Journal Description
Mathematics
Mathematics
is a peer-reviewed, open access journal which provides an advanced forum for studies related to mathematics, and is published semimonthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT) and International Society for the Study of Information (IS4SI) are affiliated with Mathematics and their members receive a discount on article processing charges.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), and many other databases.
- Journal Rank: JCR - Q1 (Mathematics) / CiteScore - Q1 (General Mathematics)
- Rapid Publication: manuscripts are peer-reviewed and a first decision provided to authors approximately 17.6 days after submission; acceptance to publication is undertaken in 3.7 days (median values for papers published in this journal in the first half of 2021).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Sections: published in thirteen topical sections.
- Companion journals for Mathematics include: Foundations and AppliedMath.
Impact Factor:
2.258 (2020)
;
5-Year Impact Factor:
2.165 (2020)
Latest Articles
Evaluation of Paris MoU Maritime Inspections Using a STATIS Approach
Mathematics 2021, 9(17), 2092; https://doi.org/10.3390/math9172092 (registering DOI) - 29 Aug 2021
Abstract
Port state control inspections implemented under the Paris Memorandum of Understanding (MoU) have become known as one of the best instruments for maritime administrations in European Union (EU) Member States to ensure that the ships docked in their ports comply with all maritime
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Port state control inspections implemented under the Paris Memorandum of Understanding (MoU) have become known as one of the best instruments for maritime administrations in European Union (EU) Member States to ensure that the ships docked in their ports comply with all maritime safety requirements. This paper focuses on the analysis of all inspections made between 2013 and 2018 in the top ten EU ports incorporated in the Paris MoU (17,880 inspections). The methodology consists of a multivariate statistical information system (STATIS) analysis using the inspected ship’s characteristics as explanatory variables. The variables used describe both the inspected ships (classification society, flag, age and gross tonnage) and the inspection (type of inspection and number of deficiencies), yielding a dataset with more than 600,000 elements in the data matrix. The most important results are that the classifications obtained match the performance lists published annually by the Paris MoU and the classification societies. Therefore, the approach is a potentially valid classification method and would then be useful to maritime authorities as an additional indicator of a ship’s risk profile to decide inspection priorities and as a tool to measure the evolution in the risk profile of the flag over time.
Full article
(This article belongs to the Special Issue Multivariate Statistics: Theory and Its Applications)
Open AccessArticle
Frequency Domain Feature Extraction Investigation to Increase the Accuracy of an Intelligent Nondestructive System for Volume Fraction and Regime Determination of Gas-Water-Oil Three-Phase Flows
Mathematics 2021, 9(17), 2091; https://doi.org/10.3390/math9172091 (registering DOI) - 29 Aug 2021
Abstract
In this research, a methodology consisting of an X-ray tube, one Pyrex-glass pipe, and two NaI detectors was investigated to determine the type of flow regimes and volume fractions of gas-oil-water three-phase flows. Three prevalent flow patterns—namely annular, stratified, and homogenous—in various volume
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In this research, a methodology consisting of an X-ray tube, one Pyrex-glass pipe, and two NaI detectors was investigated to determine the type of flow regimes and volume fractions of gas-oil-water three-phase flows. Three prevalent flow patterns—namely annular, stratified, and homogenous—in various volume percentages—10% to 80% with the step of 10%—were simulated by MCNP-X code. After simulating all the states and collecting the signals, the Fast Fourier Transform (FFT) was used to convert the data to the frequency domain. The first and second dominant frequency amplitudes were extracted to be used as the inputs of neural networks. Three Radial Basis Function Neural Networks (RBFNN) were trained for determining the type of flow regimes and predicting gas and water volume fractions. The correct detection of all flow regimes and the determination of volume percentages with a Mean Relative Error (MRE) of less than 2.02% shows that the use of frequency characteristics in determining these important parameters can be very effective. Although X-ray radiation-based two-phase flowmeters have a lot of advantages over the radioisotope-based ones, they suffer from lower measurement accuracy. One reason might be that the X-ray multi-energy spectrum recorded in the detector has been analyzed in a simple way. It is worth mentioning that the X-ray sources generate multi-energy photons despite radioisotopes that generate single energy photons, therefore data analyzing of radioisotope sources would be easier than X-ray ones. As mentioned, one of the problems researchers have encountered is the lower measurement accuracy of the X-ray, radiation-based three-phase flowmeters. The aim of the present work is to resolve this problem by improving the precision of the X-ray, radiation-based three-phase flowmeter using artificial neural network (ANN) and feature extraction techniques.
