A model of money income diffusion is constructed taking into account the processes of social comparison and the development of the income formation spatial structure. To implement such model, the analytical theory of continued fractions is used and the corresponding differential equation solution is found in the form of a formal functional continued fraction. The values of the approach fractions of a continuous fraction describing the dynamics of changes in the level of money income give an approximation of the real values with almost predetermined, arbitrarily high accuracy. This allowed us to qualitatively describe the general dynamics of the money income diffusion process.
{"title":"Model of money income diffusion in the European integration context","authors":"L. Dmytryshyn, M. Dmytryshyn, A. Olejnik","doi":"10.23939/mmc2023.02.583","DOIUrl":"https://doi.org/10.23939/mmc2023.02.583","url":null,"abstract":"A model of money income diffusion is constructed taking into account the processes of social comparison and the development of the income formation spatial structure. To implement such model, the analytical theory of continued fractions is used and the corresponding differential equation solution is found in the form of a formal functional continued fraction. The values of the approach fractions of a continuous fraction describing the dynamics of changes in the level of money income give an approximation of the real values with almost predetermined, arbitrarily high accuracy. This allowed us to qualitatively describe the general dynamics of the money income diffusion process.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68768831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Graph mining techniques have received a lot of attention to discover important subgraphs based on certain criteria. These techniques have become increasingly important due to the growing number of applications that rely on graph-based data. Some examples are: (i) microarray data analysis in bioinformatics, (ii) transportation network analysis, (iii) social network analysis. In this study, we propose a graph decomposition algorithm using the non-dominance criterion to identify important subgraphs based on two characteristics: edge connectivity and diameter. The proposed method uses a multi-objective optimization approach to maximize the edge connectivity and minimize the diameter. In a similar vein, identifying communities within a network can improve our comprehension of the network's characteristics and properties. Therefore, the detection of community structures in networks has been extensively studied. As a result, in this paper an innovative community detection method is presented based on our approach. The performance of the proposed technique is examined on both real-life and synthetically generated data sets.
{"title":"Important subgraph discovery using non-dominance criterion","authors":"T. Ouaderhman, Hasna Chamlal, A. Oubaouzine","doi":"10.23939/mmc2023.03.733","DOIUrl":"https://doi.org/10.23939/mmc2023.03.733","url":null,"abstract":"Graph mining techniques have received a lot of attention to discover important subgraphs based on certain criteria. These techniques have become increasingly important due to the growing number of applications that rely on graph-based data. Some examples are: (i) microarray data analysis in bioinformatics, (ii) transportation network analysis, (iii) social network analysis. In this study, we propose a graph decomposition algorithm using the non-dominance criterion to identify important subgraphs based on two characteristics: edge connectivity and diameter. The proposed method uses a multi-objective optimization approach to maximize the edge connectivity and minimize the diameter. In a similar vein, identifying communities within a network can improve our comprehension of the network's characteristics and properties. Therefore, the detection of community structures in networks has been extensively studied. As a result, in this paper an innovative community detection method is presented based on our approach. The performance of the proposed technique is examined on both real-life and synthetically generated data sets.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68769033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The COVID-19 is a major danger that threatens the whole world. In this context, mathematical modeling is a very powerful tool for knowing more about how such a disease is transmitted within a host population of humans. In this regard, we propose in the current study a stochastic epidemic model that describes the COVID-19 dynamics under the application of quarantine and coverage media strategies, and we give a rigorous mathematical analysis of this model to obtain an overview of COVID-19 dissemination behavior.
