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1.	Grevholm, Barbro (författare) Recent Nordic research in mathematics education illustrated by examples from NORMA17 2021 Ingår i: Mathematics. - 2227-7390. ; 9:8, s. 1-26 Tidskriftsartikel (refereegranskat)abstract A characterization of recent Nordic research in didactics of mathematics is presented based on the 32 research reports from the Nordic and Baltic countries in the proceedings from NORMA17 (The eighth Nordic conference on didactics of mathematics). Recent Nordic research in didactics of mathematics is observed from several aspects such as choice of problem, theory, method, result, and target for the message. The analyses of the papers on different levels and from a manifold of perspectives build up an image of what Nordic research in DM (didactics of mathematics) contains and represents currently. The closeness and cooperation between researchers in the Nordic countries is characteristic as well as the breadth and variation in the choice of questions, theories, and methods. Research activity seems to flourish most in Norway. Small-scale studies as well as larger projects are visible. A variety of messages about mathematics teaching and learning for all age groups are directed to students, mathematics teachers, teacher educators, and policymakers. Quantitative and qualitative empirical studies dominate. Conceptual or theoretical investigations are rare. Studies of outcomes of interventions, including teaching approaches and experiments are most common, followed by studies of learning and cognition, including problem-solving. There is a need for surveys and overviews as so many new results are exposed.
2.	Ait-Mlouk, Addi, et al. (författare) WINFRA : A Web-Based Platform for Semantic Data Retrieval and Data Analytics 2020 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 8:11 Tidskriftsartikel (refereegranskat)abstract Given the huge amount of heterogeneous data stored in different locations, it needs to be federated and semantically interconnected for further use. This paper introduces WINFRA, a comprehensive open-access platform for semantic web data and advanced analytics based on natural language processing (NLP) and data mining techniques (e.g., association rules, clustering, classification based on associations). The system is designed to facilitate federated data analysis, knowledge discovery, information retrieval, and new techniques to deal with semantic web and knowledge graph representation. The processing step integrates data from multiple sources virtually by creating virtual databases. Afterwards, the developed RDF Generator is built to generate RDF files for different data sources, together with SPARQL queries, to support semantic data search and knowledge graph representation. Furthermore, some application cases are provided to demonstrate how it facilitates advanced data analytics over semantic data and showcase our proposed approach toward semantic association rules.
3.	Amo-Navarro, Jesus, et al. (författare) Two-Dimensional Compact-Finite-Difference Schemes for Solving the bi-Laplacian Operator with Homogeneous Wall-Normal Derivatives 2021 Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 9:19 Tidskriftsartikel (refereegranskat)abstract In fluid mechanics, the bi-Laplacian operator with Neumann homogeneous boundary conditions emerges when transforming the Navier-Stokes equations to the vorticity-velocity formulation. In the case of problems with a periodic direction, the problem can be transformed into multiple, independent, two-dimensional fourth-order elliptic problems. An efficient method to solve these two-dimensional bi-Laplacian operators with Neumann homogeneus boundary conditions was designed and validated using 2D compact finite difference schemes. The solution is formulated as a linear combination of auxiliary solutions, as many as the number of points on the boundary, a method that was prohibitive some years ago due to the large memory requirements to store all these auxiliary functions. The validation has been made for different field configurations, grid sizes, and stencils of the numerical scheme, showing its potential to tackle high gradient fields as those that can be found in turbulent flows.
4.	Anderson, Johan, 1973 (författare) Information Geometric Investigation of Solutions to the Fractional Fokker-Planck Equation 2020 Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 8:5 Tidskriftsartikel (refereegranskat)abstract A novel method for measuring distances between statistical states as represented by probability distribution functions (PDF) has been proposed, namely the information length. The information length enables the computation of the total number of statistically different states that a system evolves through in time. Anomalous transport can presumably be modeled fractional velocity derivatives and Langevin dynamics in a Fractional Fokker-Planck (FFP) approach. The numerical solutions or PDFs are found for varying degree of fractionality (alpha) of the stable Levy distribution as solutions to the FFP equation. Specifically, the information length of time-dependent PDFs for a given fractional index alpha is computed.
5.	Anjum, Asad Ur Rehman, et al. (författare) Sensitivity Analysis of Mathematical Model to Study the Effect of T Cells Infusion in Treatment of CLL 2020 Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 8:4 Tidskriftsartikel (refereegranskat)abstract In this paper, we considered a mathematical model concerned with the treatment of Chronic Lymphocytic Leukemia (CLL) taking into account the effect of superficially infused T cells in this particular type of tumor. The model is described thoroughly by the system of non-linear differential equations explaining the interaction of naive, infected, cancer and immune cell population. The detailed sensitivity analysis with the application is the major part of this paper. The basic objective is to provide insight to how parameters' behavior varies model results by elaborating the results obtained from the application of sensitivity analysis. The sensitivity of the model was evaluated not only theoretically, but also with the help of a numerical approach, producing graphs providing better imminent of results. We argue that the application of the sensitivity analysis method endows an insight into how and which parameters are of primary significance in controlling the spread of leukemia.
6.	Brändas, Erkki J., 1940- (författare) There Are Quantum Jumps 2015 Ingår i: Mathematics. - : Published by MDPI AG, Basel, Switzerland. - 2227-7390. ; 3:2, s. 319-328 Tidskriftsartikel (refereegranskat)abstract In this communication we take up the age-old problem of the possibility to incorporate quantum jumps. Unusually, we investigate quantum jumps in an extended quantum setting, but one of rigorous mathematical significance. The general background for this formulation originates in the Balslev-Combes theorem for dilatation analytic Hamiltonians and associated complex symmetric representations. The actual jump is mapped into a Jordan block of order two and a detailed derivation is discussed for the case of the emission of a photon by an atom. The result can be easily reassigned to analogous cases as well as generalized to Segrè characteristics of arbitrary order.