Full article
(This article belongs to the Special Issue Computational Mathematics and Soft Computing Techniques for Non-destructive Testing and Evaluation (NDT/NDE) and Data Fusion)
Open AccessArticle
An Oblivious Approach to Machine Translation Quality Estimation
by
and
Mathematics 2021, 9(17), 2090; https://doi.org/10.3390/math9172090 (registering DOI) - 29 Aug 2021
Abstract
Machine translation (MT) is being used by millions of people daily, and therefore evaluating the quality of such systems is an important task. While human expert evaluation of MT output remains the most accurate method, it is not scalable by any means. Automatic
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Machine translation (MT) is being used by millions of people daily, and therefore evaluating the quality of such systems is an important task. While human expert evaluation of MT output remains the most accurate method, it is not scalable by any means. Automatic procedures that perform the task of Machine Translation Quality Estimation (MT-QE) are typically trained on a large corpus of source–target sentence pairs, which are labeled with human judgment scores. Furthermore, the test set is typically drawn from the same distribution as the train. However, recently, interest in low-resource and unsupervised MT-QE has gained momentum. In this paper, we define and study a further restriction of the unsupervised MT-QE setting that we call oblivious MT-QE. Besides having no access no human judgment scores, the algorithm has no access to the test text’s distribution. We propose an oblivious MT-QE system based on a new notion of sentence cohesiveness that we introduce. We tested our system on standard competition datasets for various language pairs. In all cases, the performance of our system was comparable to the performance of the non-oblivious baseline system provided by the competition organizers. Our results suggest that reasonable MT-QE can be carried out even in the restrictive oblivious setting.
Full article
(This article belongs to the Special Issue Multidisciplinary Models and Applications of Machine Learning and Computational Statistics)
Open AccessArticle
New Criteria for Sharp Oscillation of Second-OrderNeutral Delay Differential Equations
Mathematics 2021, 9(17), 2089; https://doi.org/10.3390/math9172089 (registering DOI) - 29 Aug 2021
Abstract
In this paper, new oscillation criteria for second-order half-linear neutral delay differential equations are established, using a recently developed method of iteratively improved monotonicity properties of a nonoscillatory solution. Our approach allows removing several disadvantages which were commonly associated with the method based
[...] Read more.
In this paper, new oscillation criteria for second-order half-linear neutral delay differential equations are established, using a recently developed method of iteratively improved monotonicity properties of a nonoscillatory solution. Our approach allows removing several disadvantages which were commonly associated with the method based on a priori bound for the nonoscillatory solution, and deriving new results which are optimal in a nonneutral case. It is shown that the newly obtained results significantly improve a large number of existing ones.
