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), RePEc, and other databases.
- Journal Rank: JCR - Q1 (Mathematics) / CiteScore - Q1 (General Mathematics)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 16.9 days after submission; acceptance to publication is undertaken in 2.6 days (median values for papers published in this journal in the second half of 2023).
- 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 13 topical sections.
- Companion journals for Mathematics include: Foundations, AppliedMath, Analytics, International Journal of Topology, Geometry and Logics.
Impact Factor:
2.4 (2022);
5-Year Impact Factor:
2.3 (2022)
Latest Articles
Boundary-Match U-Shaped Temporal Convolutional Network for Vulgar Action Segmentation
Mathematics 2024, 12(6), 899; https://doi.org/10.3390/math12060899 (registering DOI) - 18 Mar 2024
Abstract
The advent of deep learning has provided solutions to many challenges posed by the Internet. However, efficient localization and recognition of vulgar segments within videos remain formidable tasks. This difficulty arises from the blurring of spatial features in vulgar actions, which can render
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The advent of deep learning has provided solutions to many challenges posed by the Internet. However, efficient localization and recognition of vulgar segments within videos remain formidable tasks. This difficulty arises from the blurring of spatial features in vulgar actions, which can render them indistinguishable from general actions. Furthermore, issues of boundary ambiguity and over-segmentation complicate the segmentation of vulgar actions. To address these issues, we present the Boundary-Match U-shaped Temporal Convolutional Network (BMUTCN), a novel approach for the segmentation of vulgar actions. The BMUTCN employs a U-shaped architecture within an encoder–decoder temporal convolutional network to bolster feature recognition by leveraging the context of the video. Additionally, we introduce a boundary-match map that fuses action boundary inform ation with greater precision for frames that exhibit ambiguous boundaries. Moreover, we propose an adaptive internal block suppression technique, which substantially mitigates over-segmentation errors while preserving accuracy. Our methodology, tested across several public datasets as well as a bespoke vulgar dataset, has demonstrated state-of-the-art performance on the latter.
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(This article belongs to the Special Issue New Trends in Computer Vision, Deep Learning and Artificial Intelligence)
Open AccessArticle
Research on the Deformation Prediction Method for the Laser Deposition Manufacturing of Metal Components Based on Feature Partitioning and the Inherent Strain Method
by
Bobo Li, Enze Gao, Jun Yin, Xiaodan Li, Guang Yang and Qi Liu
Mathematics 2024, 12(6), 898; https://doi.org/10.3390/math12060898 (registering DOI) - 18 Mar 2024
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Laser deposition manufacturing (LDM) has drawn unprecedented attention for its advantages in manufacturing large-scale and complex metal components. During the process of LDM, a large thermal gradient is generated due to thermal cycling and heat accumulation. As a result, large residual stress and
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Laser deposition manufacturing (LDM) has drawn unprecedented attention for its advantages in manufacturing large-scale and complex metal components. During the process of LDM, a large thermal gradient is generated due to thermal cycling and heat accumulation. As a result, large residual stress and deformation are formed in the LDM metal components. Then, the dimensional accuracy of the metal components becomes poor. To achieve deformation control and increase dimensional accuracy, the deformation prediction of metal components is very meaningful and directional. However, the traditional thermoelastic–plastic method can only achieve deformation prediction for small-scale LDM metal components. Because of the low computational efficiency, it is extremely difficult to meet deformation prediction demand for large-scale metal components. Based on feature partitioning and the inherent strain method, a rapid deformation prediction method is proposed for large-scale metal components in this manuscript. Firstly, to solve the problem of poor consistency of formation quality due to the randomness of the partition process, the partitioning process was established according to typical geometric features. Secondly, the inherent strain values for different partitions were obtained by considering the effects of the extraction method, mesh size, equivalent value layer, and partition size on the inherent strain values. Then, using the inherent strain method, the deformation of large-scale components was predicted rapidly. Comparing the simulation results with the experimental results, the following conclusions were obtained. The deformation predicted by the method proposed in this manuscript is consistent with the deformations predicted using the traditional thermoelastic–plastic method and the experimental method. Significantly, applying the method proposed in this manuscript to predict the deformation of LDM metal components, computational efficiency is improved by 27.25 times compared with results using the conventional thermoelastic–plastic method.