7.	Dai, Deliang, et al. (författare) High-Dimensional Mahalanobis Distances of Complex Random Vectors 2021 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 9:16 Tidskriftsartikel (refereegranskat)abstract In this paper, we investigate the asymptotic distributions of two types of Mahalanobis distance (MD): leave-one-out MD and classical MD with both Gaussian- and non-Gaussian-distributed complex random vectors, when the sample size n and the dimension of variables p increase under a fixed ratio c = p/n -> infinity. We investigate the distributional properties of complex MD when the random samples are independent, but not necessarily identically distributed. Some results regarding the F-matrix F = S2-1S1-the product of a sample covariance matrix S-1 (from the independent variable array (be(Z(i))(1xn)) with the inverse of another covariance matrix S-2 (from the independent variable array (Z(j not equal i))(pxn))-are used to develop the asymptotic distributions of MDs. We generalize the F-matrix results so that the independence between the two components S-1 and S-2 of the F-matrix is not required.
8.	Enayat, Ali, 1959, et al. (författare) On Effectively Indiscernible Projective Sets and the Leibniz-Mycielski Axiom 2021 Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 9:14 Tidskriftsartikel (refereegranskat)abstract Examples of effectively indiscernible projective sets of real numbers in various models of set theory are presented. We prove that it is true, in Miller and Laver generic extensions of the constructible universe, that there exists a lightface Π21 equivalence relation on the set of all nonconstructible reals, having exactly two equivalence classes, neither one of which is ordinal definable, and therefore the classes are OD-indiscernible. A similar but somewhat weaker result is obtained for Silver extensions. The other main result is that for any n, starting with 2, the existence of a pair of countable disjoint OD-indiscernible sets, whose associated equivalence relation belongs to lightface Πn1, does not imply the existence of such a pair with the associated relation in Σn1 or in a lower class.
9.	Ghandour, Elsa, et al. (författare) Almost complex surfaces in the nearly Kähler SL(2, R) × SL(2, R) 2020 Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 8:7 Tidskriftsartikel (refereegranskat)abstract The space SL(2, R) × SL(2, R) admits a natural homogeneous pseudo-Riemannian nearly Kahler structure. We investigate almost complex surfaces in this space. In particular, we obtain a complete classification of the totally geodesic almost complex surfaces and of the almost complex surfaces with parallel second fundamental form.
10.	Grevholm, Barbro (författare) Recent Nordic research in mathematics education illustrated by examples from NORMA17 2021 Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 9:8, s. 1-26 Tidskriftsartikel (refereegranskat)abstract A characterization of recent Nordic research in didactics of mathematics is presented based on the 32 research reports from the Nordic and Baltic countries in the proceedings from NORMA17 (The eighth Nordic conference on didactics of mathematics). Recent Nordic research in didactics of mathematics is observed from several aspects such as choice of problem, theory, method, result, and target for the message. The analyses of the papers on different levels and from a manifold of perspectives build up an image of what Nordic research in DM (didactics of mathematics) contains and represents currently. The closeness and cooperation between researchers in the Nordic countries is characteristic as well as the breadth and variation in the choice of questions, theories, and methods. Research activity seems to flourish most in Norway. Small-scale studies as well as larger projects are visible. A variety of messages about mathematics teaching and learning for all age groups are directed to students, mathematics teachers,teacher educators, and policymakers. Quantitative and qualitative empirical studies dominate. Conceptual or theoretical investigations are rare. Studies of outcomes of interventions, including teaching approaches and experiments are most common, followed by studies of learning and cognition, including problem-solving. There is a need for surveys and overviews as so many new results are exposed.
11.	Hatzikirou, Haralampos, et al. (författare) A Novel Averaging Principle Provides Insights in the Impact of Intratumoral Heterogeneity on Tumor Progression 2021 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 9:20 Tidskriftsartikel (refereegranskat)abstract Typically stochastic differential equations (SDEs) involve an additive or multiplicative noise term. Here, we are interested in stochastic differential equations for which the white noise is nonlinearly integrated into the corresponding evolution term, typically termed as random ordinary differential equations (RODEs). The classical averaging methods fail to treat such RODEs. Therefore, we introduce a novel averaging method appropriate to be applied to a specific class of RODEs. To exemplify the importance of our method, we apply it to an important biomedical problem, in particular, we implement the method to the assessment of intratumoral heterogeneity impact on tumor dynamics. Precisely, we model gliomas according to a well-known Go or Grow (GoG) model, and tumor heterogeneity is modeled as a stochastic process. It has been shown that the corresponding deterministic GoG model exhibits an emerging Allee effect (bistability). In contrast, we analytically and computationally show that the introduction of white noise, as a model of intratumoral heterogeneity, leads to monostable tumor growth. This monostability behavior is also derived even when spatial cell diffusion is taken into account.
12.	Hoibakk, Ralph, et al. (författare) A New Development of the Classical Single Ladder Problem via Converting the Ladder to a Staircase 2021 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 9:4 Tidskriftsartikel (refereegranskat)abstract Our purpose is to shed some new light on problems arising from a study of the classical Single Ladder Problem (SLP). The basic idea is to convert the SLP to a corresponding Single Staircase Problem. The main result (Theorem 1) shows that this idea works fine and new results can be obtained by just calculating rational solutions of an algebraic equation. Some examples of such concrete calculations are given and examples of new results are also given. In particular, we derive a number of integer SLPs with congruent ladders, where a set of rectangular boxes with integer sides constitutes a staircase along a common ladder. Finally, the case with a regular staircase along a given ladder is investigated and illustrated with concrete examples.
