Mathematics

The transient electromagnetic (TEM) method is a non-contact technique used to identify underground structures, commonly used in mineral resource exploration. However, the induced polarization (IP) will increase the nonlinearity of TEM inversion, and it is difficult to predict the geoelectric structure from TEM response signals in conventional gradient inversion. We select a heuristic algorithm suitable for nonlinear inversion—a whale optimization algorithm to perform TEM inversion with an IP effect. The inverse framework is optimized by opposition-based learning (OBL) and an adaptive weighted factor (AWF). OBL improves initial population distribution for better global search, while the AWF replaces random operators to balance global and local search, enhancing solution accuracy and ensuring stable convergence. Tests on layered geoelectric models demonstrate that our improved WOA effectively reconstructs geoelectric structures, extracts IP information, and performs robustly in noisy environments. Compared to other nonlinear inversion methods, our proposed approach shows superior convergence and accuracy, effectively extracting IP information from TEM signals, with an error of less than 8%. Full article

The purpose of the present paper is to study the complete lifts of a QSNMC from an LP-Sasakian manifold to its tangent bundle. The lifts of the curvature tensor, Ricci tensor, projective Ricci tensor, and lifts of Einstein manifold endowed with QSNMC in an LP-Sasakian manifold to its tangent bundle are investigated. Necessary and sufficient conditions for the lifts of the Ricci tensor to be symmetric and skew-symmetric and the lifts of the projective Ricci tensor to be skew-symmetric in the tangent bundle are given. An example of complete lifts of four-dimensional LP-Sasakian manifolds in the tangent bundle is shown. Full article

The study examines scenarios involving a single pursuer tracking a single evader, as well as situations where multiple pursuers are involved in chasing multiple evaders. We formulate this problem as a search and pursuit problem for unmanned aerial vehicles (UAVs). Game theory offers a mathematical framework to model and examine strategic interactions involving multiple decision-makers. By employing game theory principles to address the search and pursuit problem, our objective is to optimize the efficiency of strategies for detecting and capturing unmanned aerial vehicles (UAVs). Full article

Based on various factors in information sharing between innovation alliance groups, this paper analyzes innovation information sharing under the influence of various factors and its evolutionary path to provide a reference for the decision-making of innovation information sharing between innovation alliance groups. Firstly, the paper analyzes the main factors influencing alliance group innovation information-sharing behavior. Secondly, based on the evolutionary game theory, an evolutionary game model of innovative information sharing under the cooperative trust degree of group decision-makers is constructed, and the related stable strategies are given. Finally, the sensitivity of innovative information-sharing strategies to key influencing factors is analyzed with the help of actual case data. The results show that a reasonable amount of innovation information sharing and fair profit distribution can improve the innovation information-sharing behavior among the industry–university–research alliance. Considering the trust degree of vertical partners, the alliance group pays more attention to the profit distribution ratio of collaborative innovation of the innovation alliance than the profit amount. When horizontal partner trust is considered, horizontal cooperation trust can promote information sharing among enterprises, universities, and research institutes in the short term but impedes information sharing among groups in the long term. Full article

Iris recognition is a biometric method using the pattern of the iris seated between the pupil and the sclera for recognizing people. It is widely applied in various fields owing to its high accuracy in recognition and high security. A spoof detection method for discriminating a spoof attack is essential in biometric recognition systems that include iris recognition. However, previous studies have mainly investigated spoofing attack detection methods based on printed or photographed images, video replaying, artificial eyes, and patterned contact lenses fabricated using iris images from information leakage. On the other hand, there have only been a few studies on spoof attack detection using iris images generated through a generative adversarial network (GAN), which is a method that has drawn considerable research interest with the recent development of deep learning, and the enhancement of spoof detection accuracy by the methods proposed in previous research is limited. To address this problem, the possibility of an attack on a conventional iris recognition system with spoofed iris images generated using cycle-consistent adversarial networks (CycleGAN), which was the motivation of this study, was investigated. In addition, a local region-based fake-iris detection network (LRFID-Net) was developed. It provides a novel method for discriminating fake iris images by segmenting the iris image into three regions based on the iris region. Experimental results using two open databases, the Warsaw LiveDet-Iris-2017 and the Notre Dame Contact Lens Detection LiveDet-Iris-2017 datasets, showed that the average classification error rate of spoof detection by the proposed method was 0.03% for the Warsaw dataset and 0.11% for the Notre Dame Contact Lens Detection dataset. The results confirmed that the proposed method outperformed the state-of-the-art methods. Full article