{"title":"A mathematical study of the COVID-19 propagation through a stochastic epidemic model","authors":"D. Kiouach, S. E. A. El-idrissi, Y. Sabbar","doi":"10.23939/mmc2023.03.784","DOIUrl":"https://doi.org/10.23939/mmc2023.03.784","url":null,"abstract":"The COVID-19 is a major danger that threatens the whole world. In this context, mathematical modeling is a very powerful tool for knowing more about how such a disease is transmitted within a host population of humans. In this regard, we propose in the current study a stochastic epidemic model that describes the COVID-19 dynamics under the application of quarantine and coverage media strategies, and we give a rigorous mathematical analysis of this model to obtain an overview of COVID-19 dissemination behavior.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68769130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Water management is crucial for agriculture, as it is the primary source of irrigation for crops. Effective water management can help farmers to improve crop yields, reduce water waste, and increase resilience to drought. This can include practices such as precision irrigation, using sensors and technology to deliver water only where and when it is needed, and conservation tillage, which helps to reduce evaporation and retain moisture in the soil. Additionally, farmers can implement water-saving techniques such as crop selection, crop rotation, and soil conservation to reduce their water use. Thus, studies aimed at saving the use of water in the irrigation process have increased over the years. This research suggests using advanced technologies such as IoT and AI to manage irrigation in a way that maximizes crop yield while minimizing water consumption, in line with Agriculture 4.0 principles. Using sensors in controlled environments, data on plant growth was quickly collected. Thanks to the analysis and training of these data between several models among them, we find the K-Nearest Neighbors (KNN), Support Vector Machine (SVM) and Naive Bayes (NB), the KNN has shown interesting results with 98.4 accuracy rate and 0.016 root mean squared error (RMSE).
{"title":"Implementation of smart irrigation using IoT and Artificial Intelligence","authors":"Y. Tace, S. Elfilali, M. Tabaa, C. Leghris","doi":"10.23939/mmc2023.02.575","DOIUrl":"https://doi.org/10.23939/mmc2023.02.575","url":null,"abstract":"Water management is crucial for agriculture, as it is the primary source of irrigation for crops. Effective water management can help farmers to improve crop yields, reduce water waste, and increase resilience to drought. This can include practices such as precision irrigation, using sensors and technology to deliver water only where and when it is needed, and conservation tillage, which helps to reduce evaporation and retain moisture in the soil. Additionally, farmers can implement water-saving techniques such as crop selection, crop rotation, and soil conservation to reduce their water use. Thus, studies aimed at saving the use of water in the irrigation process have increased over the years. This research suggests using advanced technologies such as IoT and AI to manage irrigation in a way that maximizes crop yield while minimizing water consumption, in line with Agriculture 4.0 principles. Using sensors in controlled environments, data on plant growth was quickly collected. Thanks to the analysis and training of these data between several models among them, we find the K-Nearest Neighbors (KNN), Support Vector Machine (SVM) and Naive Bayes (NB), the KNN has shown interesting results with 98.4 accuracy rate and 0.016 root mean squared error (RMSE).","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68769303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we determine the continuous solutions of the integral functional equation of Stetkær's extension of the sine addition law ∫Gf(xyt)dμ(t)=f(x)χ1(y)+χ2(x)f(y), x,y∈G, where f:G→C, G is a locally compact Hausdorff group, μ is a regular, compactly supported, complex-valued Borel measure on G and χ1, χ2 are fixed characters on G.
{"title":"Integral of an extension of the sine addition formula","authors":"M. Tial","doi":"10.23939/mmc2023.03.833","DOIUrl":"https://doi.org/10.23939/mmc2023.03.833","url":null,"abstract":"In this paper, we determine the continuous solutions of the integral functional equation of Stetkær's extension of the sine addition law ∫Gf(xyt)dμ(t)=f(x)χ1(y)+χ2(x)f(y), x,y∈G, where f:G→C, G is a locally compact Hausdorff group, μ is a regular, compactly supported, complex-valued Borel measure on G and χ1, χ2 are fixed characters on G.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68769437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Since the first computer, researchers always try to simulate human behave. For Chatbots, one of the first goals is to interact with the user like a human using Natural Language. For Health chatbots, another goal is as much important: be able to provide the correct answer to the user request. Over Years, many health chatbots have been developed for many fields such as cancer, diagnosis orientation, psychiatrics, etc. breastfeeding companion are, however, rare (only two breastfeeding chatbots). In this paper, we have developed ALMA, a Breastfeeding Chatbot (BC) that can converse with a breastfeeding mom throw natural language understanding (NLU) and natural language generation (NLG), and provide her – breastfeeding mom – with the relevant information using AIML knowledge base and CNN pre-trained model. We made ALMA available for a normal WhatsApp conversation throw Twilio API. ALMA was tested by volunteering breastfeeding moms and the results validated by breastfeeding consult.
