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Mathematics
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Mathematical Modeling, Data Analysis and Artificial Intelligence in Interdisciplinary Research
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Mathematical Modeling, Data Analysis and Artificial Intelligence in Interdisciplinary Research

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 14642

Special Issue Editors

Prof. Dr. Petr Nikitin

E-Mail Website
Guest Editor
Department of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, 125167 Moscow, Russia
Interests: artificial intelligence in education; data analysis in social; educational and economic research; machine learning; deep learning; reinforcement learning; predictive analytics
Prof. Dr. Sergey Korchagin

E-Mail Website
Guest Editor
Department of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, 125167 Moscow, Russia
Interests: machine learning; data analysis; mathematical modeling; numerical methods; software systems; mathematical physics
Prof. Dr. Sergey Grigoriev

E-Mail Website
Guest Editor
Professor, Department of Informatics, Management and Technology, Moscow City Pedagogical University, 129226 Moscow, Russia
Interests: mathematical methods in scientific research; robotic educational systems; mathematical logic; data analysis and machine learning; mathematical modeling

Special Issue Information

Dear Colleagues,

This Special Issue is devoted to researching mathematical modeling, data analyses, and artificial intelligence (integral parts of scientific research), especially if they are interdisciplinary, their us in applied interdisciplinary tasks and research, as well as application methods, predictive analytics, machine and deep learning, reinforcement learning; the development of recommendation systems in the fields of education, psychology, and social and economic sciences; agriculture, physics, chemistry, and other sciences. In addition, articles related to theoretical and computational studies of mathematical modeling and artificial intelligence emphasizing models, optimization, data analyses, and machine learning are welcome.

Prof. Dr. Petr Nikitin
Prof. Dr. Sergey Korchagin
Prof. Dr. Sergey Grigoriev
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical modeling
  • artificial intelligence
  • data analysis
  • predictive analytics
  • interdisciplinary research
  • neural networks
  • deep learning
  • machine learning
  • optimization algorithms
  • reinforcement learning
  • recommendation systems

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Published Papers (6 papers)

