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Let J be a symmetric Jacobi matrix associated with some Toda lattice. We find conditions for Jacobi matrix J to admit factorization J = LU (or J = 𝔘𝔏) with L (or 𝔏) and U (or 𝔘) being lower and upper triangular two-diagonal matrices, respectively. In this case, the Darboux transformation of J is the symmetric Jacobi matrix J(p) = UL (or J(d) = 𝔏𝔘), which is associated with another Toda lattice. In addition, we found explicit transformation formulas for orthogonal polynomials, m-functions and Toda lattices associated with the Jacobi matrices and their Darboux transformations.

This study proposes and analyzes a deterministic mathematical model to describe the dynamics of corruption transmission. We began by proving that the solution to the model is bounded and positive. The next-generation matrix approach is used to compute the basic reproduction number (R0) in relation to corruption-free equilibrium. The Jacobian and Lyapunov functions are used to show that corruption-free equilibrium is asymptotically stable in both locally and globally when R0

Option pricing is crucial in enabling investors to hedge against risks. The Black–Scholes option pricing model is widely used for this purpose. This paper investigates whether the Black–Scholes model is a good indicator of option pricing in the United States stock market. We examine the relevance of the Black–Scholes model to certain stocks using paired sample t-test and Corrado and Miller’s approximation for the implied volatility. Empirical tests are applied to determine the significance of the relationship between the actual market values and the Black–Scholes model values. Paired sample t-tests are applied to 582 call options and 579 put options. The empirical test results show that there is no significant difference between the actual market premium value and the Black–Scholes model premium value for seven out of nine stocks considered for call options, and four out of nine stocks considered for put options. Thus, we conclude that the Black–Scholes option pricing model can be used to price call options but is not suitable for pricing put options in the United States stock market.

This study introduces a five-parameter continuous probability model named the Beta-Exponential-Gaussian distribution by extending the three-parameter Exponential-Gaussian distribution with the beta transformation method. The basic properties of the new distribution, including reliability measure, hazard function, survival function, moment, skewness, kurtosis, order statistics, and asymptotic behavior, are established. Using the acceptance-rejection algorithm, simulation studies are conducted. The new model is fitted to the simulated and real data sets, and its performance is reported. The Beta-Exponential-Gaussian distribution is found to be more flexible and has better performance in many aspects. It is suggested that the new distribution would be used in modeling data having skewness and bimodal distribution.

This research introduces a sophisticated mathematical model for understanding the transmission dynamics of COVID-19, incorporating both integer and fractional derivatives. The model undergoes a rigorous analysis, examining equilibrium points, the reproduction number, and feasibility. The application of fixed point theory establishes the existence of a unique solution, demonstrating stability in the model. To derive approximate solutions, the generalized Adams-Bashforth-Moulton method is employed, further enhancing the study's analytical depth. Through a numerical simulation based on Thailand's data, the research delves into the intricacies of COVID-19 transmission, encompassing thorough data analysis and parameter estimation. The study advocates for a holistic approach, recommending a combined strategy of precautionary measures and home remedies, showcasing their substantial impact on pandemic mitigation. This comprehensive investigation significantly contributes to the broader understanding and effective management of the COVID-19 crisis, providing valuable insights for shaping public health strategies and guiding individual actions.

Tuberculosis and COVID-19 co-infection is currently the major issue of public health in many nations, including Ghana. Therefore, to explore the effects of the two Tuberculosis strains on COVID-19, we suggest a Tuberculosis and COVID-19 co-infection model. The study also provides the most economical and effective control methods to reduce the co-infection of tuberculosis and COVID-19. Based on the behavioral patterns of the two Tuberculosis strains and COVID-19 reproduction numbers, the stability of the co-infection model is examined. We explore the sensitivity of the parameters to examine the effect of the drug-resistant and drug-sensitive strain of Tuberculosis on the co-infection of COVID-19. We determine the most cost-effective and optimal treatment strategies that aim to maximize outcomes while minimizing tuberculosis and/or COVID-19 incidences, cost-effectiveness, and optimization approaches. The outcomes of this work contribute to a better understanding of Tuberculosis and COVID-19 epidemiology and provide insights into implementing interventions needed to minimize Tuberculosis and COVID-19 burden in similar settings worldwide.