13.	Hosseini, Zahra Shah, et al. (författare) A Fully Resolved Computational Fluid Dynamics Study of the Boundary Layer Flow of an Aqueous Nanoliquid Comprising Gyrotactic Microorganisms over a Stretching Sheet : The Validity of Conventional Similarity Models 2021 Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 9:21, s. 2655- Tidskriftsartikel (refereegranskat)abstract When materials are processed in the form of sheets that are stretched, cooling is often required. Coolants have been developed to maximize the rate of heat transfer away from the sheet, including by adding nanoparticles and microorganisms to control the physical properties of the fluid. Such coolants perform well, but the interaction between them and the sheet is not yet fully understood. Most of the articles found in the literature have used similarity models to solve the set of governing equations. In this method, the governing equations can be mapped into a set of 1-D equations and solved easily. However, care should be taken when using this method as the validity of this method is ensured only in the fully developed region, far away enough from the extrusion slit. The present study, therefore, aims to explore the reliability of a similarity model by comparing it with a full computational fluid dynamics (CFD) approach. In this work, the boundary layer flow of a nanoliquid comprising gyrotactic microorganisms in both the developed and undeveloped regions of a stretching sheet is studied using computational fluid dynamics with the finite difference approach, implemented using FORTRAN. The results of the CFD method are compared against the similarity analysis results for the length of the developed and undeveloped regions. This study, for the first time, distinguishes between the undeveloped and fully developed regions and finds the region in which the similarity analysis is valid. The numerical results show that the critical Reynolds numbers for the boundary layers of the concentration of the nano-additives and of density of the microorganisms are equal. To achieve an agreement between the CFD and the similarity model within 5%, the Grashof number for the hydrodynamic boundary layer must be Gr < 10(5). Nonetheless, this length reduces significantly when the Grashof number increases from 10(5) to 10(6). The reduced Nusselt number, Nu(r), increases when the density difference of the microorganisms increases.
14.	Høibakk, Ralph, et al. (författare) A New Look at the Single Ladder Problem (SLP) via Integer Parametric Solutions to the Corresponding Quartic Equation 2020 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 8:2, s. 1-21 Tidskriftsartikel (refereegranskat)abstract The aim is to put new light on the single ladder problem (SLP). Some new methods for finding complete integer solutions to the corresponding quartic equation z(4) - 2Lz(3) + ( L-2 - a(2) - b(2))z(2) + 2La(2)z - L(2)a(2) = 0 are developed. For the case L >= L-min, these methods imply a complete parametric representation for integer solutions of SLP in the first quadrant. Some corresponding (less complete) results for the case L > L-min are also pointed out.
15.	Jiang, Bo, et al. (författare) Dynamic graph learning: A structure-driven approach 2021 Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 9:2, s. 1-20 Tidskriftsartikel (refereegranskat)abstract The purpose of this paper is to infer a dynamic graph as a global (collective) model of time-varying measurements at a set of network nodes. This model captures both pairwise as well as higher order interactions (i.e., more than two nodes) among the nodes. The motivation of this work lies in the search for a connectome model which properly captures brain functionality across all regions of the brain, and possibly at individual neurons. We formulate it as an optimization problem, a quadratic objective functional and tensor information of observed node signals over short time intervals. The proper regularization constraints reflect the graph smoothness and other dynamics involving the underlying graph’s Laplacian, as well as the time evolution smoothness of the underlying graph. The resulting joint optimization is solved by a continuous relaxation of the weight parameters and an introduced novel gradient-projection scheme. While the work may be applicable to any time-evolving data set (e.g., fMRI), we apply our algorithm to a real-world dataset comprising recorded activities of individual brain cells. The resulting model is shown to be not only viable but also efficiently computable.
16.	Koloseni, David, et al. (författare) AHP-Like Matrices and Structures : Absolute and Relative Preferences 2020 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 8:5 Tidskriftsartikel (refereegranskat)abstract Aggregation functions are extensively used in decision making processes to combine available information. Arithmetic mean and weighted mean are some of the most used ones. In order to use a weighted mean, we need to define its weights. The Analytical Hierarchy Process (AHP) is a well known technique used to obtain weights based on interviews with experts. From the interviews we define a matrix of pairwise comparisons of the importance of the weights. We call these AHP-like matrices absolute preferences of weights. We propose another type of matrix that we call a relative preference matrix. We define this matrix with the same goal—to find the weights for weighted aggregators. We discuss how it can be used for eliciting the weights for the weighted mean and define a similar approach for the Choquet integral.
17.	Nakonechnyi, Oleksandr, et al. (författare) Guaranteed Estimation of Solutions to the Cauchy Problem When the Restrictions on Unknown Initial Data Are Not Posed 2021 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 9:24 Tidskriftsartikel (refereegranskat)abstract The paper deals with Cauchy problems for first-order systems of linear ordinary differential equations with unknown data. It is assumed that the right-hand sides of equations belong to certain bounded sets in the space of square-integrable vector-functions, and the information about the initial conditions is absent. From indirect noisy observations of solutions to the Cauchy problems on a finite system of points and intervals, the guaranteed mean square estimates of linear functionals on unknown solutions of the problems under consideration are obtained. Under an assumption that the statistical characteristics of noise in observations are not known exactly, it is proved that such estimates can be expressed in terms of solutions to well-defined boundary value problems for linear systems of impulsive ordinary differential equations.
18.	Pourhadi, Ehsan, Researcher, 1986-, et al. (författare) Application of Fixed-Point Theory for a Nonlinear Fractional Three-Point Boundary-Value Problem 2019 Ingår i: Mathematics. - Basel, Switzerland : MDPI. - 2227-7390. ; 7:6, s. 1-11 Tidskriftsartikel (refereegranskat)abstract Throughout this paper, via the Schauder fixed-point theorem, a generalization of Krasnoselskii’s fixed-point theorem in a cone, as well as some inequalities relevant to Green’s function, we study the existence of positive solutions of a nonlinear, fractional three-point boundary-value problem with a term of the first order derivative [...]
19.	Sirjani, Marjan, et al. (författare) Verification of Cyberphysical Systems 2020 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 8:7 Tidskriftsartikel (refereegranskat)abstract The value of verification of cyberphysical systems depends on the relationship between the state of the software and the state of the physical system. This relationship can be complex because of the real-time nature and different timelines of the physical plant, the sensors and actuators, and the software that is almost always concurrent and distributed. In this paper, we study different ways to construct a transition system model for the distributed and concurrent software components of a CPS. The purpose of the transition system model is to enable model checking, an established and widely used verification technique. We describe a logical-time-based transition system model, which is commonly used for verifying programs written in synchronous languages, and derive the conditions under which such a model faithfully reflects physical states. When these conditions are not met (a common situation), a finer-grained event-based transition system model may be required. We propose an approach for formal verification of cyberphysical systems using Lingua Franca, a language designed for programming cyberphysical systems, and Rebeca, an actor-based language designed for model checking distributed event-driven systems. We focus on the cyber part and model a faithful interface to the physical part. Our method relies on the assumption that the alignment of different timelines during the execution of the system is the responsibility of the underlying platforms. We make those assumptions explicit and clear.
