignment methods, and other alignment methods based on evolutionary algorithms with single-objective and many-objective. The experiment results conducted on BAliBASE 2.0 and BAliBASE 3.0 benchmark confirm that the MOAFS algorithm provides a greater accuracy statistical significance in terms of SP or CS scores.

Impact of alignment algorithm on the estimation of pairwise genetic similarity of porcine reproductive and respiratory syndrome virus (PRRSV)

BackgroundPorcine reproductive and respiratory syndrome (PRRS) is a major threat to the swine industry. It is caused by the PRRS virus (PRRSV). Determination and comparison of the nucleotide sequences of PRRSV strains provides useful information in support of control initiatives or epidemiological studies on transmission patterns. The alignment of sequences is the first step in analyzing sequence data, with multiple algorithms being available, but little is known on the impact of this methodological choice. Here, a study was conducted to evaluate the impact of different alignment algorithms on the resulting aligned sequence dataset and on practical issues when applied to a large field database of PRRSV open reading frame (ORF) 5 sequences collected in Quebec, Canada, from 2010 to 2014. Five multiple sequence alignment programs were compared: Clustal W, Clustal Omega, Muscle, T-Coffee and MAFFT.ResultsThe resulting alignments showed very similar results in terms of average pairwise genetic similarity, proportion of pairwise comparisons having ≥97.5% genetic similarity and sum of pairs (SP) score, except for T-Coffee where increased length of aligned datasets as well as limitation to handle large datasets were observed.ConclusionsBased on efficiency at minimizing the number of gaps in different dataset sizes with default open gap values as well as the capability to handle a large number of sequences in a timely manner, the use of Clustal Omega might be recommended for the management of PRRSV extensive database for both research and surveillance purposes.

MAFFT-DASH: integrated protein sequence and structural alignment.

Here, we describe a web server that integrates structural alignments with the MAFFT multiple sequence alignment (MSA) tool. For this purpose, we have prepared a web-based Database of Aligned Structural Homologs (DASH), which provides structural alignments at the domain and chain levels for all proteins in the Protein Data Bank (PDB), and can be queried interactively or by a simple REST-like API. MAFFT-DASH integration can be invoked with a single flag on either the web (https://mafft.cbrc.jp/alignment/server/) or command-line versions of MAFFT. In our benchmarks using 878 cases from the BAliBase, HomFam, OXFam, Mattbench and SISYPHUS datasets, MAFFT-DASH showed 10–20% improvement over standard MAFFT for MSA problems with weak similarity, in terms of Sum-of-Pairs (SP), a measure of how well a program succeeds at aligning input sequences in comparison to a reference alignment. When MAFFT alignments were supplemented with homologous sequences, further improvement was observed. Potential applications of DASH beyond MSA enrichment include functional annotation through detection of remote homology and assembly of template libraries for homology modeling.

LACE CURVES

Two families of lace curves generated as partial Minkowski sum or product of pairs of curves in Euclidean 3D-space are presented in this paper. Some of their basic geometric properties are derived from the properties of Minkowski operation basic components. Illustrations of various interesting shapes resulting from the combinations of simple curve segments are included.

Additive invariants for knots, links and graphs in 3–manifolds

We define two new families of invariants for (3-manifold, graph) pairs which detect the unknot and are additive under connected sum of pairs and (-1/2)-additive under trivalent vertex sum of pairs. The first of these families is closely related to both bridge number and tunnel number. The second of these families is a variation and generalization of Gabai's width for knots in the 3-sphere. We give applications to the tunnel number and higher genus bridge number of connected sums of knots.

Product design of a lawn mower tool for agriculture

A lawn mower is a machine used to mow grass or plants. This machine is commonly used to tidy up the garden and also to clear the fields from grass or other types of grass. The commonly used lawn mowers are made of thin, hard and very sharp iron plates, so they can easily mow the grass. In the process of making the design of this lawn mower product, we first use the technique brainstorming to determine the characteristics of the product to be made, then draw conclusions from the brainstorming that has been collected. The technique is then carried out sampling by distributing an open and closed questionnaire to determine the type of product. After the open and closed questionnaires were finished, the conducted survey was market using technique sampling, and determined the validity and reliability test of main product with competitor product I, competitor II and competitor III. The step problem to the sub problem is determined to classify the objectives to be made on the design of the lawn mower products. The step sub-problem to the sub solution is performed to determine the Quality Function Deployment (QFD) of the product. The step sub solution to the solution is determined to generate and evaluate alternatives with the sum of matrix pairs between attributes.

The Total Eccentricity Sum of Non-adjacent Vertex Pairs in Graphs

Classical topological indices, such as Zagreb indices ( $$M_{1}$$ and $$M_2$$ ) and the well-studied eccentric connectivity index ( $$\xi ^{c}$$ ) directly or indirectly consider the total contribution of all edges in a graph. By considering the total degree sum of all non-adjacent vertex pairs in a graph, Ashrafi et al. (Discrete Appl Math 158:1571–1578, 2010) proposed two new Zagreb-type indices, namely the first Zagreb coindex ( $$\overline{M}_{1}$$ ) and second Zagreb coindex ( $$\overline{M}_{2}$$ ), respectively. Motivated by Ashrafi et al., we consider the total eccentricity sum of all non-adjacent vertex pairs, which we call the eccentric connectivity coindex ( $$\overline{\xi }^{c}$$ ), of a connected graph. In this paper, we study the extremal problems of $$\overline{\xi }^{c}$$ for connected graphs of given order, connected graphs of given order and size, and the trees, unicyclic graphs, bipartite graphs containing cycles and triangle-free graphs of given order, respectively. Additionally, we establish various lower bounds for $$\overline{\xi }^{c}$$ in terms of several other graph parameters.