Compartmental models are widely used in mathematical epidemiology to describe the dynamics of infectious diseases or in mathematical models of population genetics. In this study, we study a time-dependent Susceptible-Infectious-Susceptible (SIS) Partial Differential Equation (PDE) model that is based on a diffusion-drift approximation of a probability density from a well-known discrete-time Markov chain model. This SIS-PDE model is conservative due to the degeneracy of the diffusion term at the origin. The main results of this article are the qualitative behavior of weak solutions, the dependence of the local asymptotic property of these solutions on initial data, and the existence of Dirac delta function type solutions. Moreover, we study the long-term behavior of solutions and confirm our analysis with numerical computations.

Corruption is a global problem that affects many countries by destroying economic, social, and political development. Therefore, we have formulated and analyzed a mathematical model to understand better control measures that reduce corruption transmission with optimal control strategies. To verify the validity of this model, we examined a model analysis showing that the solution of the model is positive and bounded. The basic reproduction number R0 was computed by using the next-generation matrix. The formulated model was studied analytically and numerically in the context of corruption dynamics. The stability analysis of the formulated model showed that the corruption-free equilibrium is locally and globally asymptotically stable for R0 < 1, but the corruption-endemic equilibrium is globally asymptotically stable for R0 > 1. Furthermore, the optimal control strategy was expressed through the Pontryagin Maximum Principle by incorporating two control variables. Finally, numerical simulations for the optimal control model were performed using the Runge-Kutta fourth order forward and backward methods. This study showed that applying both mass education and law enforcement is the most efficient strategy to reduce the spread of corruption.

This paper focusses on the nonlinear fractional Kadomtsev–Petviashvili (FKP) equation in space–time, employing the conformable fractional derivative (CFD) approach. The main objective of this paper is to examine the application of the (G’/G)-expansion method in order to find analytical solutions to the FKP equation. The (G’/G)-expansion method is a powerful tool for constructing traveling wave solutions of nonlinear evolution equations. However, its application to the FKP equation remains relatively unexplored. By employing traveling wave transformation, the FKP equation was transformed into an ordinary differential equation (ODE) to acquire exact wave solutions. A range of exact analytical solutions for the FKP equation is obtained. Graphical illustrations are included to elucidate the physical characteristics of the acquired solutions. To demonstrate the impact of the fractional operator on results, the acquired solutions are exhibited for different values of the fractional order α, with a comparison to their corresponding exact solutions when taking the conventional scenario where α equals 1. The results indicate that the (G’/G)-expansion method serves as an efficient method and dependable in solving the nonlinear FKP equation.

The learning speed of feed-forward neural networks is notoriously slow and has presented a bottleneck in deep learning applications for several decades. For instance, gradient-based learning algorithms, which are used extensively to train neural networks, tend to work slowly when all of the network parameters must be iteratively tuned. To counter this, both researchers and practitioners have tried introducing randomness to reduce the learning requirement. Based on the original construction of Igelnik and Pao, single layer neural-networks with random input-to-hidden layer weights and biases have seen success in practice, but the necessary theoretical justification is lacking. In this study, we begin to fill this theoretical gap. We then extend this result to the non-asymptotic setting using a concentration inequality for Monte-Carlo integral approximations. We provide a (corrected) rigorous proof that the Igelnik and Pao construction is a universal approximator for continuous functions on compact domains, with approximation error squared decaying asymptotically like O(1/n) for the number n of network nodes. We then extend this result to the non-asymptotic setting, proving that one can achieve any desired approximation error with high probability provided n is sufficiently large. We further adapt this randomized neural network architecture to approximate functions on smooth, compact submanifolds of Euclidean space, providing theoretical guarantees in both the asymptotic and non-asymptotic forms. Finally, we illustrate our results on manifolds with numerical experiments.