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Research

19 pages, 7293 KiB  
Article
Robotic-Arm-Based Force Control by Deep Deterministic Policy Gradient in Neurosurgical Practice
by Ibai Inziarte-Hidalgo, Erik Gorospe, Ekaitz Zulueta, Jose Manuel Lopez-Guede, Unai Fernandez-Gamiz and Saioa Etxebarria
Mathematics 2023, 11(19), 4133; https://doi.org/10.3390/math11194133 - 30 Sep 2023
Viewed by 943
Abstract
This research continues the previous work “Robotic-Arm-Based Force Control in Neurosurgical Practice”. In that study, authors acquired an optimal control arm speed shape for neurological surgery which minimized a cost function that uses an adaptive scheme to determine the brain tissue force. At [...] Read more.
This research continues the previous work “Robotic-Arm-Based Force Control in Neurosurgical Practice”. In that study, authors acquired an optimal control arm speed shape for neurological surgery which minimized a cost function that uses an adaptive scheme to determine the brain tissue force. At the end, the authors proposed the use of reinforcement learning, more specifically Deep Deterministic Policy Gradient (DDPG), to create an agent that could obtain the optimal solution through self-training. In this article, that proposal is carried out by creating an environment, agent (actor and critic), and reward function, that obtain a solution for our problem. However, we have drawn conclusions for potential future enhancements. Additionally, we analyzed the results and identified mistakes that can be improved upon in the future, such as exploring the use of varying desired distances of retraction to enhance training. Full article
(This article belongs to the Special Issue Mathematical Modeling, Data Analysis and Artificial Intelligence in Interdisciplinary Research)
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16 pages, 1360 KiB  
Article
POFCM: A Parallel Fuzzy Clustering Algorithm for Large Datasets
by Joaquín Pérez-Ortega, César David Rey-Figueroa, Sandra Silvia Roblero-Aguilar, Nelva Nely Almanza-Ortega, Crispín Zavala-Díaz, Salomón García-Paredes and Vanesa Landero-Nájera
Mathematics 2023, 11(8), 1920; https://doi.org/10.3390/math11081920 - 19 Apr 2023
Cited by 3 | Viewed by 1469
Abstract
Clustering algorithms have proven to be a useful tool to extract knowledge and support decision making by processing large volumes of data. Hard and fuzzy clustering algorithms have been used successfully to identify patterns and trends in many areas, such as finance, healthcare, [...] Read more.
Clustering algorithms have proven to be a useful tool to extract knowledge and support decision making by processing large volumes of data. Hard and fuzzy clustering algorithms have been used successfully to identify patterns and trends in many areas, such as finance, healthcare, and marketing. However, these algorithms significantly increase their solution time as the size of the datasets to be solved increase, making their use unfeasible. In this sense, the parallel processing of algorithms has proven to be an efficient alternative to reduce their solution time. It has been established that the parallel implementation of algorithms requires its redesign to optimise the hardware resources of the platform that will be used. In this article, we propose a new parallel implementation of the Hybrid OK-Means Fuzzy C-Means (HOFCM) algorithm, which is an efficient variant of Fuzzy C-Means, in OpenMP. An advantage of using OpenMP is its scalability. The efficiency of the implementation is compared against the HOFCM algorithm. The experimental results of processing large real and synthetic datasets show that our implementation tends to more efficiently solve instances with a large number of clusters and dimensions. Additionally, the implementation shows excellent results concerning speedup and parallel efficiency metrics. Our main contribution is a Fuzzy clustering algorithm for large datasets that is scalable and not limited to a specific domain. Full article
(This article belongs to the Special Issue Mathematical Modeling, Data Analysis and Artificial Intelligence in Interdisciplinary Research)
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12 pages, 2253 KiB  
Article
Robotic-Arm-Based Force Control in Neurosurgical Practice
by Ibai Inziarte-Hidalgo, Irantzu Uriarte, Unai Fernandez-Gamiz, Gorka Sorrosal and Ekaitz Zulueta
Mathematics 2023, 11(4), 828; https://doi.org/10.3390/math11040828 - 6 Feb 2023
Cited by 2 | Viewed by 1654
Abstract
This research proposes an optimal robotic arm speed shape in neurological surgery to minimise a cost functional that uses an adaptive scheme to determine the brain tissue force. Until now, there have been no studies or theories on the shape of the robotic [...] Read more.
This research proposes an optimal robotic arm speed shape in neurological surgery to minimise a cost functional that uses an adaptive scheme to determine the brain tissue force. Until now, there have been no studies or theories on the shape of the robotic arm speed in such a context. The authors have applied a robotic arm with optimal speed control in neurological surgery. The results of this research are as follows: In this article, the authors propose a control scheme that minimises a cost functional which depends on the position error, trajectory speed and brain tissue force. This work allowed us to achieve an optimal speed shape or trajectory to reduce brain retraction damage during surgery. The authors have reached two main conclusions. The first is that optimal control techniques are very well suited for robotic control of neurological surgery. The second conclusion is that several studies on functional cost parameters are needed to achieve the best trajectory speed of the robotic arm. These studies could attempt to optimise the functional cost parameters and provide a mechanical characterisation of brain tissue based on real data. Full article
(This article belongs to the Special Issue Mathematical Modeling, Data Analysis and Artificial Intelligence in Interdisciplinary Research)
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13 pages, 1040 KiB  
Article
Prediction of Parkinson’s Disease Depression Using LIME-Based Stacking Ensemble Model
by Hung Viet Nguyen and Haewon Byeon
Mathematics 2023, 11(3), 708; https://doi.org/10.3390/math11030708 - 30 Jan 2023
Cited by 15 | Viewed by 2531
Abstract
Depression symptoms are comparable to Parkinson’s disease symptoms, including attention deficit, fatigue, and sleep disruption, as well as symptoms of dementia such as apathy. As a result, it is difficult for Parkinson’s disease caregivers to diagnose depression early. We examined a LIME-based stacking [...] Read more.
