Mathematics

Unravelling how the human brain structure gives rise to function is a central question in neuroscience and remains partially answered. Recent studies show that the graph Laplacian of the human brain’s structural connectivity (SC) plays a dominant role in shaping the pattern of resting-state functional connectivity (FC). The modeling of FC using the graph Laplacian of the brain’s SC is limited, owing to the sparseness of the Laplacian matrix. It is unable to model the negative functional correlations. We extended the graph Laplacian to the hypergraph p-Laplacian in order to describe better the nonlinear and high-order relations between SC and FC. First we estimated those possible links showing negative correlations between the brain areas shared across subjects by statistical analysis. Then we presented a hypergraph p-Laplacian model by embedding the two matrices referring to the sign of the correlations between the brain areas relying on the brain structural connectome. We tested the model on two experimental connectome datasets and evaluated the predicted FC by estimating its Pearson correlation with the empirical FC matrices. The results showed that the proposed diffusion model based on hypergraph p-Laplacian can predict functional correlations more accurately than the models using graph Laplacian as well as hypergraph Laplacian. Full article

The aim of this paper is to define and study the composition vector spaces as a type of tri-operational algebras. In this regard, by presenting nontrivial examples, it is emphasized that they are a proper generalization of vector spaces and their structure can be characterized by using linear operators. Additionally, some related properties about foundations, composition subspaces and residual elements are investigated. Moreover, it is shown how to endow a vector space with a composition structure by using bijective linear operators. Finally, more properties of the composition vector spaces are presented in connection with linear transformations. Full article

The commonly used Geographically Weighted Regression (GWR) fitting method for a spatial varying coefficient model is to select a bandwidth h for the geographic location (u, v), and assign the same weight to the two dimensions. However, spatial data usually present anisotropy. The introduction of a two-dimensional bandwidth matrix not only gives weight from two dimensions separately, but also increases the direction of kernel smoothness. The adaptive bandwidth matrix is more flexible. Therefore, in this paper, a two dimensional bandwidth matrix is introduced into the spatial varying coefficient model for parameter estimation. Through simulation experiments, the results obtained under the adaptive bandwidth matrix are compared with those obtained under the global bandwidth matrix, indicating the effectiveness of introducing the adaptive bandwidth matrix. Full article

The paper considers the features of numerical reconstruction of the advection coefficient when solving the coefficient inverse problem for a nonlinear singularly perturbed equation of the reaction-diffusion-advection type. Information on the position of a reaction front is used as data of the inverse problem. An important question arises: is it possible to obtain a mathematical connection between the unknown coefficient and the data of the inverse problem? The methods of asymptotic analysis of the direct problem help to solve this question. But the reduced statement of the inverse problem obtained by the methods of asymptotic analysis contains a nonlinear integral equation for the unknown coefficient. The features of its solution are discussed. Numerical experiments demonstrate the possibility of solving problems of such class using the proposed methods. Full article

The paper deals with a Volterra integral equation with delay. In order to apply the w-weak generalized contraction theorem for the study of existence and uniqueness of solutions, we rewrite the equation as a fixed point problem. The assumptions take into account the support of w-distance and the complexity of the delay equation. Gronwall-type theorem and comparison theorem are also discussed using a weak Picard operator technique. In the end, an example is provided to support our results. Full article

In this paper, the non-linear dynamical behavior of a 3D autonomous dissipative system of Hopf–Langford type is investigated. Through the help of a mode transformation (as the system’s energy is included) it is shown that the 3D nonlinear system can be separated of two coupled subsystems in the master (drive)-slave (response) synchronization type. After that, based on the computing first and second Lyapunov values for master system, we have attempted to give a general framework (from bifurcation theory point of view) for understanding the structural stability and bifurcation behavior of original system. Moreover, a family of exact solutions of the master system is obtained and discussed. The effect of synchronization on the dynamic behavior of original system is also studied by numerical simulations. Full article