We introduce a new method of choosing parameters for margin trading protocols in the Constant Product Model and apply it to our new DeFi Margin Trading protocol Primex, which can work with different DEXs and DeFi platforms. The main advantages of Primex, in comparison with existing DeFi protocols, are the following: (1) the possibility to trade with leverage, using large asset amounts and having only a small part (deposit) in one of the assets; (2) full explanation and justification of the choice of protocol parameters and relations (such as liquidation condition, maximum leverage, different fees, etc.), which allows to estimate different risks (for Lenders and the protocol) and reduce them to the required level; (3) additional decentralization and, at the same time, protection against different faults in protocol functioning, achieved by the usage of the decentralized Keeper; (4) transparent rules and conditions for all participants—Lenders, Traders, and Keepers. We give a detailed explanation for our approach to set protocol parameters and build a corresponding method to obtain their numerical values in the case of the Constant Product Model. The obtained numerical results provide additional indirect confirmation of the consistency of our method. Note that it also may be applied (after the corresponding recalculation of some coefficients) to other models, such as the Order Book Model, Constant Sum Model, or the Mixed Constant Sum/Constant Product Model (as described in the Curve whitepaper), and even other types of DeFi protocols after some modification. Full article

The control chart is a fundamental tool in statistical process control (SPC), widely employed in manufacturing and construction industries for process monitoring with the primary objective of maintaining quality standards and improving operational efficiency. Control charts play a crucial role in identifying special cause variations and guiding the process back to statistical control. While Shewhart control charts excel at detecting significant shifts, EWMA and CUSUM charts are better suited for detecting smaller to moderate shifts. However, the effectiveness of all these control charts is compromised when the underlying distribution deviates from normality. In response to this challenge, this study introduces a robust mixed EWMA-CUSUM control chart tailored for monitoring processes characterized via symmetric but non-normal distributions. The key innovation of the proposed approach lies in the integration of a robust estimator, based on order statistics, that leverages the generalized least square (GLS) technique developed by Lloyd. This integration enhances the chart’s robustness and minimizes estimator variance, even in the presence of non-normality. To demonstrate the effectiveness of the proposed control chart, a comprehensive comparison is conducted with several well-known control charts. Results of the study clearly show that the proposed chart exhibits superior sensitivity to small and moderate shifts in process parameters when compared to its predecessors. Through a compelling illustrative example, a real-life application of the enhanced performance of the proposed control chart is provided in comparison to existing alternatives. Full article

Medical comparative studies often involve collecting data from paired organs, which can produce either bilateral or unilateral data. While many testing procedures are available that account for the intra-class correlation between paired organs for bilateral data, more research needs to be conducted to determine how to analyze combined correlated bilateral and unilateral data. In practice, stratification is often used in analysis to ensure participants are allocated equally to each experimental condition. In this paper, we propose three Maximum Likelihood Estimation (MLE)-based methods for testing the homogeneity of differences between two proportions for stratified bilateral and unilateral data across strata using Donner’s model. We compare the performance of these methods with a model-based method based on Generalized Estimating Equations using Monte Carlo simulations. We also provide a real example to illustrate the proposed methodologies. Our findings suggest that the Score test performs well and offers a valuable alternative to the exact tests in future studies. Full article

In this paper, we propose an enhanced model for pricing vulnerable options. Specifically, our model assumes that parameters such as interest rates, jump intensity, and asset value volatility are governed by an observable continuous-time finite-state Markov chain. We take into account European vulnerable options that are exposed to both default risk and rare shocks from underlying and counterparty assets. We also consider stochastic default barriers driven by a regime-switching model and geometric Brownian motion, thus improving upon the assumption of fixed default barriers. The risky assets follow a related jump-diffusion process, whereas the default barriers are influenced by a geometric Brownian motion correlated with the risky assets. Within the framework of our model, we derive an explicit pricing formula for European vulnerable options. Furthermore, we conduct numerical simulations to examine the effects of default barriers and other related parameters on option prices. Our findings indicate that stochastic default barriers increase credit risk, resulting in a decrease in option prices. By considering the aforementioned factors, our research contributes to a better understanding of pricing vulnerable options in the context of counterparty credit risk in over-the-counter trading. Full article