IntroductionThe first case of COVID-19 in Kenya was reported on March 13, 2020, prompting the collection of baseline data during the initial spread of the disease. Subsequently, the Kenyan government implemented non-pharmaceutical interventions (NPIs) on April 9, 2020, to mitigate disease transmission over a two-month period. These measures were later gradually relaxed starting from June 9, 2020.MethodsWe applied a deterministic mathematical model to simulate the dynamics of COVID-19 transmission in Kenya. Using baseline data, we estimated transmission and recovery rates and proposed a mathematical model of how NPIs affect disease transmission rates. The model extends to interventions that yield an increase in disease transmission, unlike previous models that were limited to a decrease in transmission. We computed the mitigation and relaxation fractions and hence deduced the impact of the interventions.ResultsThe mitigation measures imposed from April 9, 2020, reduced the disease transmission by 43.7% from the baseline level, while the relaxation from June 9, 2020, increased the transmission by 32% over the mitigation level. Without intervention, the model predicts that infections would have peaked at 30% by late May 2020. However, due to the combined effect of mitigation and relaxation, the epidemic peaked at 13% infection in mid-July 2020.DiscussionThe model’s projections closely align with observed data, providing valuable insights for planning. Ongoing research aims to refine the model to capture sub-waves and spikes, as well as simulate multiple waves of infection. These efforts will enhance our understanding of COVID-19 dynamics and inform effective public health strategies. The estimated basic reproduction number R0=2.76, consistent with previous findings, underscores the validity of our model and its relevance in predicting disease transmission dynamics.

This research article presents a mathematical model that tracks and monitors the spread of COVID-19 strains in a discrete time frame. The study incorporates two control strategies to reduce the transmission of these strains: vaccination and providing appropriate treatment and medication for each strain separately. Optimal controls were established using Pontryagin's maximum principle in discrete time, and the optimality system was solved using an iterative method. To validate the effectiveness of the theoretical findings, numerical simulations were conducted to demonstrate the impact of the implemented strategies in limiting the spread of COVID-19 mutant strains.

IntroductionIn research, it is crucial to accurately estimate treatment effects and analyze experimental results. Common methods include comparing outcome differences between different groups and using linear regression models for analysis. However, observational studies may have significantly different distributions of confounding variables between control and treatment groups, leading to errors in estimating treatment effects.MethodsThe propensity score methods can address this issue by weighting or matching samples to approximate the scenario of a randomized experiment and allow for more accurate estimation of treatment this paper.ResultsWe use propensity score methods to analyze three datasets from observational studies and draw conclusions different from those in the original text. Furthermore, we simulate three scenarios, and the results demonstrate the superiority of propensity score methods over methods such as linear regression in addressing selection bias.DiscussionTherefore, it is essential to thoroughly consider the characteristics of the data and select appropriate methods to ensure reliable conclusions in practical data analysis.

In this study, we explore the nexus between sustainable development and finance, with a specific focus on the African region–a critical yet underexplored context in the existing literature. Against the backdrop of evolving challenges in financial inclusion, improved access, and the growing prevalence of financial technology (FinTech), we aim to fill a research gap by investigating the connection between FinTech, financial inclusion, and sustainable development. The empirical exploration spans 25 African countries from 2011 to 2019, employing econometric methods such as dynamic panel (SGMM two-steps) and static panel (OLS, FE, LSDV). Utilizing key indicators like Adjusted Net Savings (ANS) and Gross Saving rate (GS), our findings reveal a substantial positive impact of financial inclusion and FinTech on sustainable development. However, an intriguing discovery emerges as the interaction between these variables exhibits a weak negative and significant effect. As a unique contribution to the existing literature, we estimate marginal effects at various levels of FinTech and financial inclusion on sustainable development. Beyond insights, our study offers vital policy recommendations, emphasizing the necessity for improved collaboration among financial service providers to avoid redundancy. Furthermore, we highlight the critical need to expand financial infrastructure, advocate for FinTech promotion, and foster inter-African cooperation.