Full article
(This article belongs to the Special Issue Recent Advances in Oscillation Theory of Differential Equations: Problems, Solutions and Applications)
Open AccessArticle
Price Appreciation and Roughness Duality in Bitcoin: A Multifractal Analysis
Mathematics 2021, 9(17), 2088; https://doi.org/10.3390/math9172088 (registering DOI) - 29 Aug 2021
Abstract
Since its launch in 2009, bitcoin has thrived, attracting the attention of investors, regulators, academia, and the public in general. Its price dynamics, characterized by extreme volatility, severe jumps, and impressive long-term appreciation, suggest that bitcoin is a new digital asset. This study
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Since its launch in 2009, bitcoin has thrived, attracting the attention of investors, regulators, academia, and the public in general. Its price dynamics, characterized by extreme volatility, severe jumps, and impressive long-term appreciation, suggest that bitcoin is a new digital asset. This study presents a comprehensive overview of the fractality of bitcoin in a high-frequency framework, namely by applying Multifractal Detrended Fluctuation Analysis (MF-DFA) and a Multifractal Regime Detecting Method (MRDM) to Bitstamp 1 min bitcoin returns from January 2013 to July 2020. The results suggest that bitcoin is multifractal, with smaller and larger fluctuations being persistent and anti-persistent, respectively. Multifractality comes from significant long-range correlations, which cast some doubts on the informational efficiency at this frequency, but mainly comes from fat-tails, which highlights the significant risks undertaken by investors in this market. Our most important result is that the degree and richness of multifractality is time-varying and increased after 2017, when volumes and prices experienced an explosive behaviour. This complexity puts into perspective the duality of bitcoin: while it is characterized by long-run attractiveness and increasing valuation, it also has a high short-run instability. Hence, this study provides some empirical evidence supporting the relationship between these two observable features.
Full article
(This article belongs to the Special Issue Mathematics and Mathematical Physics Applied to Financial Markets)
Open AccessArticle
Fast Localization of Small Inhomogeneities from Far-Field Pattern Data in the Limited-Aperture Inverse Scattering Problem
Mathematics 2021, 9(17), 2087; https://doi.org/10.3390/math9172087 (registering DOI) - 29 Aug 2021
Abstract
In this study, we consider a sampling-type algorithm for the fast localization of small electromagnetic inhomogeneities from measured far-field pattern data in the limited-aperture inverse scattering problem. For this purpose, we designed an indicator function based on the structure of left- and right-singular
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In this study, we consider a sampling-type algorithm for the fast localization of small electromagnetic inhomogeneities from measured far-field pattern data in the limited-aperture inverse scattering problem. For this purpose, we designed an indicator function based on the structure of left- and right-singular vectors of a multistatic response matrix, the elements of which were measured far-field pattern data. We then rigorously investigated the mathematical structure of the indicator function in terms of purely dielectric permittivity and magnetic permeability contrast cases by establishing a relationship with an infinite series of Bessel functions of an integer order of the first kind and a range of incident and observation directions before exploring various intrinsic properties of the algorithm, including its feasibility and limitations. Simulation results with synthetic data corrupted by random noise are presented to support the theoretical results.
Full article
(This article belongs to the Section Computational and Applied Mathematics)
Open AccessArticle
Clustering of Latvian Pension Funds Using Convolutional Neural Network Extracted Features
Mathematics 2021, 9(17), 2086; https://doi.org/10.3390/math9172086 (registering DOI) - 29 Aug 2021
Abstract
Pension funds became a fundamental part of financial security in pensioners’ lives, guaranteeing stable income throughout the years and reducing the chance of living below the poverty level. However, participating in a pension accumulation scheme does not ensure financial safety at an older
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Pension funds became a fundamental part of financial security in pensioners’ lives, guaranteeing stable income throughout the years and reducing the chance of living below the poverty level. However, participating in a pension accumulation scheme does not ensure financial safety at an older age. Various pension funds exist that result in different investment outcomes ranging from high return rates to underperformance. This paper aims to demonstrate alternative clustering of Latvian second pillar pension funds, which may help system participants make long-range decisions. Due to the demonstrated ability to extract meaningful features from raw time-series data, the convolutional neural network was chosen as a pension fund feature extractor that was used prior to the clustering process. In this paper, pension fund cluster analysis was performed using trained (on daily stock prices) convolutional neural network feature extractors. The extractors were combined with different clustering algorithms. The feature extractors operate using the black-box principle, meaning the features they learned to recognize have low explainability. In total, 32 models were trained, and eight different clustering methods were used to group 20 second-pillar pension funds from Latvia. During the analysis, the 12 best-performing models were selected, and various cluster combinations were analyzed. The results show that funds from the same manager or similar performance measures are frequently clustered together.