20.	Truica, Ciprian-Octavian, et al. (författare) MisRoB ae RTa : Transformers versus Misinformation 2022 Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 10:4 Tidskriftsartikel (refereegranskat)abstract Misinformation is considered a threat to our democratic values and principles. The spread of such content on social media polarizes society and undermines public discourse by distorting public perceptions and generating social unrest while lacking the rigor of traditional journalism. Transformers and transfer learning proved to be state-of-the-art methods for multiple well-known natural language processing tasks. In this paper, we propose MisRoB ae RTa, a novel transformer-based deep neural ensemble architecture for misinformation detection. MisRoB ae RTa takes advantage of two state-of-the art transformers, i.e., BART and RoBERTa, to improve the performance of discriminating between real news and different types of fake news. We also benchmarked and evaluated the performances of multiple transformers on the task of misinformation detection. For training and testing, we used a large real-world news articles dataset (i.e., 100,000 records) labeled with 10 classes, thus addressing two shortcomings in the current research: (1) increasing the size of the dataset from small to large, and (2) moving the focus of fake news detection from binary classification to multi-class classification. For this dataset, we manually verified the content of the news articles to ensure that they were correctly labeled. The experimental results show that the accuracy of transformers on the misinformation detection problem was significantly influenced by the method employed to learn the context, dataset size, and vocabulary dimension. We observe empirically that the best accuracy performance among the classification models that use only one transformer is obtained by BART, while DistilRoBERTa obtains the best accuracy in the least amount of time required for fine-tuning and training. However, the proposed MisRoB ae RTa outperforms the other transformer models in the task of misinformation detection. To arrive at this conclusion, we performed ample ablation and sensitivity testing with MisRoB ae RTa on two datasets.
21.	Wen, Qianyun, et al. (författare) Fuzzy Ensemble of Multi-Criteria Decision Making Methods for Heating Energy Transition in Danish Households 2021 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 9:19 Tidskriftsartikel (refereegranskat)abstract More than 110 countries, including 500 cities worldwide, have set the goal of reaching carbon neutrality. Heating contributes to most of the residential energy consumption and carbon emissions. The green energy transition of fossil-based heating systems is needed to reach the emission goals. However, heating systems vary in energy source, heating technology, equipment location, and these complexities make it challenging for households to compare heating systems and make decisions. Hence, a decision support tool that provides a generalized ranking of individual heating alternatives is proposed for households as decision makers to identify the optimal choice. This paper presents an analysis of 13 heating alternatives and 19 quantitative criteria in technological, environmental, and financial aspects, combines ideal solution-based multi-criteria decision making with 6 weighting methods and 4 normalization methods, and introduces ensemble learning with a fuzzy membership function derived from Cauchy distribution to finalize the ultimate ranking. The robustness of the proposed method is verified by three sensitive analyses from different aspects. Air-to-water heat pump, solar heating and direct district heating are the top three rankings in the final result under Danish national average data. A framework is designed to guide decision makers to apply this ranking guideline with their practical, feasible situations.
22.	Abgaryan, Garnik V., et al. (författare) TE-Polarized Electromagnetic Wave Diffraction by a Circular Slotted Cylinder 2023 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 11:9 Tidskriftsartikel (refereegranskat)abstract The problem of diffraction of a TE-polarized electromagnetic wave by a circular slotted cylinder is investigated. The boundary value problem in question for the Helmholtz equation is reduced to an infinite system of linear algebraic equations of the second kind (SLAE-II) using integral summation identities (ISI). A detailed study of the matrix operator of the problem is performed and its Fredholm property in the weighted Hilbert space of infinite sequences is proven. The convergence of the truncation method constructed in the paper for the numerical solution of SLAE-II is justified and the results of computations are presented and discussed, specifically considering the determination of resonance modes.
23.	Barrera Diaz, Carlos Alberto, 1987-, et al. (författare) An Enhanced Simulation-Based Multi-Objective Optimization Approach with Knowledge Discovery for Reconfigurable Manufacturing Systems 2023 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 11:6 Tidskriftsartikel (refereegranskat)abstract In today’s uncertain and competitive market, where manufacturing enterprises are subjected to increasingly shortened product lifecycles and frequent volume changes, reconfigurable manufacturing system (RMS) applications play significant roles in the success of the manufacturing industry. Despite the advantages offered by RMSs, achieving high efficiency constitutes a challenging task for stakeholders and decision makers when they face the trade-off decisions inherent in these complex systems. This study addresses work task and resource allocations to workstations together with buffer capacity allocation in an RMS. The aim is to simultaneously maximize throughput and to minimize total buffer capacity under fluctuating production volumes and capacity changes while considering the stochastic behavior of the system. An enhanced simulation-based multi-objective optimization (SMO) approach with customized simulation and optimization components is proposed to address the abovementioned challenges. Apart from presenting the optimal solutions subject to volume and capacity changes, the proposed approach supports decision makers with knowledge discovery to further understand RMS design. In particular, this study presents a customized SMO approach combined with a novel flexible pattern mining method for optimizing an RMS and conducts post-optimal analyses. To this extent, this study demonstrates the benefits of applying SMO and knowledge discovery methods for fast decision support and production planning of an RMS.
