Pub Date : 2023-10-01DOI: 10.46793/match.91-2.415k
Muhammad Asif Khan, Qamar Din
This article delves into an investigation of the dynamic behavior exhibited by a fractional order cubic autocatalator chemical reaction model. Specifically, our focus lies on exploring codimension-one bifurcations associated with period-doubling bifurcation and Neimark-Sacker bifurcation. Additionally, we undertake an analysis of codimension-two bifurcations linked to resonances of the types 1:2, 1:3, and 1:4. To achieve these outcomes, we employ the normal form method and bifurcation theory. The results are presented through comprehensive numerical simulations, encompassing visual representations such as phase portraits, two-parameter bifurcation diagrams, and maximum Lyapunov exponents diagrams. These simulations aptly examine the behavior of a system governed by two distinct parameters that vary within a three-dimensional space. Furthermore, the simulations effectively illustrate the theoretical findings while providing valuable insights into the underlying dynamics.
{"title":"Codimension-One and Codimension-Two Bifurcations of a Fractional-Order Cubic Autocatalator Chemical Reaction System","authors":"Muhammad Asif Khan, Qamar Din","doi":"10.46793/match.91-2.415k","DOIUrl":"https://doi.org/10.46793/match.91-2.415k","url":null,"abstract":"This article delves into an investigation of the dynamic behavior exhibited by a fractional order cubic autocatalator chemical reaction model. Specifically, our focus lies on exploring codimension-one bifurcations associated with period-doubling bifurcation and Neimark-Sacker bifurcation. Additionally, we undertake an analysis of codimension-two bifurcations linked to resonances of the types 1:2, 1:3, and 1:4. To achieve these outcomes, we employ the normal form method and bifurcation theory. The results are presented through comprehensive numerical simulations, encompassing visual representations such as phase portraits, two-parameter bifurcation diagrams, and maximum Lyapunov exponents diagrams. These simulations aptly examine the behavior of a system governed by two distinct parameters that vary within a three-dimensional space. Furthermore, the simulations effectively illustrate the theoretical findings while providing valuable insights into the underlying dynamics.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"132 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136093345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.46793/match.91-1.135y
Mingao Yuan
Topological indices play a significant role in mathematical chemistry. Given a graph $mathcal{G}$ with vertex set $mathcal{V}={1,2,dots,n}$ and edge set $mathcal{E}$, let $d_i$ be the degree of node $i$. The degree-based topological index is defined as $mathcal{I}_n=$ $sum_{{i,j}in mathcal{E}}f(d_i,d_j)$, where $f(x,y)$ is a symmetric function. In this paper, we investigate the asymptotic distribution of the degree-based topological indices of a heterogeneous ErdH{o}s-R'{e}nyi random graph. We show that after suitably centered and scaled, the topological indices converges in distribution to the standard normal distribution. Interestingly, we find that the general Randi'{c} index with $f(x,y)=(xy)^{tau}$ for a constant $tau$ exhibits a phase change at $tau=-frac{1}{2}$.
{"title":"Asymptotic Distribution of Degree-Based Topological Indices","authors":"Mingao Yuan","doi":"10.46793/match.91-1.135y","DOIUrl":"https://doi.org/10.46793/match.91-1.135y","url":null,"abstract":"Topological indices play a significant role in mathematical chemistry. Given a graph $mathcal{G}$ with vertex set $mathcal{V}={1,2,dots,n}$ and edge set $mathcal{E}$, let $d_i$ be the degree of node $i$. The degree-based topological index is defined as $mathcal{I}_n=$ $sum_{{i,j}in mathcal{E}}f(d_i,d_j)$, where $f(x,y)$ is a symmetric function. In this paper, we investigate the asymptotic distribution of the degree-based topological indices of a heterogeneous ErdH{o}s-R'{e}nyi random graph. We show that after suitably centered and scaled, the topological indices converges in distribution to the standard normal distribution. Interestingly, we find that the general Randi'{c} index with $f(x,y)=(xy)^{tau}$ for a constant $tau$ exhibits a phase change at $tau=-frac{1}{2}$.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"125 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136056274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.46793/match.91-1.235s
Shashwath S Shetty, K. Arathi Bhat
Recently, the Sombor index of a graph was defined, and a large amount of study was conducted quite quickly. It has been proposed to generalise the idea of vertex degree-based topological indices from graphs to hypergraphs. We give the bounds for the Sombor index of hypergraphs and bipartite hypergraphs using the total number of vertices in the graph. Hypertrees are the connected hypergraph, where the removal of any hyperedge disconnects the hypergraph. A -uniform hypergraph is a hypergraph with k vertices in every hyperedge and a linear hypergraph is a hypergraph where any two hyperedges can have at most one vertex in common. We give the extremal hypergraphs among the class of uniform, linear and general hypertrees. The expected generalisation of some vertex degree based topological indices from graphs to hypergraphs has been listed.