Full article
(This article belongs to the Special Issue Artificial Intelligence with Applications of Soft Computing)
Open AccessArticle
An Improved Estimation Algorithm of Space Targets Pose Based on Multi-Modal Feature Fusion
Mathematics 2021, 9(17), 2085; https://doi.org/10.3390/math9172085 (registering DOI) - 29 Aug 2021
Abstract
The traditional estimation methods of space targets pose are based on artificial features to match the transformation relationship between the image and the object model. With the explosion of deep learning technology, the approach based on deep neural networks (DNN) has significantly improved
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The traditional estimation methods of space targets pose are based on artificial features to match the transformation relationship between the image and the object model. With the explosion of deep learning technology, the approach based on deep neural networks (DNN) has significantly improved the performance of pose estimation. However, the current methods still have problems such as complex calculation, low accuracy, and poor real-time performance. Therefore, a new pose estimation algorithm is proposed in this paper. Firstly, the mask image of the target is obtained by the instance segmentation algorithm, and its point cloud image is obtained based on a depth map combined with camera parameters. Finally, the correlation among points is established to realize the prediction of pose based on multi-modal feature fusion. Experimental results in the YCB-Video dataset show that the proposed algorithm can recognize complex images at a speed of about 24 images per second with an accuracy of more than 80%. In conclusion, the proposed algorithm can realize fast pose estimation for complex stacked objects and has strong stability for different objects.
Full article
Open AccessArticle
Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities
by
, , and
Mathematics 2021, 9(17), 2084; https://doi.org/10.3390/math9172084 (registering DOI) - 28 Aug 2021
Abstract
In this paper, we study the recently proposed fractional-order operators with general analytic kernels. The kernel of these operators is a locally uniformly convergent power series that can be chosen adequately to obtain a family of fractional operators and, in particular, the main
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In this paper, we study the recently proposed fractional-order operators with general analytic kernels. The kernel of these operators is a locally uniformly convergent power series that can be chosen adequately to obtain a family of fractional operators and, in particular, the main existing fractional derivatives. Based on the conditions for the Laplace transform of these operators, in this paper, some new results are obtained—for example, relationships between Riemann–Liouville and Caputo derivatives and inverse operators. Later, employing a representation for the product of two functions, we determine a form of calculating its fractional derivative; this result is essential due to its connection to the fractional derivative of Lyapunov functions. In addition, some other new results are developed, leading to Lyapunov-like theorems and a Lyapunov direct method that serves to prove asymptotic stability in the sense of the operators with general analytic kernels. The FOB-stability concept is introduced, which generalizes the classical Mittag–Leffler stability for a wide class of systems. Some inequalities are established for operators with general analytic kernels, which generalize others in the literature. Finally, some new stability results via convex Lyapunov functions are presented, whose importance lies in avoiding the calculation of fractional derivatives for the stability analysis of dynamical systems. Some illustrative examples are given.
Full article
(This article belongs to the Special Issue Fractional Calculus and Nonlinear Systems)
Open AccessArticle
Energy Crisis in Pakistan and Economic Progress: Decoupling the Impact of Coal Energy Consumption in Power and Brick Kilns
Mathematics 2021, 9(17), 2083; https://doi.org/10.3390/math9172083 (registering DOI) - 28 Aug 2021
Abstract
This study aims to examine the impact of coal energy consumption on the economic progress in Pakistan by using annual time series data during 1972–2019. Three-unit root tests were employed to rectify the variables’ stationarity. The quantile regression approach with the extension of
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This study aims to examine the impact of coal energy consumption on the economic progress in Pakistan by using annual time series data during 1972–2019. Three-unit root tests were employed to rectify the variables’ stationarity. The quantile regression approach with the extension of cointegration regression test was utilized to check the variables interaction with the economic progress. The outcomes of the quantile regression uncover that coal energy consumption in power sector and coal energy consumption in brick kilns have adverse influence to the economic progress, while total coal energy consumption has a productive association with the economic progress. Similarly, the findings of cointegration regression analysis uncover that via FMOLS (Fully Modified Least Squares) and DOLS (Dynamic Least Squares) that variables coal energy consumption in power sector and brick kilns have an adverse connection with the economic progress, while total coal energy consumption uncover a productive linkage to the economic progress in Pakistan. Pakistan is still facing a deep energy crisis because of the lack of energy production from cheap sources. New possible policies are required in this direction to improve the energy sector by paying more attention to the alternative energy sources to foster the economic progress.