24.	Ben Khedher, Nidhal, et al. (författare) Numerical Study of the Flow and Thermomagnetic Convection Heat Transfer of a Power Law Non-Newtonian Ferrofluid within a Circular Cavity with a Permanent Magnet 2022 Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 10:15 Tidskriftsartikel (refereegranskat)abstract The aim of this study is to analyze the thermo-magnetic-gravitational convection of a non-Newtonian power law ferrofluid within a circular cavity. The ferrofluid is exposed to the magnetic field of a permanent magnet. The finite element method is employed to solve the non-dimensional controlling equations. A grid sensitivity analysis and the validation of the used method are conducted. The effect of alterable parameters, including the power law index, 0.7 <= n <= 1.3, gravitational Rayleigh number, 10(4) <= Ra-T <= 10(6), magnetic Rayleigh number, 10(5) <= Ra-M <= 10(8), the location of the hot and cold surfaces, 0 <= lambda <= pi/2, and the length of the magnet normalized with respect to the diameter of the cavity, 0.1 <= L <= 0.65, on the flow and heat transfer characteristics are explored. The results show that the heat transfer rate increases at the end of both arcs compared to the central region because of buoyancy effects, and it is greater close to the hot arc. The location of the arcs does not affect the heat transfer rate considerably. An increase in the magnetic Rayleigh number contributes to stronger circulation of the flow inside and higher heat transfer. When the Kelvin force is the only one imposed on the flow, it enhances the heat transfer for magnets of length 0.2 <= L <= 0.3.
25.	Di Nunno, Giulia, et al. (författare) From Constant to Rough : A Survey of Continuous Volatility Modeling 2023 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 11:19 Forskningsöversikt (refereegranskat)abstract In this paper, we present a comprehensive survey of continuous stochastic volatility models, discussing their historical development and the key stylized facts that have driven the field. Special attention is dedicated to fractional and rough methods: without advocating for either roughness or long memory, we outline the motivation behind them and characterize some landmark models. In addition, we briefly touch on the problem of VIX modeling and recent advances in the SPX-VIX joint calibration puzzle.
26.	Ernst, Thomas (författare) Applications of q-Real Numbers to Triple q-Hypergeometric Functions and q-Horn Functions 2023 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 11:10 Tidskriftsartikel (refereegranskat)abstract The purpose of this article is to study how q-real numbers can be used for computations of convergence regions, q-integral representations of certain multiple triple q-Lauricella functions. The corresponding q-difference equations are also given without proof. In the process, we slightly improve Exton's original formulas. We also survey the current attempts to generalize the above functions to triple and quadruple hypergeometric functions. Finally, we compute some q-analogues of transformation formulas for Horn functions.
27.	Goranko, Valentin, 1959- (författare) Preplay Negotiations with Unconditional Offers of Side Payments in Two-Player Strategic-Form Games : Towards Non-Cooperative Cooperation 2022 Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 10:14 Tidskriftsartikel (refereegranskat)abstract I consider strategic-form games with transferable utility extended with a phase of negotiations before the actual play of the game, where players can exchange a series of alternating (turn-based) unilaterally binding offers to each other for incentive payments of utilities after the play, conditional only on the recipients playing the strategy indicated in the offer. Every such offer transforms the game payoff matrix by accordingly transferring the offered amount from the offering player's payoff to the recipient's in all outcomes where the indicated strategy is played by the latter. That exchange of offers generates an unbounded-horizon, extensive-form preplay negotiations game, which is the focus of this study. In this paper, I study the case where the players assume that their opponents can terminate the preplay negotiations phase at any stage. Consequently, in their negotiation strategies, the players are guided by myopic rationality reasoning and aim at optimising each of their offers. The main results and findings include a concrete algorithmic procedure for computing players' best offers in the preplay negotiations phase and using it to demonstrate that these negotiations can generally lead to substantial improvement of the payoffs for both players in the transformed game, but they do not always lead to optimal outcomes, as one might expect.
28.	Hosseinzadeh Dadash, Amirhossein, 1986-, et al. (författare) Infinite-Horizon Degradation Control Based on Optimization of Degradation-Aware Cost Function 2024 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 12:5 Tidskriftsartikel (refereegranskat)abstract Controlling machine degradation enhances the accuracy of the remaining-useful-life estimation and offers the ability to control failure type and time. In order to achieve optimal degradation control, the system controller must be cognizant of the consequences of its actions by considering the degradation each action imposes on the system. This article presents a method for designing cost-aware controllers for linear systems, to increase system reliability and availability through degradation control. The proposed framework enables learning independent of the system's physical structure and working conditions, enabling controllers to choose actions that reduce system degradation while increasing system lifetime. To this end, the cost of each controller's action is calculated based on its effect on the state of health. A mathematical structure is proposed, to incorporate these costs into the cost function of the linear-quadratic controller, allowing for optimal feedback for degradation control. A simulation validates the proposed method, demonstrating that the optimal-control method based on the proposed cost function outperforms the linear-quadratic regulator in several ways.
29.	Hu, Gang, et al. (författare) EJS: Multi-Strategy Enhanced Jellyfish Search Algorithm for Engineering Applications 2023 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 11:4 Tidskriftsartikel (refereegranskat)abstract The jellyfish search (JS) algorithm impersonates the foraging behavior of jellyfish in the ocean. It is a newly developed metaheuristic algorithm that solves complex and real-world optimization problems. The global exploration capability and robustness of the JS algorithm are strong, but the JS algorithm still has significant development space for solving complex optimization problems with high dimensions and multiple local optima. Therefore, in this study, an enhanced jellyfish search (EJS) algorithm is developed, and three improvements are made: (i) By adding a sine and cosine learning factors strategy, the jellyfish can learn from both random individuals and the best individual during Type B motion in the swarm to enhance optimization capability and accelerate convergence speed. (ii) By adding a local escape operator, the algorithm can skip the trap of local optimization, and thereby, can enhance the exploitation ability of the JS algorithm. (iii) By applying an opposition-based learning and quasi-opposition learning strategy, the population distribution is increased, strengthened, and more diversified, and better individuals are selected from the present and the new opposition solution to participate in the next iteration, which can enhance the solutions quality, meanwhile, convergence speed is faster and the algorithms precision is increased. In addition, the performance of the developed EJS algorithm was compared with those of the incomplete improved algorithms, and some previously outstanding and advanced methods were evaluated on the CEC2019 test set as well as six examples of real engineering cases. The results demonstrate that the EJS algorithm can skip the trap of local optimization, can enhance the solutions quality, and can increase the calculation speed. In addition, the practical engineering applications of the EJS algorithm also verify its superiority and effectiveness in solving both constrained and unconstrained optimization problems, and therefore, suggests future possible applications for solving such optimization problems.