In this study, the initial-boundary value problems to semilinear integro-differential equations with multi-term fractional Caputo derivatives are analyzed. A particular case of these equations models oxygen diffusion through capillaries. Under proper requirements on the given data in the model, the classical and strong solvability of these problems for any finite time interval [0, T] are proved via so-called continuation method. The key point in this approach is finding suitable a priori estimates of a solution in the fractional Hölder and Sobolev spaces.

There is a growing interest in the joint modeling of the dynamics of disease and health-related beliefs and attitudes, but coupling mechanisms are yet to be understood. We introduce a model where risk information, which can be delayed, comes in two flavors, including historical risk derived from perceived incidence data and predicted risk information. Our model also includes an interpretation domain where the behavioral response to risk information is subject to in-group pressure. We then simulate how the strength of behavioral reaction impacts epidemic severity as measured by epidemic peak size, number of waves, and final size. Simulated behavioral response is not effective when the level of protection that prophylactic behavior provides is as small as 50% or lower. At a higher level of 75% or more, we see the emergence of multiple epidemic waves. In addition, simulations show that different behavioral response profiles can lead to various epidemic outcomes that are non-monotonic with the strength of reaction to risk information. We also modeled heterogeneity in the response profile of a population and find they can lead to less severe epidemic outcome in terms of peak size.

IntroductionRealized volatility analysis of assets in the Brazilian market within a multivariate framework is the focus of this study. Despite the success of volatility models in univariate scenarios, challenges arise due to increasing dimensionality of covariance matrices and lower asset liquidity in emerging markets.MethodsIn this study, we utilize intraday stock trading data from the Brazilian Market to compute daily covariance matrices using various specifications. To mitigate dimensionality issues in covariance matrix estimation, we implement penalization restrictions on coefficients through regressions with shrinkage techniques using Ridge, LASSO, or Elastic Net estimators. These techniques are employed to capture the dynamics of covariance matrices.ResultsComparison of covariance construction models is performed using the Model Confidence Set (MCS) algorithm, which selects the best models based on their predictive performance. The findings indicate that the method used for estimating the covariance matrix significantly impacts the selection of the best models. Additionally, it is observed that more liquid sectors demonstrate greater intra-sectoral dynamics.DiscussionWhile the results benefit from shrinkage techniques, the high correlation between assets presents challenges in capturing stock or sector idiosyncrasies. This suggests the need for further exploration and refinement of methods to better capture the complexities of volatility dynamics in emerging markets like Brazil.

This article describes a non-parametric clustering algorithm with an outlier removal step. Our method is based on tools from topological data analysis: we define a new filtration on metric spaces which is a variant of the Vietoris–Rips filtration that adds information about the points' nearest neighbor to the persistence diagram. We prove a stability theorem for this filtration, and evaluate our method on point cloud and graph datasets, showing that it can compete with state-of-the-art methods while being non-parametric.

Scheduling is one of the many skills required for advancement in today’s modern industry. The flow-shop scheduling problem is a well-known combinatorial optimization challenge. Scheduling issues for flow shops are NP-hard and challenging. The present research investigates a two-stage flow shop scheduling problem with decoupled processing and setup times, where a correlation exists between probabilities, job processing times, and setup times. This study proposes a novel heuristic algorithm that optimally sequences jobs to minimize the makespan and eliminates machine idle time, thereby reducing machine rental costs. The proposed algorithm’s efficacy is demonstrated through several computational examples implemented in MATLAB 2021a. The results are compared with the existing approaches such as those by Johnson, Palmer, NEH, and Nailwal to highlight the proposed algorithm’s superior performance.