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Open AccessArticle
Modelling Profitability Determinants in the Banking Sector: The Case of the Eurozone
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Vera Mirović, Branimir Kalaš, Nada Milenković, Jelena Andrašić and Miloš Đaković
Mathematics 2024, 12(6), 897; https://doi.org/10.3390/math12060897 (registering DOI) - 18 Mar 2024
Abstract
The aim of this study is to analyze which factors affect the profitability of banks in the eurozone and to make recommendations for supporting them to achieve higher levels of profitability in particular eurozone countries. The banks operating in the eurozone are specific
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The aim of this study is to analyze which factors affect the profitability of banks in the eurozone and to make recommendations for supporting them to achieve higher levels of profitability in particular eurozone countries. The banks operating in the eurozone are specific that they are under one monetary policy. The main purpose of the banks’ profitability analysis is to identify main bank-specific and macroeconomic determinants and help bank management to more fully comprehend their importance of bank-specific determinants and macroeconomic determinants’ influence when measuring and evaluating bank profitability. For the purpose of this research, we analyze the impact of bank-specific determinants (NPL, CIR, NIM, NIF and NIT) and macroeconomic determinants (GDP, INF, UNM and DEBT) on bank profitability in the eurozone for the period of 2015–2020 using a random effects model, fixed effects model, and the general method of moments (GMM). This empirical research analyzed quarterly data series from Eurostat for eighteen countries in the eurozone. We came to the results that on the eurozone-level NPL, the cost-to-income ratio has a negative impact on the banks’ profitability, while the net interest income to the operating income, the net income for trading assets to the operating income and the net fee and commission income to the operating income have a positive impact on the banks’ profitability. Considering the macroeconomic variables, we found a positive impact only in the case of GDP, while the inflation rate, unemployment rate and gross government debt have shown a negative impact on the banks’ profitability. The main contribution of this study implies different panel techniques with two uncommonly used macroeconomic variables such as the unemployment rate and debt ratio. The results on the country level differ from country to country and these findings can give a lead to policy makers on the national level on how to enhance the banks’ profitability levels.
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(This article belongs to the Special Issue Statistical Methods of Analyzing Financial Equilibrium, Performance and Risk, 2nd Edition)
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Open AccessArticle
BV Solutions to Evolution Inclusion with a Time and Space Dependent Maximal Monotone Operator
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Charles Castaing, Christiane Godet-Thobie and Manuel D. P. M. Marques
Mathematics 2024, 12(6), 896; https://doi.org/10.3390/math12060896 (registering DOI) - 18 Mar 2024
Abstract
This paper deals with the research of solutions of bounded variation (BV) to evolution inclusion coupled with a time and state dependent maximal monotone operator. Different problems are studied: existence of solutions, unicity of the solution, existence of periodic and bounded variation right
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This paper deals with the research of solutions of bounded variation (BV) to evolution inclusion coupled with a time and state dependent maximal monotone operator. Different problems are studied: existence of solutions, unicity of the solution, existence of periodic and bounded variation right continuous (BVRC) solutions. Second-order evolution inclusions and fractional (Caputo and Riemann–Liouville) differential inclusions are also considered. A result of the Skorohod problem driven by a time- and space-dependent operator under rough signal and a Volterra integral perturbation in the BRC setting is given. The paper finishes with some results for fractional differential inclusions under rough signals and Young integrals. Many of the given results are novel.