Unsupervised feature selection (UFS) has received great interest in various areas of research that require dimensionality reduction, including machine learning, data mining, and statistical analysis. However, UFS algorithms are known to perform poorly on datasets with missing data, exhibiting a significant computational load and learning bias. In this work, we propose a novel and robust UFS method, designated PFA-Nipals, that works with missing data without the need for deletion or imputation. This is achieved by considering an iterative nonlinear estimation of principal components by partial least squares, while the relevant features are selected through minibatch K-means clustering. The proposed method is successfully applied to select the relevant features of a robust health dataset with missing data, outperforming other UFS methods in terms of computational load and learning bias. Furthermore, the proposed method is capable of finding a consistent set of relevant features without biasing the explained variability, even under increasing missing data. Finally, it is expected that the proposed method could be used in several areas, such as machine learning and big data with applications in different areas of the medical and engineering sciences. Full article

Intuitionistic fuzzy information is a potent tool for medical diagnosis applications as it can represent imprecise and uncertain data. However, making decisions based on this information can be challenging due to its inherent ambiguity. To overcome this, power aggregation operators can effectively combine various sources of information, including expert opinions and patient data, to arrive at a more accurate diagnosis. The timely and accurate diagnosis of medical conditions is crucial for determining the appropriate treatment plans and improving patient outcomes. In this paper, we developed a novel approach for the three-way decision model by utilizing decision-theoretic rough sets and power aggregation operators. The decision-theoretic rough set approach is essential in medical diagnosis as it can manage vague and uncertain data. The redesign of the model using interval-valued classes for intuitionistic fuzzy information further improved the accuracy of the diagnoses. The intuitionistic fuzzy power weighted average (IFPWA) and intuitionistic fuzzy power weighted geometric (IFPWG) aggregation operators are used to aggregate the attribute values of the information system. The established operators are used to combine information within the intuitionistic fuzzy information system. The outcomes of various alternatives are then transformed into interval-valued classes through discretization. Bayesian decision rules, incorporating expected loss factors, are subsequently generated based on this foundation. This approach helps in effectively combining various sources of information to arrive at more accurate diagnoses. The proposed approach is validated through a medical case study where the participants are classified into three different regions based on their symptoms. In conclusion, the decision-theoretic rough set approach, along with power aggregation operators, can effectively manage vague and uncertain information in medical diagnosis applications. The proposed approach can lead to timely and accurate diagnoses, thereby improving patient outcomes. Full article

Overlapping coefficients (OVL) are commonly used to estimate the similarity between populations in terms of their density functions. In this paper, we consider Pianka’s overlap coefficient for two exponential populations. The methods for statistical inference of Pianka’s coefficient are presented. The bias and mean square error (MSE) of the maximum likelihood estimator (MLE) and the Bayes estimator of Pianka’s overlap coefficient are investigated by simulation. Confidence intervals for Pianka’s overlap measure are constructed. Full article

The fundamental stages in designing a stock portfolio are each stock’s selection and capital weighting. Selection and weighting must be conducted through diversification and price movement analysis to maximize profits and minimize losses. The problem is how the technical implementations of both are carried out. Based on this problem, this study aims to design these selection and weighting mechanisms. Stock selection is based on clusters and price movement trends. The optimal stock clusters are formed using the K-Means algorithm, and price movement analyses are carried out using the moving average indicator. The selected stocks are those whose prices have increasing trends with the most significant Sharpe ratio in each cluster. Then, the capital weighting for each preferred stock is carried out using the mean-variance model with transaction cost and income tax. After designing the mechanism, it is applied to Indonesia’s 80 index stock data. In addition, a comparison is conducted between the estimated portfolio return and the actual one day ahead. Finally, the sensitivity of investors’ courage in taking risks to their profits and losses is also analyzed. This research is expected to assist investors in diversification and price movement analysis of the stocks in the portfolios they form. Full article