Full article
(This article belongs to the Special Issue Mathematical Methods in Energy Economy)
Open AccessArticle
Dynamical Continuous Discrete Assessment of Competencies Achievement: An Approach to Continuous Assessment
by
, , and
Mathematics 2021, 9(17), 2082; https://doi.org/10.3390/math9172082 (registering DOI) - 28 Aug 2021
Abstract
Learning is a non-deterministic complex dynamical system where students transform inputs (classes, assignments, personal work, gamification activities, etc.) into outcomes (acquired knowledge, skills, and competencies). In the process, students generate outputs in a variety of ways (exams, tests, portfolios, etc.). The result of
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Learning is a non-deterministic complex dynamical system where students transform inputs (classes, assignments, personal work, gamification activities, etc.) into outcomes (acquired knowledge, skills, and competencies). In the process, students generate outputs in a variety of ways (exams, tests, portfolios, etc.). The result of these outputs is a grade aimed at measuring the (level of) competencies achieved by each student. We revisit the relevance of continuous assessment to obtain this grading. We simultaneously investigate the generated outputs in different moments as modifiers of the system itself, since they may reveal a variation of the level of competencies achievement previously assessed. This is a novelty in the literature, and a cornerstone of our methodology. This process is called a Dynamical Continuous Discrete assessment, which is a form of blended assessment that may be used under traditional or blended learning environments. This article provides an 11-year perspective of applying this Dynamical Continuous Discrete assessment in a Mathematics class for aerospace engineering students, as well as the students’ perception of continuous assessments.
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(This article belongs to the Special Issue Advanced Methods in Computational Mathematical Physics)
Open AccessArticle
Imputation for Repeated Bounded Outcome Data: Statistical and Machine-Learning Approaches
Mathematics 2021, 9(17), 2081; https://doi.org/10.3390/math9172081 (registering DOI) - 28 Aug 2021
Abstract
Real-life data are bounded and heavy-tailed variables. Zero-one-inflated beta (ZOIB) regression is used for modelling them. There are no appropriate methods to address the problem of missing data in repeated bounded outcomes. We developed an imputation method using ZOIB (i-ZOIB) and compared its
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Real-life data are bounded and heavy-tailed variables. Zero-one-inflated beta (ZOIB) regression is used for modelling them. There are no appropriate methods to address the problem of missing data in repeated bounded outcomes. We developed an imputation method using ZOIB (i-ZOIB) and compared its performance with those of the naïve and machine-learning methods, using different distribution shapes and settings designed in the simulation study. The performance was measured employing the absolute error (MAE), root-mean-square-error (RMSE) and the unscaled mean bounded relative absolute error (UMBRAE) methods. The results varied depending on the missingness rate and mechanism. The i-ZOIB and the machine-learning ANN, SVR and RF methods showed the best performance.