This paper presents the study of multi-objective optimization of a pharmaceutical portfolio when both cost and return values are uncertain. Decision makers in the pharmaceutical industry encounter several challenges in deciding the optimal selection of drug projects for their portfolio since they have to consider several key aspects such as a long product-development process split into multiple phases, high cost and low probability of success. Additionally, the optimization often involves more than a single objective (goal) with a non-deterministic nature. The aim of the study is to develop a stochastic multi-objective approach in the frame of chance-constrained goal programming. The application of the results of this study allows pharmaceutical decision makers to handle two goals simultaneously, where one objective is to achieve a target return and another is to keep the cost within a finite annual budget. Finally, the numerical results for portfolio optimization are presented and discussed. Full article

In the modern world, the systems getting smarter leads to a rapid increase in the usage of electricity, thereby increasing the load on the grids. The utilities are forced to meet the demand and are under stress during the peak hours due to the shortfall in power generation. The abovesaid deficit signifies the explicit need for a strategy that reduces the peak demand by rescheduling the load pattern, as well as reduces the stress on grids. Demand-side management (DSM) uses several algorithms for proper reallocation of loads, collectively known as demand response (DR). DR strategies effectively culminate in monetary benefits for customers and the utilities using dynamic pricing (DP) and incentive-based procedures. This study attempts to analyze the DP schemes of DR such as time-of-use (TOU) and real-time pricing (RTP) for different load scenarios in a smart grid (SG). Centralized and distributed algorithms are used to analyze the price-based DR problem using RTP. A techno-economic analysis was performed by using particle swarm optimization (PSO) and the strawberry (SBY) optimization algorithms used in handling the DP strategies with 109, 1992, and 7807 controllable industrial, commercial, and residential loads. A better optimization algorithm to go along with the pricing scheme to reduce the peak-to-average ratio (PAR) was identified. The results demonstrate that centralized RTP using the SBY optimization algorithm helped to achieve 14.80%, 21.7%, and 21.84% in cost reduction and outperformed the PSO. Full article

In some multi-attribute decision-making (MADM) models studying attributes’ interactive phenomena is very important for the minimizing decision risks. Usually, the Choquet integral type aggregations are considered in such problems. However, the Choquet integral aggregations do not consider all attributes’ interactions; therefore, in many cases, when these interactions are revealed in less degree, they do not perceive these interactions and their utility in MADM problems is less useful. For the decision of this problem, we create the Choquet integral-based new aggregation operators’ family which considers all pair interactions between attributes. The problem under the discrimination q-rung picture linguistic and q-rung orthopair fuzzy environments is considered. Construction of a 2-order additive fuzzy measure (TOAFM) involves pair interaction indices and importance values of attributes of a MADM model. Based on the attributes’ pair interactions for the identification of associated probabilities of a 2-order additive fuzzy measure, the Shapley entropy maximum principle is used. The associated probabilities q-rung picture linguistic weighted averaging (APs-q-RPLWA) and the associated probabilities q-rung picture linguistic weighted geometric (APs-q-RPLWG) aggregation operators are constructed with respect to TOAFM. For an uncertainty pole of experts’ evaluations on attributes regarding the possible alternatives, the associated probabilities of a fuzzy measure are used. The second pole of experts’ evaluations as arguments of the aggregation operators by discrimination q-rung picture linguistic values is presented. Discrimination q-rung picture linguistic evaluations specify the attribute’s dominant, neutral and non-dominant impacts on the selection of concrete alternative from all alternatives. Constructed operators consider the all relatedness between attributes in any consonant attribute structure. Main properties on the rightness of extensions are showed: APs-q-RPLWA and APs-q-RPLWG operators match with q-rung picture linguistic Choquet integral averaging and geometric operators for the lower and upper capacities of order two. The conjugation among the constructed operators is also considered. Connections between the new operators and the compositions of dual triangular norms $\left(T_p,S_p^q\right)$ and $(T_{\min },S_{\max })$ are also constructed. Constructed operators are used in evaluation of a selection reliability index (SRI) of candidate service centers in the facility location selection problem, when small degree interactions are observed between attributes. In example MADM, the difference in optimal solutions is observed between the Choquet integral aggregation operators and their new extensions. The difference, however, is due to the need to use indices of all interactions between attributes. Full article