In classical survival analysis, it is assumed that all the individuals will experience the event of interest. However, if there is a proportion of subjects who will never experience the event, then a standard survival approach is not appropriate, and cure models should be considered instead. This paper deals with the problem of adapting a machine learning approach for classical survival analysis to a situation when cure (i.e., not suffering the event) is a possibility. Specifically, a brief review of cure models and recent machine learning methodologies is presented, and an adaptation of machine learning approaches to account for cured individuals is introduced. In order to validate the proposed methods, we present an extensive simulation study in which we compare the performance of the adapted machine learning algorithms with existing cure models. The results show the good behavior of the semiparametric or the nonparametric approaches, depending on the simulated scenario. The practical utility of the methodology is showcased through two real-world dataset illustrations. In the first one, the results show the gain of using the nonparametric mixture cure model approach. In the second example, the results show the poor performance of some machine learning methods for small sample sizes. Full article

Analytical mechanics provides methods for analyzing multibody systems with mathematically equivalent elastic elements. The paper analyzes several of these models, highlighting the advantages and disadvantages offered by each of these methods. The main methods used by the researchers are described in a unitary form, presenting the methods of obtaining the evolution equations in each of these cases, mentioning the strengths and weaknesses of each method. The equations of Lagrange, Gibbs–Appell, Kane, Maggi, and Hamilton are analyzed for the particular case of two-dimensional systems, which present certain particularities that facilitate the analysis. Full article

A household consumption and optimal portfolio problem pertinent to life insurance (LI) in a continuous time setting is examined. The family receives a random income before the parents’ retirement date. The price of the risky asset is driven by the exponential Ornstein–Uhlenbeck (O-U) process, which can better reflect the state of the financial market. If the parents pass away prior to their retirement time, the children do not have any work income and LI can be purchased to hedge the loss of wealth due to the parents’ accidental death. Meanwhile, utility functions (UFs) of the parents and children are individually taken into account in relation to the uncertain lifetime. The purpose of the family is to appropriately maximize the weighted average of the corresponding utilities of the parents and children. The optimal strategies of the problem are achieved using a dynamic programming approach to solve the associated Hamilton–Jacobi–Bellman (HJB) equation by employing the convex dual theory and Legendre transform (LT). Finally, we aim to examine how variations in the weight of the parents’ UF and the coefficient of risk aversion affect the optimal policies. Full article

Physics-Informed Neural Networks (PINNs) improve the efficiency of data utilization by combining physical principles with neural network algorithms and thus ensure that their predictions are consistent and stable with the physical laws. PINNs open up a new approach to address inverse problems in fluid mechanics. Based on the single-relaxation-time lattice Boltzmann method (SRT-LBM) with the Bhatnagar–Gross–Krook (BGK) collision operator, the PINN-SRT-LBM model is proposed in this paper for solving the inverse problem in fluid mechanics. The PINN-SRT-LBM model consists of three components. The first component involves a deep neural network that predicts equilibrium control equations in different discrete velocity directions within the SRT-LBM. The second component employs another deep neural network to predict non-equilibrium control equations, enabling the inference of the fluid’s non-equilibrium characteristics. The third component, a physics-informed function, translates the outputs of the first two networks into physical information. By minimizing the residuals of the physical partial differential equations (PDEs), the physics-informed function infers relevant macroscopic quantities of the flow. The model evolves two sub-models that are applicable to different dimensions, named the PINN-SRT-LBM-I and PINN-SRT-LBM-II models according to the construction of the physics-informed function. The innovation of this work is the introduction of SRT-LBM and discrete velocity models as physical drivers into a neural network through the interpretation function. Therefore, the PINN-SRT-LBM allows a given neural network to handle inverse problems of various dimensions and focus on problem-specific solving. Our experimental results confirm the accurate prediction by this model of flow information at different Reynolds numbers within the computational domain. Relying on the PINN-SRT-LBM models, inverse problems in fluid mechanics can be solved efficiently. Full article

Our aim in this paper is extending the applicability domain of the Rao–Blackwell theorem, our methodology is using conditional expectation and generalizing sufficient statistics, and one result is a generalization of the Lehmann–Scheffé theorem; as a conclusion, some problems that could not be solved by an earlier version of the Lehmann–Scheffé theorem become solvable by our new generalization. Full article