{"title":"Sombor Index of Hypergraphs","authors":"Shashwath S Shetty, K. Arathi Bhat","doi":"10.46793/match.91-1.235s","DOIUrl":"https://doi.org/10.46793/match.91-1.235s","url":null,"abstract":"Recently, the Sombor index of a graph was defined, and a large amount of study was conducted quite quickly. It has been proposed to generalise the idea of vertex degree-based topological indices from graphs to hypergraphs. We give the bounds for the Sombor index of hypergraphs and bipartite hypergraphs using the total number of vertices in the graph. Hypertrees are the connected hypergraph, where the removal of any hyperedge disconnects the hypergraph. A -uniform hypergraph is a hypergraph with k vertices in every hyperedge and a linear hypergraph is a hypergraph where any two hyperedges can have at most one vertex in common. We give the extremal hypergraphs among the class of uniform, linear and general hypertrees. The expected generalisation of some vertex degree based topological indices from graphs to hypergraphs has been listed.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136056379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.46793/match.91-1.079k
Vitaliy Kurlin
The most fundamental model of a molecule is a cloud of unordered atoms, even without chemical bonds that can depend on thresholds for distances and angles. The strongest equivalence between clouds of atoms is rigid motion, which is a composition of translations and rotations. The existing datasets of experimental and simulated molecules require a continuous quantification of similarity in terms of a distance metric. While clouds of m ordered points were continuously classified by Lagrange’s quadratic forms (distance matrices or Gram matrices), their extensions to m unordered points are impractical due to the exponential number of m! permutations. We propose new metrics that are continuous in general position and are computable in a polynomial time in the number m of unordered points in any Euclidean space of a fixed dimension n.
{"title":"Polynomial-Time Algorithms for Continuous Metrics on Atomic Clouds of Unordered Points","authors":"Vitaliy Kurlin","doi":"10.46793/match.91-1.079k","DOIUrl":"https://doi.org/10.46793/match.91-1.079k","url":null,"abstract":"The most fundamental model of a molecule is a cloud of unordered atoms, even without chemical bonds that can depend on thresholds for distances and angles. The strongest equivalence between clouds of atoms is rigid motion, which is a composition of translations and rotations. The existing datasets of experimental and simulated molecules require a continuous quantification of similarity in terms of a distance metric. While clouds of m ordered points were continuously classified by Lagrange’s quadratic forms (distance matrices or Gram matrices), their extensions to m unordered points are impractical due to the exponential number of m! permutations. We propose new metrics that are continuous in general position and are computable in a polynomial time in the number m of unordered points in any Euclidean space of a fixed dimension n.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136056386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.46793/match.91-2.307m
Muhammad Marwan, Anda Xiong, Maoan Han, Ramla Khan
This research examines a chaotic chemical reaction system based on the variation of the Lorenz system. This study demonstrates that although the first phase portraits of the chemical models under consideration and the Lorenz models are comparable, they do not fully follow all the features of the Lorenz system. Questions about the existence of fractals in systems based on chemical reactions are addressed in the current work. Moreover, we have worked on the hidden information inside in each wings of a chaotic system generated through fractal process, for the first time, with the aid of basin for fractals. Additionally, we looked closely at the dynamics of the model across the basin, which revealed additional details regarding the existence of hidden and cyclic attractors inside each wing. We also produced multi-wings for system (1) in the current study, demonstrating in a general manner that the number of cyclic attractors increase in a direct relation to the number of wings. Moreover, Julia approach is used to accomplish the work of multi-wings, whereas for searching cyclic attractors inside each extra wing, we have used fifteen million initial conditions and compiled them as a basin set. The data generated in this work is also provided within this paper for the ease of readers.