30.	Hussain, Sajid, et al. (författare) Families of Extended Exponentiated Generalized Distributions and Applications of Medical Data Using Burr III Extended Exponentiated Weibull Distribution 2023 Ingår i: Mathematics. - 2227-7390. ; 11:14 Tidskriftsartikel (refereegranskat)abstract In this article, four new families named as Weibull extended exponentiated-X (WEE-X), Lomax extended exponentiated-X (LEE-X), Logistic extended exponentiated-X (LGCEE-X), and Burr III extended exponentiated-X (BIIIEE-X) with their quantile functions are proposed. The expressions for distribution function and density function of BIIIEE-X family are written in terms of linear combinations of the exponentiated densities based to parent model. New models, i.e., Weibul extended exponentiated Weibull (WEEW), Lomax extended exponentiated Weibull (LEEW), Logistic extended exponentiated Weibull (LGCEEW), and Burr III extended exponentiated-Weibull (BIIIEEW) distributions are derived, were plotted for functions of probability density and hazard rate at different levels of parameters. Some mathematical properties of the BIIIEEW model are disclosed. The maximum likelihood method for the BIIIEEW model are described. Numerical applications of the BIIIEEW model to disease of cancer datasets are provided.
31.	Hussain, Sajid, et al. (författare) The Exponentiated Power Alpha Index Generalized Family of Distributions : Properties and Applications 2023 Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 11:4, s. 900-900 Tidskriftsartikel (refereegranskat)abstract The study of hydrological characteristics has a vital role in designing, planning, and managing water resources. The selection of appropriate probability distributions and methods of estimations are basic elements in hydrology analyses. In this article, a new family named the ‘exponentiated power alpha index generalized’ (EPAIG)-G is proposed to develop several new distributions. Using this proposed family, we developed a new model, called the EPAIG-exponential (EPAIG-E). A few structural properties of the EPAIG-G were obtained. The EPAIG-E parameters were estimated through the method of maximum likelihood (MML). The study of the Monte Carlo simulation (MCS) was produced for the EPAIG-E. The model performance is illustrated using real data.
32.	Hussain, Sajid, et al. (författare) The Generalized Alpha Exponent Power Family of Distributions : Properties and Applications 2022 Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 10:9 Tidskriftsartikel (refereegranskat)abstract Here, a new method is recommended to characterize a new continuous distribution class, named the generalized alpha exponent power family of distributions (GAEPFDs). A particular sub-model is presented for exemplifying the objective. The basic statistical properties, such as ordinary moments, the probability weighted moments, mode, quantile, order statistics, entropy measures, and moment generating functions, etc., were explored. To gauge the GAEPPRD parameters, the ML technique was utilized. The estimator behaviour was studied by a Monte Carlo simulation study (MCSS). The effectiveness of GAEPFDs was demonstrated observationally through lifetime data. The applications show that GAEPFDs can offer preferable results over other competitive models.
33.	Hussain, Sajid, et al. (författare) The Generalized Exponential Extended Exponentiated Family of Distributions : Theory, Properties, and Applications 2022 Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 10:19 Tidskriftsartikel (refereegranskat)abstract Here, we propose a new generalized exponential extended exponentiated (NGE3) family of distributions. Some statistical properties of proposed family are gained. The most extreme probability method, maximum likelihood (ML), is utilized for parameter estimation. We explore an exceptional model called NGE3-Exponential (NGE3E). NGE3E is estimated with ML, and the performance of estimators is demonstrated by utilizing a simulation. Moreover, two applications are given to show the significance and adaptability of the proposed model in comparison to some generalized models (GMs).
34.	L. Cedeño, Angel, et al. (författare) On Filtering and Smoothing Algorithms for Linear State-Space Models Having Quantized Output Data 2023 Ingår i: Mathematics. - : MDPI AG. - 2227-7390. Tidskriftsartikel (refereegranskat)abstract The problem of state estimation of a linear, dynamical state-space system where the output is subject to quantization is challenging and important in different areas of research, such as control systems, communications, and power systems. There are a number of methods and algorithms to deal with this state estimation problem. However, there is no consensus in the control and estimation community on (1) which methods are more suitable for a particular application and why, and (2) how these methods compare in terms of accuracy, computational cost, and user friendliness. In this paper, we provide a comprehensive overview of the state-of-the-art algorithms to deal with state estimation subject to quantized measurements, and an exhaustive comparison among them. The comparison analysis is performed in terms of the accuracy of the state estimation, dimensionality issues, hyperparameter selection, user friendliness, and computational cost. We consider classical approaches and a new development in the literature to obtain the filtering and smoothing distributions of the state conditioned to quantized data. The classical approaches include the extended Kalman filter/smoother, the quantized Kalman filter/smoother, the unscented Kalman filter/smoother, and the sequential Monte Carlo sampling method, also called particle filter/smoother, with its most relevant variants. We also consider a new approach based on the Gaussian sum filter/smoother. Extensive numerical simulations—including a practical application—are presented in order to analyze the accuracy of the state estimation and the computational cost.
35.	Lou, Chuyue, et al. (författare) Unknown Health States Recognition with Collective-Decision-Based Deep Learning Networks in Predictive Maintenance Applications 2024 Ingår i: Mathematics. - Basel : MDPI. - 2227-7390. ; 12:1 Tidskriftsartikel (refereegranskat)abstract At present, decision-making solutions developed based on deep learning (DL) models have received extensive attention in predictive maintenance (PM) applications along with the rapid improvement of computing power. Relying on the superior properties of shared weights and spatial pooling, convolutional neural networks (CNNs) can learn effective representations of health states from industrial data. Many developed CNN-based schemes, such as advanced CNNs that introduce residual learning and multi-scale learning, have shown good performance in health states recognition tasks under the assumption that all the classes are known. However, these schemes have no ability to deal with new abnormal samples that belong to state classes not part of the training set. In this paper, a collective decision framework for different CNNs is proposed. It is based on a one-vs.-rest network (OVRN) to simultaneously achieve classification of known and unknown health states. OVRNs learn class-specific discriminative features and enhance the ability to reject new abnormal samples incorporated to different CNNs. According to the validation results on the public dataset of the Tennessee Eastman process (TEP), the proposed CNN-based decision schemes incorporating an OVRN have outstanding recognition ability for samples of unknown heath states while maintaining satisfactory accuracy on known states. The results show that the new DL framework outperforms state-of-the-art CNNs, and the one based on residual and multi-scale learning has the best overall performance. © 2023 by the authors.