Full article
(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)
Open AccessArticle
Metamaterial Acoustics on the (2 + 1)D Einstein Cylinder
Mathematics 2021, 9(17), 2079; https://doi.org/10.3390/math9172079 (registering DOI) - 28 Aug 2021
Abstract
The Einstein cylinder is the first cosmological model for our universe in modern history. Its geometry not only describes a static universe—a universe being invariant under time reversal—but it is also the prototype for a maximally symmetric spacetime with constant positive curvature. As
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The Einstein cylinder is the first cosmological model for our universe in modern history. Its geometry not only describes a static universe—a universe being invariant under time reversal—but it is also the prototype for a maximally symmetric spacetime with constant positive curvature. As such, it is still of crucial importance in numerous areas of physics and engineering, offering a fruitful playground for simulations and new theories. Here, we focus on the implementation and simulation of acoustic wave propagation on the Einstein cylinder. Engineering such an extraordinary device is the territory of metamaterial science, and we will propose an appropriate tuning of the relevant acoustic parameters in such a way as to mimic the geometric properties of this spacetime in acoustic space. Moreover, for probing such a space, we derive the corresponding wave equation from a variational principle for the underlying curved spacetime manifold and examine some of its solutions. In particular, fully analytical results are obtained for concentric wave propagation. We present predictions for this case and thereby investigate the most significant features of this spacetime. Finally, we produce simulation results for a more sophisticated test model which can only be tackled numerically.
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(This article belongs to the Special Issue Mathematical Models and Methods in Engineering and Social Sciences)
Open AccessArticle
Decision-Making under Group Commitment
by
Mathematics 2021, 9(17), 2080; https://doi.org/10.3390/math9172080 (registering DOI) - 27 Aug 2021
Abstract
Coordination is essential for establishing and sustaining teamwork. Agents in a team must agree on their tasks and plans, and thus, group decision-making techniques are necessary to reach agreements in teams. For instance, to agree on a joint task, the agents can provide
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Coordination is essential for establishing and sustaining teamwork. Agents in a team must agree on their tasks and plans, and thus, group decision-making techniques are necessary to reach agreements in teams. For instance, to agree on a joint task, the agents can provide their preferences for the alternative tasks, and the best alternative could be selected by majority. Previous works assumed that agents only provide their preferences for the alternatives. However, when selecting a joint task for teamwork, it is essential to consider not only the preferences of the agents, but also the probability of the agents being able to execute the task if it is selected. In this paper, we propose a novel model, the decIsion-MAking under Group commItmeNt modEl (IMAGINE), for computing the optimal decision for a team considering several parameters. Each agent provides: (1) the utility of each alternative for the team, (2) the associated cost for the agent by executing the alternative, and (3) the probability that the agent will be able to execute the alternative task. The IMAGINE gathers these data from the agents, as well as the requisite quorum for each alternative task, which is the minimum number of agents required to complete the task successfully. Given this information, the IMAGINE determines the optimal decision for the group. We evaluated the IMAGINE by comparing it to a baseline method that does not consider the quorum requirement. We show that the IMAGINE generally comes up with a better decision than the baseline method and that the higher the quorum, the better the decisions the IMAGINE makes are.
Full article
(This article belongs to the Special Issue Multi-Criteria Decision Making and Data Mining)
Open AccessArticle
Intelligent Decision Support System for Predicting Student’s E-Learning Performance Using Ensemble Machine Learning
Mathematics 2021, 9(17), 2078; https://doi.org/10.3390/math9172078 (registering DOI) - 27 Aug 2021
Abstract
Electronic learning management systems provide live environments for students and faculty members to connect with their institutional online portals and perform educational activities virtually. Although modern technologies proactively support these online sessions, students’ active participation remains a challenge that has been discussed in
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Electronic learning management systems provide live environments for students and faculty members to connect with their institutional online portals and perform educational activities virtually. Although modern technologies proactively support these online sessions, students’ active participation remains a challenge that has been discussed in previous research. Additionally, one concern for both parents and teachers is how to accurately measure student performance using different attributes collected during online sessions. Therefore, the research idea undertaken in this study is to understand and predict the performance of the students based on features extracted from electronic learning management systems. The dataset chosen in this study belongs to one of the learning management systems providing a number of features predicting student’s performance. The integrated machine learning model proposed in this research can be useful to make proactive and intelligent decisions according to student performance evaluated through the electronic system’s data. The proposed model consists of five traditional machine learning algorithms, which are further enhanced by applying four ensemble techniques: bagging, boosting, stacking, and voting. The overall F1 scores of the single models are as follows: DT (0.675), RF (0.777), GBT (0.714), NB (0.654), and KNN (0.664). The model performance has shown remarkable improvement using ensemble approaches. The stacking model by combining all five classifiers has outperformed and recorded the highest F1 score (0.8195) among other ensemble methods. The integration of the ML models has improved the prediction ratio and performed better than all other ensemble approaches. The proposed model can be useful for predicting student performance and helping educators to make informed decisions by proactively notifying the students.