{"title":"Chaotic Behavior of Lorenz-Based Chemical System under the Influence of Fractals","authors":"Muhammad Marwan, Anda Xiong, Maoan Han, Ramla Khan","doi":"10.46793/match.91-2.307m","DOIUrl":"https://doi.org/10.46793/match.91-2.307m","url":null,"abstract":"This research examines a chaotic chemical reaction system based on the variation of the Lorenz system. This study demonstrates that although the first phase portraits of the chemical models under consideration and the Lorenz models are comparable, they do not fully follow all the features of the Lorenz system. Questions about the existence of fractals in systems based on chemical reactions are addressed in the current work. Moreover, we have worked on the hidden information inside in each wings of a chaotic system generated through fractal process, for the first time, with the aid of basin for fractals. Additionally, we looked closely at the dynamics of the model across the basin, which revealed additional details regarding the existence of hidden and cyclic attractors inside each wing. We also produced multi-wings for system (1) in the current study, demonstrating in a general manner that the number of cyclic attractors increase in a direct relation to the number of wings. Moreover, Julia approach is used to accomplish the work of multi-wings, whereas for searching cyclic attractors inside each extra wing, we have used fifteen million initial conditions and compiled them as a basin set. The data generated in this work is also provided within this paper for the ease of readers.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136159905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.46793/match.91-2.287g
Ivan Gutman, Boris Furtula, Izudin Redžepović
{"title":"On Topological Indices and Their Reciprocals","authors":"Ivan Gutman, Boris Furtula, Izudin Redžepović","doi":"10.46793/match.91-2.287g","DOIUrl":"https://doi.org/10.46793/match.91-2.287g","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136159855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Palladium (Pd)-catalyzed cross coupling reactions are of great significance in organic synthesis. However, the reaction route is more complex, time-consuming and costly. For addressing the above problems, a model-related feature selection strategy is introduced, focusing on iterative optimization of feature description and prediction to guide and strengthen each other. Then, we combine the lightweight convolution neural network (CNN) driven by attention mechanism with CatBoost to build an intelligent chemical synthesis reaction analysis model-ChemCNet. Moreover, we conduct the interpretability analysis based on ChemCNet model. The results show that ChemCNet model has achieved relatively high prediction accuracy and generalization, and it is helpful to provide reliable decision-making information for the experimenter or institution.
{"title":"ChemCNet: An Explainable Integrated Model for Intelligent Analyzing Chemistry Synthesis Reactions","authors":"Lanfeng Wang, Hengzhe Wang, Shuoshi Liu, Zixin Li, Yaping Yu, Yun Chai, Xiaohui Yang","doi":"10.46793/match.91-1.041w","DOIUrl":"https://doi.org/10.46793/match.91-1.041w","url":null,"abstract":"Palladium (Pd)-catalyzed cross coupling reactions are of great significance in organic synthesis. However, the reaction route is more complex, time-consuming and costly. For addressing the above problems, a model-related feature selection strategy is introduced, focusing on iterative optimization of feature description and prediction to guide and strengthen each other. Then, we combine the lightweight convolution neural network (CNN) driven by attention mechanism with CatBoost to build an intelligent chemical synthesis reaction analysis model-ChemCNet. Moreover, we conduct the interpretability analysis based on ChemCNet model. The results show that ChemCNet model has achieved relatively high prediction accuracy and generalization, and it is helpful to provide reliable decision-making information for the experimenter or institution.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136056272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.46793/match.91-2.489a
Noor A’lawiah Abd Aziz, Nader Jafari Rad, Hailiza Kamarulhaili
{"title":"New Bounds on the Energy of a Graph","authors":"Noor A’lawiah Abd Aziz, Nader Jafari Rad, Hailiza Kamarulhaili","doi":"10.46793/match.91-2.489a","DOIUrl":"https://doi.org/10.46793/match.91-2.489a","url":null,"abstract":"","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"238 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136093343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.46793/match.91-2.485t
Liang Wen Tang, Juan Liu, Shuangwei Qin
The energy E(G) of a graph G is the sum of the absolute values of all eigenvalues of G. Two graphs of the same order are said to be equienergetic if their energies are equal. As pointed out by Gutman, it is not known how to systematically construct any pair of equienergetic, non-cospectral trees until now. Inspired by the research of integral trees, we proposed a construction of infinite pairs of equienergetic trees of diameter 4.