Full article
(This article belongs to the Special Issue Set-Valued Analysis, 3rd Edition)
Open AccessArticle
Cauchy Problem with Summable Initial-Value Functions for Parabolic Equations with Translated Potentials
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Andrey B. Muravnik and Grigorii L. Rossovskii
Mathematics 2024, 12(6), 895; https://doi.org/10.3390/math12060895 - 18 Mar 2024
Abstract
We study the Cauchy problem for differential–difference parabolic equations with potentials undergoing translations with respect to the spatial-independent variable. Such equations are used for the modeling of various phenomena not covered by the classical theory of differential equations (such as nonlinear optics, nonclassical
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We study the Cauchy problem for differential–difference parabolic equations with potentials undergoing translations with respect to the spatial-independent variable. Such equations are used for the modeling of various phenomena not covered by the classical theory of differential equations (such as nonlinear optics, nonclassical diffusion, multilayer plates and envelopes, and others). From the viewpoint of the pure theory, they are important due to crucially new effects not arising in the case of differential equations and due to the fact that a number of classical methods, tools, and approaches turn out to be inapplicable in the nonlocal theory. The qualitative novelty of our investigation is that the initial-value function is assumed to be summable. Earlier, only the case of bounded (essentially bounded) initial-value functions was investigated. For the prototype problem (the spatial variable is single and the nonlocal term of the equation is single), we construct the integral representation of a solution and show its smoothness in the open half-plane. Further, we find a condition binding the coefficient at the nonlocal potential and the length of its translation such that this condition guarantees the uniform decay (weighted decay) of the constructed solution under the unbounded growth of time. The rate of this decay (weighted decay) is estimated as well.
Full article
(This article belongs to the Special Issue Recent Trends in Convex Analysis and Mathematical Inequalities)
Open AccessArticle
An Efficient Linearized Difference Algorithm for a Diffusive Sel′kov–Schnakenberg System
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Yange Wang and Xixian Bai
Mathematics 2024, 12(6), 894; https://doi.org/10.3390/math12060894 - 18 Mar 2024
Abstract
This study provides an efficient linearized difference algorithm for a diffusive Sel′kov–Schnakenberg system. The algorithm is developed by using a finite difference method that relies on a three-level linearization approach. The boundedness, existence and uniqueness of the solution of our proposed
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This study provides an efficient linearized difference algorithm for a diffusive Sel′kov–Schnakenberg system. The algorithm is developed by using a finite difference method that relies on a three-level linearization approach. The boundedness, existence and uniqueness of the solution of our proposed algorithm are proved. The numerical experiments not only validate the accuracy of the algorithm but also preserve the Turing patterns.
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(This article belongs to the Special Issue Numerical and Computational Methods in Engineering)
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A Study on the Nature of Complexity in the Spanish Electricity Market Using a Comprehensive Methodological Framework
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Lucía Inglada-Pérez and Sandra González y Gil
Mathematics 2024, 12(6), 893; https://doi.org/10.3390/math12060893 - 18 Mar 2024
Abstract
The existence of chaos is particularly relevant, as the identification of a chaotic behavior in a time series could lead to reliable short-term forecasting. This paper evaluates the existence of nonlinearity and chaos in the underlying process of the spot prices of the
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The existence of chaos is particularly relevant, as the identification of a chaotic behavior in a time series could lead to reliable short-term forecasting. This paper evaluates the existence of nonlinearity and chaos in the underlying process of the spot prices of the Spanish electricity market. To this end, we used daily data spanning from 1 January 2013, to 31 March 2021 and we applied a comprehensive framework that encompassed a wide range of techniques. Nonlinearity was analyzed using the BDS method, while the existence of a chaotic structure was studied through Lyapunov exponents, recurrence plots, and quantitative recurrence analysis. While nonlinearity was detected in the underlying process, conclusive evidence supporting chaos was not found. In addition, the generalized autoregressive conditional heteroscedastic (GARCH) model accounts for part of the nonlinear structure that is unveiled in the electricity market. These findings hold substantial value for electricity market forecasters, traders, producers, and market regulators.