As failures in rotating machines can have serious implications, the timely detection and diagnosis of faults in these machines is imperative for their smooth and safe operation. Although deep learning offers the advantage of autonomously learning the fault characteristics from the data, the data scarcity from different health states often limits its applicability to only binary classification (healthy or faulty). This work proposes synthetic data augmentation through virtual sensors for the deep learning-based fault diagnosis of a rotating machine with 42 different classes. The original and augmented data were processed in a transfer learning framework and through a deep learning model from scratch. The two-dimensional visualization of the feature space from the original and augmented data showed that the latter’s data clusters are more distinct than the former’s. The proposed data augmentation showed a 6–15% improvement in training accuracy, a 44–49% improvement in validation accuracy, an 86–98% decline in training loss, and a 91–98% decline in validation loss. The improved generalization through data augmentation was verified by a 39–58% improvement in the test accuracy. Full article

The search for powerful optimizers has led to the development of a multitude of metaheuristic algorithms inspired from all areas. This work focuses on the animal kingdom as a source of inspiration and performs an extensive, yet not exhaustive, review of the animal inspired metaheuristics proposed in the 2006–2021 period. The review is organized considering the biological classification of living things, with a breakdown of the simulated behavior mechanisms. The centralized data indicated that 61.6% of the animal-based algorithms are inspired from vertebrates and 38.4% from invertebrates. In addition, an analysis of the mechanisms used to ensure diversity was performed. The results obtained showed that the most frequently used mechanisms belong to the niching category. Full article

This work proposes a new algorithm for optimizing hyper-parameters of a machine learning algorithm, RHOASo, based on conditional optimization of concave asymptotic functions. A comparative analysis of the algorithm is presented, giving particular emphasis to two important properties: the capability of the algorithm to work efficiently with a small part of a dataset and to finish the tuning process automatically, that is, without making explicit, by the user, the number of iterations that the algorithm must perform. Statistical analyses over 16 public benchmark datasets comparing the performance of seven hyper-parameter optimization algorithms with RHOASo were carried out. The efficiency of RHOASo presents the positive statistically significant differences concerning the other hyper-parameter optimization algorithms considered in the experiments. Furthermore, it is shown that, on average, the algorithm needs around $70\%$ of the iterations needed by other algorithms to achieve competitive performance. The results show that the algorithm presents significant stability regarding the size of the used dataset partition. Full article

Parallel-plate compression of multicellular spheroids (MCSs) is a promising and popular technique to quantify the viscoelastic properties of living tissues. This work presents two different approaches to the simulation of the MCS compression based on viscoelastic solid and viscoelastic fluid models. The first one is the standard linear solid model implemented in ABAQUS/CAE. The second one is the new model for 3D viscoelastic free surface fluid flow, which combines the Oldroyd-B incompressible fluid model and the incompressible neo-Hookean solid model via incorporation of an additional elastic tensor and a dynamic equation for it. The simulation results indicate that either approach can be applied to model the MCS compression with reasonable accuracy. Future application of the viscoelastic free surface fluid model is the MCSs fusion highly-demanded in bioprinting. Full article

The progress experienced by society resulting from the ready availability of information through the use of technology highlights the need to develop specific learning related to informational competences (IC) in educational settings where future professionals are trained to educate others, specifically in university degrees in social sciences. This study seeks to ascertain the opinions of students enrolled in these degrees at the Universidad de Córdoba (Spain) with regard to the knowledge they consider that they possess about IC for their future professional development, through the practical application of exploratory factor analysis. The methodology designed is based on a descriptive, non-experimental, correlational survey. The results show that factor analysis is a fundamental tool for obtaining results in terms of students’ perception of their knowledge of IC because its psychometric value has confirmed construct validity and enabled us to break down the items that made up the four initial dimensions of IC into eight factors to improve the understanding and explanation of these IC. Full article