The core and the Shapley value stand out as the most renowned solutions for addressing sharing problems in cooperative game theory. These concepts are widely acknowledged for their effectiveness in tackling negotiation, resource allocation, and power dynamics. The present study aims to extend various notions of cooperative games from the standard set N to a new class of cooperative games defined on the cartesian product N×N′ (utilizing the specific coalition A*B). This extension encompasses fundamental concepts such as rationality, core, and Shapley value. The findings presented in this study demonstrate that the core concept as a solution yields a set of imputations without favoring any specific point within the set, in contrast to the Shapley value, which offers a singular solution. Moreover, the results confirm that the Shapley value satisfies the conditions defining the core of a game. Through both theoretical analysis and numerical findings, employing a practical example, it becomes evident that the Shapley value offers a more distinct solution to the sharing problem compared with the core solution.

In the last decade, the use of AI in Condensed Matter physics has seen a steep increase in the number of problems tackled and methods employed. A number of distinct Machine Learning approaches have been employed in many different topics; from prediction of material properties to computation of Density Functional Theory potentials and inter-atomic force fields. In many cases, the result is a surrogate model which returns promising predictions but is opaque on the inner mechanisms of its success. On the other hand, the typical practitioner looks for answers that are explainable and provide a clear insight into the mechanisms governing a physical phenomena. In this study, we describe a proposal to use a sophisticated combination of traditional Machine Learning methods to obtain an explainable model that outputs an explicit functional formulation for the material property of interest. We demonstrate the effectiveness of our methodology in deriving a new highly accurate expression for the enthalpy of formation of solid solutions of lanthanide orthophosphates.

Propensity score is one of the most commonly used score functions in adjusting for covariates effect in statistical inference. It is important to understand the impact with propensity score in case some of the prespecified covariates are severely imbalanced. In this article, we performed simulation evaluation the empirical type 1 error and empirical power under scenario of imbalanced covariates in several nonparametric two sample tests with propensity score or with other covariate adjustments. Our results suggest common propensity score approaches might have type 1 error inflation at scenarios with severe imbalanced covariates or model is mis-specified.

This study delves into the dynamics of Zika virus transmission by employing a mathematical model to explain virus spread with fractional order derivatives. The population is divided into two groups: the human group and the ticks group to accurately explain the transmission routes of the virus. The objective of this research is to protect susceptible individuals from infection and curb the spread of this endemic disease. To achieve this, we have included two control measures: the first is a sensibilization program, and the second is treatment. We investigate the use of optimal control strategies and fractional derivative techniques under the Caputo method to reduce the number of exposed and infected individuals. By employing the Pontryagin maximum principle to analyze and characterize the optimal controls, the proposed method is further validated through numerical simulations. The outcome of this study highlights the importance of containing the rate of dynamic dissemination in preventing the Zika epidemic.

The study deals with plastic and non-plastic sub-spaces A of the real-line ℝ with the usual Euclidean metric d. It investigates non-expansive bijections, proves properties of such maps, and demonstrates their relevance by hands of examples. Finally, it is shown that the plasticity property of a sub-space A contains at least two complementary questions, a purely geometric and a topological one. Both contribute essential aspects to the plasticity property and get more critical in higher dimensions and more abstract metric spaces.

The article investigates removability conditions for singularities of anisotropic parabolic equations and in particular for the anisotropic porous medium equation and it aims in the numerical validation of the analytical results. The preconditions on the strength of the anisotropy are analyzed, and the analytical estimates for the growth behavior of the solutions near the singularities are compared with the observed growth in numerical simulations. Despite classical estimates used in the proof, we find that the analytical estimates are surprisingly close to the numerically observed solution behavior.

The exponentiated Teissier distribution (ETD) offers an alternative for modeling survival data, taking into account flexibility in modeling data with increasing and decreasing hazard rate functions. The most popular method for parameter estimation of the ETD distribution is the maximum likelihood estimation (MLE). The MLE, on the other hand, is notoriously biased for its small sample sizes. We are therefore driven to generate virtually unbiased estimators for ETD parameters. More specifically, we focus on two methods of bias correction, bootstrapping and analytical approaches, to reduce MLE biases to the second order of bias. The performances of these approaches are compared through Monte Carlo simulations and two real-data applications.