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(This article belongs to the Special Issue Chaos Theory and Its Applications to Economic Dynamics)
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Chaotic Path-Planning Algorithm Based on Courbage–Nekorkin Artificial Neuron Model
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Dmitriy Kvitko, Vyacheslav Rybin, Oleg Bayazitov, Artur Karimov, Timur Karimov and Denis Butusov
Mathematics 2024, 12(6), 892; https://doi.org/10.3390/math12060892 - 18 Mar 2024
Abstract
Developing efficient path-planning algorithms is an essential topic in modern robotics and control theory. Autonomous rovers and wheeled and tracked robots require path generators that can efficiently cover the explorable space with minimal redundancy. In this paper, we present a new path-planning algorithm
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Developing efficient path-planning algorithms is an essential topic in modern robotics and control theory. Autonomous rovers and wheeled and tracked robots require path generators that can efficiently cover the explorable space with minimal redundancy. In this paper, we present a new path-planning algorithm based on the chaotic behavior of the Courbage–Nekorkin neuron model with a coverage control parameter. Our study aims to reduce the number of iterations required to cover the chosen investigated area, which is a typical efficiency criterion for this class of algorithms. To achieve this goal, we implemented a pseudorandom bit generator (PRBG) based on a Courbage–Nekorkin chaotic map, which demonstrates chaotic behavior and successfully passes all statistical tests for randomness. The proposed PRBG generates a bit sequence that can be used to move the tracked robot in four or eight directions in an operation area of arbitrary size. Several statistical metrics were applied to evaluate the algorithm’s performance, including the percentage of coverage of the study area and the uniformity of coverage. The performance of several competing path-planning algorithms was analyzed using the chosen metrics when exploring two test areas of the sizes 50 × 50 cells and 100 × 100 cells, respectively, in four and eight directions. The experimental results indicate that the proposed algorithm is superior compared to known chaotic path-planning methods, providing more rapid and uniform coverage with the possibility of controlling the covered area using tunable parameters. In addition, this study revealed the high dependence of the coverage rate on the starting point. To investigate how the coverage rate depends on the choice of chaotic map, we implemented six different PRBGs using various chaotic maps. The obtained results can be efficiently used for solving path-planning tasks in both real-life and virtual (e.g., video games) applications.
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(This article belongs to the Special Issue Advances in Nonlinear Analysis and Control)
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Dynamic Cooperative Oligopolies
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Ferenc Szidarovszky and Akio Matsumoto
Mathematics 2024, 12(6), 891; https://doi.org/10.3390/math12060891 - 18 Mar 2024
Abstract
An n-person cooperative oligopoly is considered without product differentiation. It is assumed that the firms know the unit price function but have no access to the cost functions of the competitors. From market data, they have information about the industry output. The
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An n-person cooperative oligopoly is considered without product differentiation. It is assumed that the firms know the unit price function but have no access to the cost functions of the competitors. From market data, they have information about the industry output. The firms want to find the output levels that guarantee maximum industry profit. First, the existence of a unique maximizer is proven, which the firms cannot determine directly because of the lack of the knowledge of the cost functions. Instead, a dynamic model is constructed, which is asymptotically stable under realistic conditions, and the state trajectories converge to the optimum output levels of the firms. Three models are constructed: first, no time delay is assumed; second, information delay is considered for the firms on the industry output; and third, in addition, information delay is also assumed about the firms’ own output levels. The stability of the resulting no-delay, one-delay, and two-delay dynamics is examined.
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(This article belongs to the Special Issue Advances in Differential Dynamical Systems with Applications to Economics and Biology, 2nd Edition)
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Dirac Geometric Approach for the Unimodular Holst Action
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Bogar Díaz, Eduardo J. S. Villaseñor and Diana Zomeño Salas
Mathematics 2024, 12(6), 890; https://doi.org/10.3390/math12060890 - 18 Mar 2024
Abstract
We perform a Hamiltonian analysis of unimodular gravity in its first-order formulation, specifically a modification of the Holst action. In order to simplify the analysis, prior studies on this theory have introduced (for several reasons) additional elements, such as parametrization, complex fields, or
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We perform a Hamiltonian analysis of unimodular gravity in its first-order formulation, specifically a modification of the Holst action. In order to simplify the analysis, prior studies on this theory have introduced (for several reasons) additional elements, such as parametrization, complex fields, or considering the Barbero–Immirzi parameter as imaginary. We show that, by using a geometric implementation of the Dirac algorithm, a comprehensive analysis of the theory can be conducted without relying on these additional ingredients. The resulting theory reproduces the behavior of metric unimodular gravity.