Full article
(This article belongs to the Special Issue Decision Making and Its Applications)
Open AccessArticle
Profiting on the Stock Market in Pandemic Times: Study of COVID-19 Effects on CESEE Stock Markets
Mathematics 2021, 9(17), 2077; https://doi.org/10.3390/math9172077 (registering DOI) - 27 Aug 2021
Abstract
This research deals with stock market reactions of Central Eastern and South Eastern European (CESEE) markets to the COVID-19 pandemic, via the event study methodology approach. Since the stock markets react quickly to certain announcements, the used methodology is appropriate to evaluate how
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This research deals with stock market reactions of Central Eastern and South Eastern European (CESEE) markets to the COVID-19 pandemic, via the event study methodology approach. Since the stock markets react quickly to certain announcements, the used methodology is appropriate to evaluate how the aforementioned markets reacted to certain events. The purpose of this research was to evaluate possibilities of obtaining profits on the stock markets during great turbulences, when a majority of the participants panic. More specifically, the contrarian trading strategies are observed if they can obtain gains, although a majority of the markets suffer great losses during pandemic shocks. The contributions to the existing literature of this research are as follows. Firstly, empirical research on CESEE stock markets regarding other relevant topics is still scarce and should be explored more. Secondly, the event study approach of COVID-19 effects utilized in this study has (to the knowledge of the author) not yet been explored on the aforementioned markets. Thirdly, based on the results of CESEE market reactions to specific announcements regarding COVID-19, a simulation of simple trading strategies will be made in order to estimate whether some investors could have profited in certain periods. The results of the study indicate promising results in terms of exploiting other investors’ panicking during the greatest decline of stock market indices. Namely, the initial results, as expected, indicate strong negative effects of specific COVID-19 announcements on the selected stock markets. Secondly, the obtained information was shown to be useful for contrarian strategy in order to exploit great dips in the stock market indices values.
Full article
(This article belongs to the Special Issue Mathematical and Statistical Methods Applications in Finance)
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Open AccessArticle
Extension of SEIR Compartmental Models for Constructive Lyapunov Control of COVID-19 and Analysis in Terms of Practical Stability
Mathematics 2021, 9(17), 2076; https://doi.org/10.3390/math9172076 (registering DOI) - 27 Aug 2021
Abstract
Due to the worldwide outbreak of COVID-19, many strategies and models have been put forward by researchers who intend to control the current situation with the given means. In particular, compartmental models are being used to model and analyze the COVID-19 dynamics of
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Due to the worldwide outbreak of COVID-19, many strategies and models have been put forward by researchers who intend to control the current situation with the given means. In particular, compartmental models are being used to model and analyze the COVID-19 dynamics of different considered populations as Susceptible, Exposed, Infected and Recovered compartments (SEIR). This study derives control-oriented compartmental models of the pandemic, together with constructive control laws based on the Lyapunov theory. The paper presents the derivation of new vaccination and quarantining strategies, found using compartmental models and design methods from the field of Lyapunov theory. The Lyapunov theory offers the possibility to track desired trajectories, guaranteeing the stability of the controlled system. Computer simulations aid to demonstrate the efficacy of the results. Stabilizing control laws are obtained and analyzed for multiple variants of the model. The stability, constructivity, and feasibility are proven for each Lyapunov-like function. Obtaining the proof of practical stability for the controlled system, several interesting system properties such as herd immunity are shown. On the basis of a generalized SEIR model and an extended variant with additional Protected and Quarantined compartments, control strategies are conceived by using two fundamental system inputs, vaccination and quarantine, whose influence on the system is a crucial part of the model. Simulation results prove that Lyapunov-based approaches yield effective control of the disease transmission.