Osteoporosis is frequent in elderly people, causing bone fractures and lowering their quality of life. The costs incurred by these fractures constitute a problem for public health. Markov chains were used to carry out an incremental cost-utility analysis of the four main drugs used in Spain to treat osteoporosis (alendronate, risedronate, denosumab and teriparatide). We considered 14 clinical transition states, from starting osteoporotic treatment at the age of 50 until death or the age of 100. Cost-effectiveness was measured by quality adjusted life years (QALYs). The values used in the Markov model were obtained from the literature. Teriparatide is the cost-effective alternative in the treatment of osteoporosis in patients with fractures from the age of 50, establishing a payment threshold of 20,000 EUR/QALY. However, it is the most expensive therapy, not appearing cost-effective in cases that do not present fracture and in ages over 80 years with fracture. Alendronate and denosumab therapies are presented as cost-effective osteoporosis treatment alternatives depending on the age of onset and duration of treatment. From the perspective of cost-effectiveness, establishing a payment threshold of 20,000 EUR/QALY, teriparatide is the cost-effective alternative in patients with fracture from the age of 50 to 70 years old in Spain. Full article

This paper examines the impact of hybrid nanoparticles on the stagnation point flow towards a curved surface. Silica (SiO₂) and alumina (Al₂O₃) nanoparticles are added into water to form SiO₂-Al₂O₃/water hybrid nanofluid. Both buoyancy-opposing and -assisting flows are considered. The governing partial differential equations are reduced to a set of ordinary differential equations, before being coded in MATLAB software to obtain the numerical solutions. Findings show that the solutions are not unique, where two solutions are obtained, for both buoyancy-assisting and -opposing flow cases. The local Nusselt number increases in the presence of the hybrid nanoparticles. The temporal stability analysis shows that only one of the solutions is stable over time. Full article

Age estimation is applicable in various fields, and among them, research on age estimation using human facial images, which are the easiest to acquire, is being actively conducted. Since the emergence of deep learning, studies on age estimation using various types of convolutional neural networks (CNN) have been conducted, and they have resulted in good performances, as clear images with high illumination were typically used in these studies. However, human facial images are typically captured in low-light environments. Age information can be lost in facial images captured in low-illumination environments, where noise and blur generated by the camera in the captured image reduce the age estimation performance. No study has yet been conducted on age estimation using facial images captured under low light. In order to overcome this problem, this study proposes a new generative adversarial network for low-light age estimation (LAE-GAN), which compensates for the brightness of human facial images captured in low-light environments, and a CNN-based age estimation method in which compensated images are input. When the experiment was conducted using the MORPH, AFAD, and FG-NET databases—which are open databases—the proposed method exhibited more accurate age estimation performance and brightness compensation in low-light images compared to state-of-the-art methods. Full article

Nowadays, because of the energy crisis, combined heat and power systems have notable benefits. One of the best devices is SOFC (Solid Oxide Fuel Cell) which joins heat and power frameworks. Some considerable failure modes arise that can affect these devices’ productivity. Generally, failure modes evaluations need an experts team to achieve uncertainties belongs to the risk assessment procedure. To improve the efficiency of the routine FMEA methodology and to represent a suitable hybrid fuzzy MCDM approach for FMEA, in this work, fully fuzzy best-worst method (FF-BWM) is employed to achieve the risk factors weights then fuzzy weighted aggregated sum product assessment (F-WASPAS) approach to detect the failure modes priorities is utilized. Ultimately, the sensitivity analyses demonstrate that the offered framework is verified and can make applicable data in risk management decision-making evaluation. Full article

In this paper, we study the matrix representation of fuzzy soft sets, complement of fuzzy soft sets, product of fuzzy soft matrices and the application of fuzzy soft matrices in medical diagnosis presented by Lavanya and Akila. Additionally, a new method (max-min average) based on fuzzy reference function is introduced instead of the max-product method by Lavanya and Akila to extend Sanchez’s technique for decision making problems in medical diagnosis. Using the same data by Lavanya and Akila, the result shows that the new method gives more information about the medical status of the patients being considered in relation to a set of diseases. Full article