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(This article belongs to the Section Mathematical Physics)
Open AccessArticle
On the Square Root Computation in Liber Abaci and De Practica Geometrie by Fibonacci
by
Trond Steihaug
Mathematics 2024, 12(6), 889; https://doi.org/10.3390/math12060889 - 18 Mar 2024
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We study the square root computation by Leonardo Fibonacci (or Leonardo of Pisa) in his MSS Liber Abaci from c1202 and c1228 and De Practica Geometrie from c1220. In this MSS, Fibonacci systematically describes finding the integer part of the square root of
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We study the square root computation by Leonardo Fibonacci (or Leonardo of Pisa) in his MSS Liber Abaci from c1202 and c1228 and De Practica Geometrie from c1220. In this MSS, Fibonacci systematically describes finding the integer part of the square root of an integer in numerous examples with three to seven decimal digits. The results of these examples are summarized in a table in the paper. Liber Abaci also describes in detail finding an approximation to the fractional part of the square root. However, in other examples in Liber Abaci and De Practica Geometrie, only the approximate values of the fractional part of the square roots are stated. This paper further explores these approximate values using techniques like reverse engineering. Contrary to many claims that Fibonacci also used other methods or approximations, we show that all examples can be explained using one digit-by-digit method to compute the integer part of the square root and one approximation scheme for the fractional part. Further, it is shown that the approximation scheme is tied to the method to compute the integer part of the square root.
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Model and Algorithm for a Two-Machine Group Scheduling Problem with Setup and Transportation Time
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Yu Ni, Shufen Dai, Shuaipeng Yuan, Bailin Wang and Zhuolun Zhang
Mathematics 2024, 12(6), 888; https://doi.org/10.3390/math12060888 - 18 Mar 2024
Abstract
This paper investigates a two-machine group scheduling problem with sequence-independent setup times and round-trip transportation times, which is derived from the production management requirements of modern steel manufacturing enterprises. The objective is to minimize the makespan. Addressing limitations in prior studies, we consider
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This paper investigates a two-machine group scheduling problem with sequence-independent setup times and round-trip transportation times, which is derived from the production management requirements of modern steel manufacturing enterprises. The objective is to minimize the makespan. Addressing limitations in prior studies, we consider a critical but largely ignored transportation method, namely round-trip transportation, and restricted transporter capacity between machines. To solve this problem, a mixed-integer programming model is first developed. Then, the problem complexity is analyzed for situations with both single and unlimited transporters. For the NP-hard case of a single transporter, we design an efficient two-stage heuristic algorithm with proven acceptable solution quality bounds. Extensive computational experiments based on steel plant data demonstrate the effectiveness of our approach in providing near-optimal solutions, and the maximum deviation between our algorithm and the optimal solution is 1.38%. This research can provide an operable optimization method that is valuable for group scheduling and transportation scheduling.
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(This article belongs to the Special Issue Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling, 2nd Edition)
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Energy-Management Strategy of Battery Energy Storage Systems in DC Microgrids: A Distributed Fuzzy Output Consensus Control Considering Multiple Cyber Attacks
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Xu Tian, Weisheng Wang, Liang Zou, Shuo Zhai, Bin Hai and Rui Wang
Mathematics 2024, 12(6), 887; https://doi.org/10.3390/math12060887 - 18 Mar 2024
Abstract
Distributed renewable sources are one of the most promising contributors for DC microgrids to reduce carbon emission and fuel consumption. Although the battery energy storage system (BESS) is widely applied to compensate the power imbalance between distributed generators (DGs) and loads, the impacts
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Distributed renewable sources are one of the most promising contributors for DC microgrids to reduce carbon emission and fuel consumption. Although the battery energy storage system (BESS) is widely applied to compensate the power imbalance between distributed generators (DGs) and loads, the impacts of disturbances, DGs, constant power loads (CPLs) and cyber attacks on this system are not simultaneously considered. Based on this, a distributed fuzzy output consensus control strategy is proposed to realize accurate current sharing and operate normally in the presence of denial of service (DoS) attacks and false data injection (FDI) attacks. Firstly, the whole model of the BESS in DC microgrids embedded into disturbance items, DGs, CPLs and resistive loads, is firstly built. This model could be further transformed into standard linear heterogeneous multi-agent systems with disturbance, which lays the foundation for the following control strategy. Then the model of FDI and DoS attacks are built. Meanwhile, the fuzzy logic controller (FLC) is applied to reduce the burden of communication among batteries. Based on these, a distributed output consensus fuzzy control is proposed to realize accurate current sharing among batteries. Moreover, the system under the proposed control in different cases is analyzed. Finally, the feasibility of the proposed control strategy is verified by numerical simulation results and experiment results.