This study aims to address the difficulties in solving coupled generalized non-linear Burger equations using local fractional calculus as a framework. The methodology used in this work, particularly in the area of local fractional calculus, combines the Elzaki transform with the Adomian decomposition method. This combination has proven to be a highly effective strategy for addressing non-linear partial differential equations within the local fractional context, which finds numerous practical applications. The proposed method offers a systematic and easily understandable procedure for tackling both linear and non-linear partial differential equations (PDEs). It provides an easy-to-follow path to solve these problems. We offer a real-world example that exhibits the method's successful use in resolving issues to corroborate its efficacy. The obtained solution is visually represented to illustrate the practical utility of this approach.2010 Mathematics Subject Classification34A34, 65M06, 26A33.

Reservoir computing is a machine learning method that is closely linked to dynamical systems theory. This connection is highlighted in a brief introduction to the general concept of reservoir computing. We then address a recently suggested approach to improve the performance of reservoir systems by incorporating past values of the input signal or of the reservoir state variables into the readout used to forecast the input or cross-predict other variables of interest. The efficiency of this extension is illustrated by a minimal example in which a three-dimensional reservoir system based on the Lorenz-63 model is used to predict the variables of a chaotic Rössler system.

This study presents a comprehensive analysis of the transmission dynamics of monkeypox, considering contaminated surfaces using a deterministic mathematical model. The study begins by calculating the basic reproduction number and the stability properties of equilibrium states, specifically focusing on the disease-free equilibrium and the endemic equilibrium. Our analytical investigation reveals the occurrence of a forward bifurcation when the basic reproduction number equals unity, indicating a critical threshold for disease spread. The non-existence of backward bifurcation indicates that the basic reproduction number is the single endemic indicator in our model. To further understand the dynamics and control strategies, sensitivity analysis is conducted to identify influential parameters. Based on these findings, the model is reconstructed as an optimal control problem, allowing for the formulation of effective control strategies. Numerical simulations are then performed to assess the impact of these control measures on the spread of monkeypox. The study contributes to the field by providing insights into the optimal control and stability analysis of monkeypox transmission dynamics. The results emphasize the significance of contaminated surfaces in disease transmission and highlight the importance of implementing targeted control measures to contain and prevent outbreaks. The findings of this research can aid in the development of evidence-based strategies for mitigating the impact of monkeypox and other similar infectious diseases.

This paper presents two standard numerical methods for solving second order initial value problems for ordinary differential equations (ODEs). The Euler and the Runge-Kutta fourth-order methods are applied without any discretization or restrictive assumptions for solving ODEs. The numerical solutions obtained by the two methods are in good agreement with the exact solutions. The convergence and error analysis which are discussed demonstrate the effectiveness of the methods. The results obtained from the two numerical methods show that the RK4 method is appropriate, consistent, convergent, quite stable, and more accurate than the Euler's method.

Point process provides a mathematical framework for characterizing neuronal spiking activities. Classical point process methods often focus on the conditional intensity function, which describes the likelihood at any time point given its spiking history. However, these models do not describe the central tendency or importance of the spike train observations. Based on the recent development on the notion of center-outward rank for point process, we propose a new modeling framework on spike train data. The new likelihood of a spike train is a product of the marginal probability on the number of spikes and the probability of spike timings conditioned on the same number. In particular, the conditioned distribution is calculated by adopting the well-known Isometric Log-Ratio transformation. We systematically compare the new likelihood with the state-of-the-art point process likelihoods in terms of ranking, outlier detection, and classification using simulations and real spike train data. This new framework can effectively identify templates as well as outliers in spike train data. It also provides a reasonable model, and the parameters can be efficiently estimated with conventional maximum likelihood methods. It is found that the proposed likelihood provides an appropriate ranking on the spike train observations, effectively detects outliers, and accurately conducts classification tasks in the given data.