{"title":"ALMA: Machine learning breastfeeding chatbot","authors":"K. Achtaich, N. Achtaich, F. Z. Fagroud, H. Toumi","doi":"10.23939/mmc2023.02.487","DOIUrl":"https://doi.org/10.23939/mmc2023.02.487","url":null,"abstract":"Since the first computer, researchers always try to simulate human behave. For Chatbots, one of the first goals is to interact with the user like a human using Natural Language. For Health chatbots, another goal is as much important: be able to provide the correct answer to the user request. Over Years, many health chatbots have been developed for many fields such as cancer, diagnosis orientation, psychiatrics, etc. breastfeeding companion are, however, rare (only two breastfeeding chatbots). In this paper, we have developed ALMA, a Breastfeeding Chatbot (BC) that can converse with a breastfeeding mom throw natural language understanding (NLU) and natural language generation (NLG), and provide her – breastfeeding mom – with the relevant information using AIML knowledge base and CNN pre-trained model. We made ALMA available for a normal WhatsApp conversation throw Twilio API. ALMA was tested by volunteering breastfeeding moms and the results validated by breastfeeding consult.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68768522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
O. Nakonechnyi, G. Kudin, P. Zinko, T. Zinko, Y. Shusharin
The article focuses on the linear estimation problems of unknown rectangular matrices, which are solutions of linear matrix equations with the right-hand sides belonging to bounded sets. The random errors of the observation vector have zero mathematical expectation, and the correlation matrix is unknown and belongs to one of two bounded sets. Explicit expressions of the guaranteed root mean square errors of estimates for linear operators acting from the space of rectangular matrices into some vector space are given. Guaranteed quasi-minimax root mean square errors of linear estimates are obtained. As the test examples, two options for solving the problem are considered, taking into account small perturbations of known observation matrices.
{"title":"Guaranteed root mean square estimates of linear matrix equations solutions under conditions of uncertainty","authors":"O. Nakonechnyi, G. Kudin, P. Zinko, T. Zinko, Y. Shusharin","doi":"10.23939/mmc2023.02.474","DOIUrl":"https://doi.org/10.23939/mmc2023.02.474","url":null,"abstract":"The article focuses on the linear estimation problems of unknown rectangular matrices, which are solutions of linear matrix equations with the right-hand sides belonging to bounded sets. The random errors of the observation vector have zero mathematical expectation, and the correlation matrix is unknown and belongs to one of two bounded sets. Explicit expressions of the guaranteed root mean square errors of estimates for linear operators acting from the space of rectangular matrices into some vector space are given. Guaranteed quasi-minimax root mean square errors of linear estimates are obtained. As the test examples, two options for solving the problem are considered, taking into account small perturbations of known observation matrices.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68768513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. Musii, U. Zhydyk, Khrystyna Drohomyretska, I. Svidrak, V. Shynder
A rectangular isotropic two-layer plate of an irregular structure is considered, the edges of which are freely supported, and a constant temperature is maintained on them. Two-dimensional Kirchhoff-type thermoelasticity equations and two-dimensional heat equations written for an inhomogeneous material were used to study the temperature stresses in the plate. Using the method of double trigonometric series in spatial variables and the Laplace integral transformation over time, the general solutions of boundary value problems of thermoelasticity and heat conductivity for this plate under the action of a locally distributed temperature field specified at the initial moment of time are written down. The normal stresses in the layers of the plate are numerically analyzed depending on the geometric parameters, heat transfer coefficient, and time.