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(This article belongs to the Special Issue Mathematical Applications in Electrical Engineering)
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Gaussian Mixture Probability Hypothesis Density Filter for Heterogeneous Multi-Sensor Registration
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Yajun Zeng, Jun Wang, Shaoming Wei, Chi Zhang, Xuan Zhou and Yingbin Lin
Mathematics 2024, 12(6), 886; https://doi.org/10.3390/math12060886 - 17 Mar 2024
Abstract
Spatial registration is a prerequisite for data fusion. Existing methods primarily focus on similar sensor scenarios and rely on accurate data association assumptions. To address the heterogeneous sensor registration in complex data association scenarios, this paper proposes a Gaussian mixture probability hypothesis density
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Spatial registration is a prerequisite for data fusion. Existing methods primarily focus on similar sensor scenarios and rely on accurate data association assumptions. To address the heterogeneous sensor registration in complex data association scenarios, this paper proposes a Gaussian mixture probability hypothesis density (GM-PHD)-based algorithm for heterogeneous sensor bias registration, accompanied by an adaptive measurement iterative update algorithm. Firstly, by constructing augmented target state motion and measurement models, a closed-form expression for prediction is derived based on Gaussian mixture (GM). In the subsequent update, a two-level Kalman filter is used to achieve an approximate decoupled estimation of the target state and measurement bias, taking into account the coupling between them through pseudo-likelihood. Notably, for heterogeneous sensors that cannot directly use sequential update techniques, sequential updates are first performed on sensors that can obtain complete measurements, followed by filtering updates using extended Kalman filter (EKF) sequential update techniques for incomplete measurements. When there are differences in sensor quality, the GM-PHD fusion filter based on measurement iteration update is sequence-sensitive. Therefore, the optimal subpattern assignment (OSPA) metric is used to optimize the fusion order and enhance registration performance. The proposed algorithms extend the multi-target information-based spatial registration algorithm to heterogeneous sensor scenarios and address the impact of different sensor-filtering orders on registration performance. Our proposed algorithms significantly improve the accuracy of bias estimation compared to the registration algorithm based on significant targets. Under different detection probabilities and clutter intensities, the average root mean square error (RMSE) of distance and angular biases decreased by 11.8% and 8.6%, respectively.
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(This article belongs to the Section Probability and Statistics)
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Spherical Gravity Forwarding of Global Discrete Grid Cells by Isoparametric Transformation
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Shujin Cao, Peng Chen, Guangyin Lu, Yihuai Deng, Dongxin Zhang and Xinyue Chen
Mathematics 2024, 12(6), 885; https://doi.org/10.3390/math12060885 - 17 Mar 2024
Abstract
For regional or even global geophysical problems, the curvature of the geophysical model cannot be approximated as a plane, and its curvature must be considered. Tesseroids can fit the curvature, but their shapes vary from almost rectangular at the equator to almost triangular
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For regional or even global geophysical problems, the curvature of the geophysical model cannot be approximated as a plane, and its curvature must be considered. Tesseroids can fit the curvature, but their shapes vary from almost rectangular at the equator to almost triangular at the poles, i.e., degradation phenomena. Unlike other spherical discrete grids (e.g., square, triangular, and rhombic grids) that can fit the curvature, the Discrete Global Grid System (DGGS) grid can not only fit the curvature but also effectively avoid degradation phenomena at the poles. In addition, since it has only edge-adjacent grids, DGGS grids have consistent adjacency and excellent angular resolution. Hence, DGGS grids are the best choice for discretizing the sphere into cells with an approximate shape and continuous scale. Compared with the tesseroid, which has no analytical solution but has a well-defined integral limit, the DGGS cell (prisms obtained from DGGS grids) has neither an analytical solution nor a fixed integral limit. Therefore, based on the isoparametric transformation, the non-regular DGGS cell in the system coordinate system is transformed into the regular hexagonal prism in the local coordinate system, and the DGGS-based forwarding algorithm of the gravitational field is realized in the spherical coordinate system. Different coordinate systems have differences in the integral kernels of gravity fields. In the current literature, the forward modeling research of polyhedrons (the DGGS cell, which is a polyhedral cell) is mostly concentrated in the Cartesian coordinate system. Therefore, the reliability of the DGGS-based forwarding algorithm is verified using the tetrahedron-based forwarding algorithm and the tesseroid-based forwarding algorithm with tiny tesseroids. From the numerical results, it can be concluded that if the distance from observations to sources is too small, the corresponding gravity field forwarding results may also have ambiguous values. Therefore, the minimum distance is not recommended for practical applications.