Depression symptoms are comparable to Parkinson’s disease symptoms, including attention deficit, fatigue, and sleep disruption, as well as symptoms of dementia such as apathy. As a result, it is difficult for Parkinson’s disease caregivers to diagnose depression early. We examined a LIME-based stacking ensemble model to predict the depression of patients with Parkinson’s disease. This study used the epidemiologic data of Parkinson’s disease dementia patients (EPD) from the Korea Disease Control and Prevention Agency’s National Biobank, which included 526 patients’ information. We used Logistic Regression (LR) as the meta-model, and five base models, including LightGBM (LGBM), K-nearest Neighbors (KNN), Random Forest (RF), Extra Trees (ET), and AdaBoost. After cleansing the data, the stacking ensemble model was trained using 261 participants’ data and 10 variables. According to the research, the best combination of the stacking ensemble model is ET + LGBM + RF + LR, a harmonious model. In order to achieve model prediction explainability, we also combined the stacking ensemble model with a LIME-based explainable model. This explainable stacking ensemble model can help identify the patients and start treatment on them early in a way that medical professionals can comprehend. Full article
(This article belongs to the Special Issue Mathematical Modeling, Data Analysis and Artificial Intelligence in Interdisciplinary Research)
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24 pages, 5678 KiB  
Article
An Integrated Method to Acquire Technological Evolution Potential to Stimulate Innovative Product Design
by Peng Shao, Runhua Tan, Qingjin Peng, Wendan Yang and Fang Liu
Mathematics 2023, 11(3), 619; https://doi.org/10.3390/math11030619 - 26 Jan 2023
Cited by 2 | Viewed by 1970
Abstract
Fast and effective forecasting of the new generation of products is key to enhancing the competitiveness of a company in the market. Although the technological evolution laws in the theory of the solution of inventive problems (TRIZ) have been used to predict the [...] Read more.
Fast and effective forecasting of the new generation of products is key to enhancing the competitiveness of a company in the market. Although the technological evolution laws in the theory of the solution of inventive problems (TRIZ) have been used to predict the potential states of products for innovation, there is a lack of effective methods to select the best technological evolution law consistently with product replacement and update, and acquiring potentially new technologies and solutions, which relies heavily on designers’ experience and makes it impossible for designers to efficiently use the technological evolution laws to stimulate product innovation. Aimed to bridge this gap, this paper proposes an integrated method consisting of three main steps, combining the technological evolution laws with back propagation neural network (BPNN), international patent classification (IPC) knowledge and company’s technological distance. The best technical evolution law is first searched by a BPNN. The functional verbs and effects in the IPC are then extracted and searched for potential technologies in the Spyder-integrated development environment. Finally, the company’s technological distance is used to select analogous sources of potential solutions in the patent database. The final innovative design is determined based on the ideality. The proposed method is applied in the development of a steel pipe-cutting machine to verify its feasibility. The proposed method reduces the dependence on designers’ experience and provides a way to access cross-domain technologies, providing a systematic approach for the technological evolution laws to motivate innovative product design. Full article
(This article belongs to the Special Issue Mathematical Modeling, Data Analysis and Artificial Intelligence in Interdisciplinary Research)
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16 pages, 1239 KiB  
Article
Petroleum Price Prediction with CNN-LSTM and CNN-GRU Using Skip-Connection
by Gun Il Kim and Beakcheol Jang
Mathematics 2023, 11(3), 547; https://doi.org/10.3390/math11030547 - 19 Jan 2023
Cited by 17 | Viewed by 4458
Abstract
Crude oil plays an important role in the global economy, as it contributes one-third of the energy consumption worldwide. However, despite its importance in policymaking and economic development, forecasting its price is still challenging due to its complexity and irregular price trends. Although [...] Read more.
Crude oil plays an important role in the global economy, as it contributes one-third of the energy consumption worldwide. However, despite its importance in policymaking and economic development, forecasting its price is still challenging due to its complexity and irregular price trends. Although a significant amount of research has been conducted to improve forecasting using external factors as well as machine-learning and deep-learning models, only a few studies have used hybrid models to improve prediction accuracy. In this study, we propose a novel hybrid model that captures the finer details and interconnections between multivariate factors to improve the accuracy of petroleum oil price prediction. Our proposed hybrid model integrates a convolutional neural network and a recurrent neural network with skip connections and is trained using petroleum oil prices and external data directly accessible from the official website of South Korea’s national oil corporation and the official Yahoo Finance site. We compare the performance of our univariate and multivariate models in terms of the Pearson correlation, mean absolute error, mean squared error, root mean squared error, and R squared (R2) evaluation metrics. Our proposed models exhibited significantly better performance than the existing models based on long short-term memory and gated recurrent units, showing correlations of 0.985 and 0.988, respectively, for 10-day price predictions and obtaining better results for longer prediction periods when compared with other deep-learning models. We validated that our proposed model with skip connections outperforms the benchmark models and showed that the convolutional neural network using gated recurrent units with skip connections is superior to the compared models. The findings suggest that, to some extent, relying on a single source of data is ineffective in predicting long-term changes in oil prices, and thus, to develop a better prediction model based on time-series based data, it is necessary to take a multivariate approach and develop an efficient computational model with skip connections. Full article
(This article belongs to the Special Issue Mathematical Modeling, Data Analysis and Artificial Intelligence in Interdisciplinary Research)
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