36.	Mapfumo, Kudzanayi Z., et al. (författare) A Model for the Proliferation–Quiescence Transition in Human Cells 2022 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 10:14 Tidskriftsartikel (refereegranskat)abstract The process of revitalising quiescent cells in order for them to proliferate plays a pivotalrole in the repair of worn-out tissues as well as for tissue homeostasis. This process is also crucialin the growth, development and well-being of higher multi-cellular organisms such as mammals.Deregulation of proliferation-quiescence transition is related to many diseases, such as cancer. Recentstudies have revealed that this proliferation–quiescence process is regulated tightly by the Rb − E2Fbistable switch mechanism. Based on experimental observations, in this study, we formulate amathematical model to examine the effect of the growth factor concentration on the proliferation–quiescence transition in human cells. Working with a non-dimensionalised model, we prove thepositivity, boundedness and uniqueness of solutions. To understand model solution behaviour closeto bifurcation points, we carry out bifurcation analysis, which is further illustrated by the use ofnumerical bifurcation analysis, sensitivity analysis and numerical simulations. Indeed, bifurcationand numerical analysis of the model predicted a transition between bistable and stable states, whichare dependent on the growth factor concentration parameter (GF). The derived predictions confirmexperimental observations.
37.	Moradi, Mahmoud, et al. (författare) Mathematical modelling of fused deposition modeling (FDM) 3D printing of poly vinyl alcohol parts through statistical design of experiments approach 2023 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 11:13 Tidskriftsartikel (refereegranskat)abstract This paper explores the 3D printing of poly vinyl alcohol (PVA) using the fused deposition modeling (FDM) process by conducting statistical modeling and optimization. This study focuses on varying the infill percentage (10–50%) and patterns (Cubic, Gyroid, tri-hexagon and triangle, Grid) as input parameters for the response surface methodology (DOE) while measuring modulus, elongation at break, and weight as experimental responses. To determine the optimal parameters, a regression equation analysis was conducted to identify the most significant parameters. The results indicate that both input parameters significantly impact the output responses. The Design Expert software was utilized to create surface and residual plots, and the interaction between the two input parameters shows that increasing the infill percentage (IP) leads to printing heavier samples, while the patterns do not affect the weight of the parts due to close printing structures. On the contrary, the discrepancy between the predicted and actual responses for the optimal samples is below 15%. This level of error is deemed acceptable for the DOE experiments.
38.	Qais, Mohammed H., et al. (författare) LSTM-Based Stacked Autoencoders for Early Anomaly Detection in Induction Heating Systems 2023 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 11:15 Tidskriftsartikel (refereegranskat)abstract Due to the contactless operation of cookware on induction heating systems, the temperature of the cookware is measured remotely using thermal sensors placed on the center of the coil. Hence, the measurement error of these sensors increases if the cookware placement is not centered on the top of the coil. Therefore, this study presents a new data-driven anomaly detection method to detect overheated cookware using the thermal sensor of the case temperature of the inverter module. This method utilizes the long short-term memory (LSTM)-based autoencoder (AE) to learn from large training data of temperatures of cookware and the inverter. The learning of the LSTM-AE model is achieved by minimizing the residual error between the input and reconstructed input data. Then, the maximum residual error can be set to be a threshold value between the normal and abnormal operation. Finally, the learned LSTM-AE model is tested using new testing data that include both normal and abnormal cases. The testing results revealed that the LSTM-AE model can detect cookware overheating by using the inverter temperature only. In addition, the LSTM-AE model can detect the faults in the inverter side, such as poor air ventilation and a faulted cooling fan. Furthermore, we utilized different deep learning algorithms, such as the recurrent neural network (RNN) and the fully connected layers, in the internal layers of the AE. The results demonstrated that the LSTM-AE could detect anomalies earlier than the other models.
39.	Sabahno, Hamed, et al. (författare) New machine-learning control charts for simultaneous monitoring of multivariate normal process parameters with detection and identification 2023 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 11:16 Tidskriftsartikel (refereegranskat)abstract Simultaneous monitoring of the process parameters in a multivariate normal process has caught researchers’ attention during the last two decades. However, only statistical control charts have been developed so far for this purpose. On the other hand, machine-learning (ML) techniques have rarely been developed to be used in control charts. In this paper, three ML control charts are proposed using the concepts of artificial neural networks, support vector machines, and random forests techniques. These ML techniques are trained to obtain linear outputs, and then based on the concepts of memory-less control charts, the process is classified into in-control or out-of-control states. Two different input scenarios and two different training methods are used for the proposed ML structures. In addition, two different process control scenarios are utilized. In one, the goal is only the detection of the out-of-control situation. In the other one, the identification of the responsible variable (s)/process parameter (s) for the out-of-control signal is also an aim (detection–identification). After developing the ML control charts for each scenario, we compare them to one another, as well as to the most recently developed statistical control charts. The results show significantly better performance of the proposed ML control charts against the traditional memory-less statistical control charts in most compared cases. Finally, an illustrative example is presented to show how the proposed scheme can be implemented in a healthcare process.