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(This article belongs to the Special Issue Mathematical Modeling, Numerical Analysis and Scientific Computing, with Their Applications)
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Are Brazilian Higher Education Institutions Efficient in Their Graduate Activities? A Two-Stage Dynamic Data-Envelopment-Analysis Cooperative Approach
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Lívia Mariana Lopes de Souza Torres and Francisco S. Ramos
Mathematics 2024, 12(6), 884; https://doi.org/10.3390/math12060884 - 17 Mar 2024
Abstract
Higher education evaluation presents itself as a worldwide trend. It aims to improve performance due to its importance for economic and personal growth. Graduate activities are essential for Brazilian research and innovation systems. However, previous studies have disregarded the importance of this educational
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Higher education evaluation presents itself as a worldwide trend. It aims to improve performance due to its importance for economic and personal growth. Graduate activities are essential for Brazilian research and innovation systems. However, previous studies have disregarded the importance of this educational level and have evaluated efficiency by jointly considering teaching and research or only undergraduate courses. Therefore, this study contributes to Brazilian reality by proving a national graduate activities efficiency evaluation that considers them as a two-stage system (formative and scientific production stages). The study provides three main methodological contributions by presenting a new centralized two-stage dynamic network data envelopment analysis (DNDEA) model with shared resources. Besides measuring efficiency, an efficiency decomposition based on a leader–follower assumption shows managers how much efficiency can alter when one of the stages needs to be prioritized. Finally, a new framework based on modified virtual inputs and outputs provides a bi-dimensional representation of the efficiency frontier. Results indicate the usefulness of the approach for ranking universities, and the need to improve scientific production, highlighting the negative impacts of COVID-19 on the formative process efficiency and showing no significant regional discrepancies regarding performance.
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(This article belongs to the Special Issue Advanced Applications of Multi-Criteria Decision-Making Methods in Operational Research)
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A Modified Cure Rate Model Based on a Piecewise Distribution with Application to Lobular Carcinoma Data
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Yolanda M. Gómez, John L. Santibañez, Vinicius F. Calsavara, Héctor W. Gómez and Diego I. Gallardo
Mathematics 2024, 12(6), 883; https://doi.org/10.3390/math12060883 - 17 Mar 2024
Abstract
A novel cure rate model is introduced by considering, for the number of concurrent causes, the modified power series distribution and, for the time to event, the recently proposed power piecewise exponential distribution. This model includes a wide variety of cure rate models,
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A novel cure rate model is introduced by considering, for the number of concurrent causes, the modified power series distribution and, for the time to event, the recently proposed power piecewise exponential distribution. This model includes a wide variety of cure rate models, such as binomial, Poisson, negative binomial, Haight, Borel, logarithmic, and restricted generalized Poisson. Some characteristics of the model are examined, and the estimation of parameters is performed using the Expectation–Maximization algorithm. A simulation study is presented to evaluate the performance of the estimators in finite samples. Finally, an application in a real medical dataset from a population-based study of incident cases of lobular carcinoma diagnosed in the state of São Paulo, Brazil, illustrates the advantages of the proposed model compared to other common cure rate models in the literature, particularly regarding the underestimation of the cure rate in other proposals and the improved precision in estimating the cure rate of our proposal.