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(This article belongs to the Special Issue Mathematical Modeling in Biophysics, Biochemistry and Physical Chemistry)
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Open AccessArticle
Identification of Nonlinear Systems Using the Infinitesimal Generator of the Koopman Semigroup—A Numerical Implementation of the Mauroy–Goncalves Method
Mathematics 2021, 9(17), 2075; https://doi.org/10.3390/math9172075 (registering DOI) - 27 Aug 2021
Abstract
Inferring the latent structure of complex nonlinear dynamical systems in a data driven setting is a challenging mathematical problem with an ever increasing spectrum of applications in sciences and engineering. Koopman operator-based linearization provides a powerful framework that is suitable for identification of
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Inferring the latent structure of complex nonlinear dynamical systems in a data driven setting is a challenging mathematical problem with an ever increasing spectrum of applications in sciences and engineering. Koopman operator-based linearization provides a powerful framework that is suitable for identification of nonlinear systems in various scenarios. A recently proposed method by Mauroy and Goncalves is based on lifting the data snapshots into a suitable finite dimensional function space and identification of the infinitesimal generator of the Koopman semigroup. This elegant and mathematically appealing approach has good analytical (convergence) properties, but numerical experiments show that software implementation of the method has certain limitations. More precisely, with the increased dimension that guarantees theoretically better approximation and ultimate convergence, the numerical implementation may become unstable and it may even break down. The main sources of numerical difficulties are the computations of the matrix representation of the compressed Koopman operator and its logarithm. This paper addresses the subtle numerical details and proposes a new implementation algorithm that alleviates these problems.
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(This article belongs to the Special Issue Dynamical Systems and Operator Theory)
Open AccessArticle
Some New Oscillation Criteria of Even-Order Quasi-Linear Delay Differential Equations with Neutral Term
Mathematics 2021, 9(17), 2074; https://doi.org/10.3390/math9172074 (registering DOI) - 27 Aug 2021
Abstract
The neutral delay differential equations have many applications in the natural sciences, technology, and population dynamics. In this paper, we establish several new oscillation criteria for a kind of even-order quasi-linear neutral delay differential equations. Comparing our results with those in the literature,
[...] Read more.
The neutral delay differential equations have many applications in the natural sciences, technology, and population dynamics. In this paper, we establish several new oscillation criteria for a kind of even-order quasi-linear neutral delay differential equations. Comparing our results with those in the literature, our criteria solve more general delay differential equations with neutral type, and our results expand the range of neutral term coefficient. Some examples are given to illustrate our conclusions.
Full article
(This article belongs to the Special Issue Recent Advances in Oscillation Theory of Differential Equations: Problems, Solutions and Applications)
Open AccessArticle
Weighted Fractional-Order Transform Based on Periodic Matrix
by
and
Mathematics 2021, 9(17), 2073; https://doi.org/10.3390/math9172073 (registering DOI) - 27 Aug 2021
Abstract
Tao et al. proposed the definition of the linear summation of fractional-order matrices based on the theory of Yeh and Pei. This definition was further extended and applied to image encryption. In this paper, we propose a reformulation of the definitions of Yeh
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Tao et al. proposed the definition of the linear summation of fractional-order matrices based on the theory of Yeh and Pei. This definition was further extended and applied to image encryption. In this paper, we propose a reformulation of the definitions of Yeh et al. and Tao et al. and analyze them theoretically. The results show that many weighted terms are invalid. Therefore, we use the proposed reformulation to prove that the effective weighted terms depend on the period of the matrix. This also shows that the image encryption methods based on the weighted fractional-order transform will lead to the security risk of key invalidation. Finally, our hypothesis is verified by the unified theoretical framework of multiple-parameter discrete fractional-order transforms.
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(This article belongs to the Special Issue Numerical Analysis and Scientific Computing)
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