{"title":"Temperature stresses in a rectangular two-layer plate under the action of a locally distributed temperature field","authors":"R. Musii, U. Zhydyk, Khrystyna Drohomyretska, I. Svidrak, V. Shynder","doi":"10.23939/mmc2023.02.435","DOIUrl":"https://doi.org/10.23939/mmc2023.02.435","url":null,"abstract":"A rectangular isotropic two-layer plate of an irregular structure is considered, the edges of which are freely supported, and a constant temperature is maintained on them. Two-dimensional Kirchhoff-type thermoelasticity equations and two-dimensional heat equations written for an inhomogeneous material were used to study the temperature stresses in the plate. Using the method of double trigonometric series in spatial variables and the Laplace integral transformation over time, the general solutions of boundary value problems of thermoelasticity and heat conductivity for this plate under the action of a locally distributed temperature field specified at the initial moment of time are written down. The normal stresses in the layers of the plate are numerically analyzed depending on the geometric parameters, heat transfer coefficient, and time.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68768626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we propose a study of the mean annual rainfall time series in order to evaluate the climate changes pattern over time. If the analysis of this time series is carried out correctly, it can contribute to improve planning and policy development. That is why we consider the problem of mathematical modeling and analysis of the mean annual rainfall of Morocco between 1901 and 2020 using descriptive statistics, structure changes analysis, spectral analysis and a nonlinear Exponential Autoregressive (EXPAR) processes to reproduce the behavior of this time series. The results indicate three main breakpoints and show that the time series has a remarkable cycles about 60, 18 and 6 years with a global decrease tendency about 0.56 mm per year. Furthermore, we have justified the choice of using a non-linear EXPAR processes rather than a linear traditional one and provided a good fitted EXPAR model.
在这项工作中，我们建议研究年平均降雨量时间序列，以评估气候随时间的变化模式。如果对这个时间序列进行正确的分析，它可以有助于改进规划和政策制定。这就是为什么我们考虑摩洛哥1901年至2020年平均年降雨量的数学建模和分析问题，使用描述性统计、结构变化分析、光谱分析和非线性指数自回归(EXPAR)过程来重现该时间序列的行为。结果表明，该时间序列在60、18和6 a左右存在显著的周期变化，全球下降趋势约为0.56 mm /年。此外，我们已经证明了使用非线性EXPAR过程而不是线性传统的EXPAR过程的选择是合理的，并提供了一个很好的拟合EXPAR模型。
{"title":"Mathematical modeling and statistical analysis of Moroccan mean annual rainfall using EXPAR processes","authors":"N. Azouagh, S. El Melhaoui","doi":"10.23939/mmc2023.03.607","DOIUrl":"https://doi.org/10.23939/mmc2023.03.607","url":null,"abstract":"In this work, we propose a study of the mean annual rainfall time series in order to evaluate the climate changes pattern over time. If the analysis of this time series is carried out correctly, it can contribute to improve planning and policy development. That is why we consider the problem of mathematical modeling and analysis of the mean annual rainfall of Morocco between 1901 and 2020 using descriptive statistics, structure changes analysis, spectral analysis and a nonlinear Exponential Autoregressive (EXPAR) processes to reproduce the behavior of this time series. The results indicate three main breakpoints and show that the time series has a remarkable cycles about 60, 18 and 6 years with a global decrease tendency about 0.56 mm per year. Furthermore, we have justified the choice of using a non-linear EXPAR processes rather than a linear traditional one and provided a good fitted EXPAR model.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68768853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Machine learning algorithms have become very frequently used in natural language processing, notably sentiment analysis, which helps determine the general feeling carried within a text. Among these algorithms, Support Vector Machines have proven powerful classifiers especially in such a task, when their performance is assessed through accuracy score and f1-score. However, they remain slow in terms of training, thus making exhaustive grid-search experimentations very time-consuming. In this paper, we present an observed pattern in SVM's accuracy, and f1-score approximated with a Lagrange polynomial.
{"title":"Towards a polynomial approximation of support vector machine accuracy applied to Arabic tweet sentiment analysis","authors":"Z. Banou, S. Elfilali, H. Benlahmar","doi":"10.23939/mmc2023.02.511","DOIUrl":"https://doi.org/10.23939/mmc2023.02.511","url":null,"abstract":"Machine learning algorithms have become very frequently used in natural language processing, notably sentiment analysis, which helps determine the general feeling carried within a text. Among these algorithms, Support Vector Machines have proven powerful classifiers especially in such a task, when their performance is assessed through accuracy score and f1-score. However, they remain slow in terms of training, thus making exhaustive grid-search experimentations very time-consuming. In this paper, we present an observed pattern in SVM's accuracy, and f1-score approximated with a Lagrange polynomial.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68768980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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