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(This article belongs to the Special Issue Advances in Biostatistics and Applications)
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On Self-Intersections of Cubic Bézier Curves
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Ying-Ying Yu, Xin Li and Ye Ji
Mathematics 2024, 12(6), 882; https://doi.org/10.3390/math12060882 - 17 Mar 2024
Abstract
Cubic Bézier curves are widely used in computer graphics and geometric modeling, favored for their intuitive design and ease of implementation. However, self-intersections within these curves can pose significant challenges in both geometric modeling and analysis. This paper presents a comprehensive approach to
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Cubic Bézier curves are widely used in computer graphics and geometric modeling, favored for their intuitive design and ease of implementation. However, self-intersections within these curves can pose significant challenges in both geometric modeling and analysis. This paper presents a comprehensive approach to detecting and computing self-intersections of cubic Bézier curves. We introduce an efficient algorithm that leverages both the geometric properties of Bézier curves and numerical methods to accurately identify intersection points. The self-intersection problem of cubic Bézier curves is firstly transformed into a quadratic problem by eliminating trivial solutions. Subsequently, this quadratic system is converted into a linear system that may be easily analyzed and solved. Finally, the parameter values corresponding to the self-intersection points are computed through the solution of the linear system. The proposed method is designed to be robust and computationally efficient, making it suitable for real-time applications.
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(This article belongs to the Section Computational and Applied Mathematics)
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An Optimized Point Multiplication Strategy in Elliptic Curve Cryptography for Resource-Constrained Devices
by
Nawras H. Sabbry and Alla B. Levina
Mathematics 2024, 12(6), 881; https://doi.org/10.3390/math12060881 - 17 Mar 2024
Abstract
Elliptic curve cryptography (ECC) is widely acknowledged as a method for implementing public key cryptography on devices with limited resources thanks to its use of small keys. A crucial and complex operation in ECC calculations is scalar point multiplication. To improve its execution
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Elliptic curve cryptography (ECC) is widely acknowledged as a method for implementing public key cryptography on devices with limited resources thanks to its use of small keys. A crucial and complex operation in ECC calculations is scalar point multiplication. To improve its execution time and computational complexity in low-power devices, such as embedded systems, several algorithms have been suggested for scalar point multiplication, with each featuring different techniques and mathematical formulas. In this research, we focused on combining some techniques to produce a scalar point multiplication algorithm for elliptic curves over finite fields. The employed methodology involved mathematical analysis to investigate commonly used point multiplication methods. The aim was to propose an efficient algorithm that combined the best computational techniques, resulting in lower computational requirements. The findings show that the proposed method can overcome certain implementation issues found in other multiplication algorithms. In certain scenarios, the proposed method offers a more efficient approach by reducing the number of point doubling and point addition operations on elliptic curves using the inverse of the targeted point.
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(This article belongs to the Special Issue Computational Algebra, Coding Theory and Cryptography)
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Open AccessArticle
Optimization of Active Learning Strategies for Causal Network Structure
by
Mengxin Zhang and Xiaojun Zhang
Mathematics 2024, 12(6), 880; https://doi.org/10.3390/math12060880 - 17 Mar 2024
Abstract
Causal structure learning is one of the major fields in causal inference. Only the Markov equivalence class (MEC) can be learned from observational data; to fully orient unoriented edges, experimental data need to be introduced from external intervention experiments to improve the identifiability
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Causal structure learning is one of the major fields in causal inference. Only the Markov equivalence class (MEC) can be learned from observational data; to fully orient unoriented edges, experimental data need to be introduced from external intervention experiments to improve the identifiability of causal graphs. Finding suitable intervention targets is key to intervention experiments. We propose a causal structure active learning strategy based on graph structures. In the context of randomized experiments, the central nodes of the directed acyclic graph (DAG) are considered as the alternative intervention targets. In each stage of the experiment, we decompose the chain graph by removing the existing directed edges; then, each connected component is oriented separately through intervention experiments. Finally, all connected components are merged to obtain a complete causal graph. We compare our algorithm with previous work in terms of the number of intervention variables, convergence rate and model accuracy. The experimental results show that the performance of the proposed method in restoring the causal structure is comparable to that of previous works. The strategy of finding the optimal intervention target is simplified, which improves the speed of the algorithm while maintaining the accuracy.
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(This article belongs to the Special Issue Research Progress and Application of Bayesian Statistics)
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