40.	Shangguan, Yidan, et al. (författare) On the Fundamental Diagram for Freeway Traffic: Exploring the Lower Bound of the Fitting Error and Correcting the Generalized Linear Regression Models 2023 Ingår i: MATHEMATICS. - 2227-7390. ; 11:16 Tidskriftsartikel (refereegranskat)abstract In traffic flow, the relationship between speed and density exhibits decreasing monotonicity and continuity, which is characterized by various models such as the Greenshields and Greenberg models. However, some existing models, i.e., the Underwood and Northwestern models, introduce bias by incorrectly utilizing linear regression for parameter calibration. Furthermore, the lower bound of the fitting errors for all these models remains unknown. To address above issues, this study first proves the bias associated with using linear regression in handling the Underwood and Northwestern models and corrects it, resulting in a significantly lower mean squared error (MSE). Second, a quadratic programming model is developed to obtain the lower bound of the MSE for these existing models. The relative gaps between the MSEs of existing models and the lower bound indicate that the existing models still have a lot of potential for improvement.
41.	Sorooshian, Shahryar, 1980 (författare) Formulation of a Grey Sequence and an Optimization Solution to Present Multi-Layer Family Networks 2023 Ingår i: Mathematics. - : MDPI AG. - 2227-7390. ; 11:1 Tidskriftsartikel (refereegranskat)abstract Despite the potential benefits of family relationships and family events, insufficient studies have been undertaken to address how to overcome their obstacles. So, the main objective of this paper is to present a systematic model for prioritizing family members in response to standing limitations on family relationships. For this, the chosen methodology is conceptual sequence modeling, and the proposed model is optimized to include family membership motives and demotivators. Moreover, multiple criteria for the membership nominations are included to respond to the dynamic scenarios and complexity of decision-making. The feasibility of the proposed model is proven in a numerical case. Thus, the contribution of the proposed model is predictable to be from event planning to relative relationship management.
42.	Torra, Vicenç (författare) Andness Directedness for t-Norms and t-Conorms 2022 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 10:9 Tidskriftsartikel (refereegranskat)abstract Tools for decision making need to be simple to use. In previous papers, we advocated that decision engineering needs to provide these tools, as well as a list of necessary properties that aggregation functions need to satisfy. When we model decisions using aggregation functions, andness-directedness is one of them. A crucial aspect in any decision is the degree of compromise between criteria. Given an aggregation function, andness establishes to what degree the function behaves in a conjunctive manner. That is, to what degree some criteria are mandatory. Nevertheless, from an engineering perspective, what we know is that some criteria are strongly required and we cannot ignore a bad evaluation even when other criteria are correctly evaluated. That is, given our requirements of andness, what are the aggregation functions we need to select. Andness is not only for mean-like functions, but it also applies to t-norms and t-conorms. In this paper, we study this problem and show how to select t-norms and t-conorms based on the andness level.
43.	Wang, Shuang, et al. (författare) Enhanced Remora Optimization Algorithm for Solving Constrained Engineering Optimization Problems 2022 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 10:10 Tidskriftsartikel (refereegranskat)abstract Remora Optimization Algorithm (ROA) is a recent population-based algorithm that mimics the intelligent traveler behavior of Remora. However, the performance of ROA is barely satisfactory; it may be stuck in local optimal regions or has a slow convergence, especially in high dimensional complicated problems. To overcome these limitations, this paper develops an improved version of ROA called Enhanced ROA (EROA) using three different techniques: adaptive dynamic probability, SFO with Levy flight, and restart strategy. The performance of EROA is tested using two different benchmarks and seven real-world engineering problems. The statistical analysis and experimental results show the efficiency of EROA.
44.	Zheng, Rong, et al. (författare) An Improved Wild Horse Optimizer for Solving Optimization Problems 2022 Ingår i: Mathematics. - : MDPI. - 2227-7390. ; 10:8 Tidskriftsartikel (refereegranskat)abstract Wild horse optimizer (WHO) is a recently proposed metaheuristic algorithm that simulates the social behavior of wild horses in nature. Although WHO shows competitive performance compared to some algorithms, it suffers from low exploitation capability and stagnation in local optima. This paper presents an improved wild horse optimizer (IWHO), which incorporates three improvements to enhance optimizing capability. The main innovation of this paper is to put forward the random running strategy (RRS) and the competition for waterhole mechanism (CWHM). The random running strategy is employed to balance exploration and exploitation, and the competition for waterhole mechanism is proposed to boost exploitation behavior. Moreover, the dynamic inertia weight strategy (DIWS) is utilized to optimize the global solution. The proposed IWHO is evaluated using twenty-three classical benchmark functions, ten CEC 2021 test functions, and five real-world optimization problems. High-dimensional cases (D = 200, 500, 1000) are also tested. Comparing nine well-known algorithms, the experimental results of test functions demonstrate that the IWHO is very competitive in terms of convergence speed, precision, accuracy, and stability. Further, the practical capability of the proposed method is verified by the results of engineering design problems.
45.	Amin, Leila, et al. (författare) Swedish national population-based study shows an increased risk of depression among patients with Hirschsprung disease. 2019 Ingår i: Acta Paediatrica. - : Wiley. - 0803-5253 .- 1651-2227. ; 108:10, s. 1867-1870 Tidskriftsartikel (refereegranskat)abstract AIM: Hirschsprung disease is usually treated during infancy. The long-term impact on mental health has not been well studied. The aim of this study was to assess the risk for depressive disorders in individuals with Hirschsprung disease.METHODS: This was a nationwide, population-based cohort study. The study exposure was Hirschsprung disease and the study outcome was depression. The exposed cohort included all individuals with Hirschsprung disease, registered in the Swedish National Patient Register between 1964 and 2013 and the unexposed cohort included ten age- and sex-matched controls per patient. The diagnosis of depression was confirmed by diagnosis in the Swedish National Patient Register.RESULTS: The cohort included 739 (76.5% males) individuals with Hirschsprung disease and 7390 (76.5% males) controls. Among the patients with Hirschsprung disease, 35 (4.7%) of the patients had had a depressive disorder and 187 (2.5%) of controls, hazard ratio 1.98, 95% confidence interval 1.38-2.84. The mean age at diagnosis of first depression was 21.9 years (SD ± 7) in Hirschsprung disease patients and 23.4 years (SD ± 7), p = 0.236 in the unexposed group. There were no significant gender differences.CONCLUSION: We found an increased risk of having depressive disorders among individuals with Hirschsprung disease compared to controls.

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