{"title":"Construction of Equienergetic Trees","authors":"Liang Wen Tang, Juan Liu, Shuangwei Qin","doi":"10.46793/match.91-2.485t","DOIUrl":"https://doi.org/10.46793/match.91-2.485t","url":null,"abstract":"The energy E(G) of a graph G is the sum of the absolute values of all eigenvalues of G. Two graphs of the same order are said to be equienergetic if their energies are equal. As pointed out by Gutman, it is not known how to systematically construct any pair of equienergetic, non-cospectral trees until now. Inspired by the research of integral trees, we proposed a construction of infinite pairs of equienergetic trees of diameter 4.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136159871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.46793/match.91-1.109z
Shengli Zhang, Ya Zhao, Yunyun Liang
In recent years, bacterial resistance becomes a serious problem due to the abuse of antibiotics. Antimicrobial peptides (AMPs) have rapidly emerged as the best alternative to antibiotics because of their ability to rapidly target bacteria, fungi, viruses, and cancer cells and counteract the toxins they produce. In this study, a two-branch ensemble framework is proposed to identify AMPs, which integrates extreme gradient boosting (XGBoost) and bidirectional long short-term memory network (Bi-LSTM) with attention mechanism to form a stronger model. First, one-hot coding and -mer are used to represent the sequence features. Then, the feature vectors are input into the two base classifiers respectively to obtain two predicted values. Finally, the prediction results are obtained by compromise. As one of the classical machine learning methods, XGBoost has strong stability and can adapt to datasets of different sizes. Bi-LSTM recurses for each peptide from N-terminal to C-terminal and C-terminal to N-terminal, respectively. As the context information is provided, the model can make more accurate prediction. Our method achieves higher or highly comparable results across the eight independent test datasets. The ACC values of XUAMP, YADAMP, DRAMP, CAMP, LAMP, APD3, dbAMP, and DBAASP are 77.9%, 98.5%, 72.5%, 99.8%, 83.0%, 92.4%, 87.5%, and 84.6%, respectively. This shows that the two-branch ensemble structure is feasible and has strong generalization. The codes and datasets are accessible at https://github.com/z11code/AMP-EF.
{"title":"AMP-EF: An Ensemble Framework of Extreme Gradient Boosting and Bidirectional Long Short-Term Memory Network for Identifying Antimicrobial Peptides","authors":"Shengli Zhang, Ya Zhao, Yunyun Liang","doi":"10.46793/match.91-1.109z","DOIUrl":"https://doi.org/10.46793/match.91-1.109z","url":null,"abstract":"In recent years, bacterial resistance becomes a serious problem due to the abuse of antibiotics. Antimicrobial peptides (AMPs) have rapidly emerged as the best alternative to antibiotics because of their ability to rapidly target bacteria, fungi, viruses, and cancer cells and counteract the toxins they produce. In this study, a two-branch ensemble framework is proposed to identify AMPs, which integrates extreme gradient boosting (XGBoost) and bidirectional long short-term memory network (Bi-LSTM) with attention mechanism to form a stronger model. First, one-hot coding and -mer are used to represent the sequence features. Then, the feature vectors are input into the two base classifiers respectively to obtain two predicted values. Finally, the prediction results are obtained by compromise. As one of the classical machine learning methods, XGBoost has strong stability and can adapt to datasets of different sizes. Bi-LSTM recurses for each peptide from N-terminal to C-terminal and C-terminal to N-terminal, respectively. As the context information is provided, the model can make more accurate prediction. Our method achieves higher or highly comparable results across the eight independent test datasets. The ACC values of XUAMP, YADAMP, DRAMP, CAMP, LAMP, APD3, dbAMP, and DBAASP are 77.9%, 98.5%, 72.5%, 99.8%, 83.0%, 92.4%, 87.5%, and 84.6%, respectively. This shows that the two-branch ensemble structure is feasible and has strong generalization. The codes and datasets are accessible at https://github.com/z11code/AMP-EF.","PeriodicalId":51115,"journal":{"name":"Match-Communications in Mathematical and in Computer Chemistry","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136056462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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