In this study, we aimed to explore the dynamics of rail passengers’ negative attitudes that can be influenced by safety concerns and unreliable train operations. We mainly formulated and analyzed a mathematical model of fractional order and derived an optimal control problem considering the Caputo fractional order derivative. In the analysis part of the model, we proved that the solutions of the model for the dynamical system are non-negative and bounded, and determined the passengers’ negative attitude-free and negative attitude persistence equilibrium points of the model. Both the local and global stabilities of these equilibrium points were examined. Furthermore, we verified the conditions necessary for the existence of optimal control strategies. We then proceeded to analyze the proposed control strategies, which aim to prevent negative attitudes and improve the attitudes of passengers who have already developed negative attitudes. Finally, we conducted numerical simulations to examine the effects of these control strategies. The results revealed that protecting passengers from developing negative attitudes and improving the attitudes of those who have already developed such attitudes are crucial for improving the overall attitude of railway passengers. These measures can effectively address any negative experiences caused by safety concerns and unreliable train operations.

Particle swarm optimization (PSO) algorithm is an optimization technique with remarkable performance for problem solving. The convergence analysis of the method is still in research. This article proposes a mechanism for controlling the velocity by applying a method involving constriction factor in standard swarm optimization algorithm, that is called CSPSO. In addition, the mathematical CSPSO model with the time step attractor is presented to study the convergence condition and the corresponding stability. As a result, constriction standard particle swarm optimization that we consider has a higher potential to balance exploration and exploitation. To avoid the PSO premature convergence, CSPSO modifies all terms of the PSO velocity equation. We test the effectiveness of the CSPSO algorithm based on constriction coefficient with some benchmark functions and compare it with other basic PSO variant algorithms. The theoretical convergence and experimental analyses results are also demonstrated in tables and graphically.

IntroductionPredicting property prices is a crucial task in the real estate market, and machine learning algorithms offer valuable tools for accurate predictions. In this study, we introduce a comprehensive comparison of eight well-known machine learning algorithms, namely, ensemble empirical mode decomposition (EEMD)–stochastic (S) + deterministic (D)–support vector machine (EEMD-SD-SVM), support vector machine (SVM), gradient boosting, random forest, K-nearest neighbors (KNN), linear regression, artificial neural networks (ANN), and decision trees. The focus is on predicting property prices in Dubai, with the primary objective of assessing the predictive performance of these algorithms within this specific market context.MethodsThe evaluation is based on four key performance metrics: R-squared (R2), mean squared error (MSE), root mean squared error (RMSE), and mean absolute percentage error (MAPE). These metrics provide insights into prediction errors, accuracy in percentage terms, and the proportion of variance in property prices explained by independent variables. The study compares the strengths and limitations of each algorithm for predicting property prices in Dubai, highlighting scenarios where certain algorithms excel based on the nature of decision boundaries, handling complex data, capturing localized patterns, and offering interpretability.ResultsFindings from the comparative analysis shed light on the performance of each algorithm in predicting property prices in Dubai. EEMD-SD-SVM and SVM excel in scenarios requiring precise decision boundaries, while gradient boosting and random forests demonstrate robust performance with complex and noisy property price data. KNN captures localized patterns effectively, linear regression is suitable for straightforward regression tasks, ANN excels with extensive datasets, and decision trees offer interpretability in understanding factors influencing property prices.DiscussionThe study emphasizes the significance of model tuning, feature selection, and data pre-processing to enhance predictive power. Additionally, practical aspects such as computational efficiency, model interpretability, and scalability in real-world applications are discussed. The comparative analysis provides valuable guidance for stakeholders, including real estate professionals, data scientists, and stakeholders interested in selecting the most suitable machine learning algorithm for predicting property prices in Dubai, with a focus on the essential evaluation metrics of MSE, RMSE, MAPE, and R2. This study offers insights into the applicability and performance of different machine learning algorithms for predicting property prices in Dubai. Stakeholders such as real estate agents, buyers, sellers, or investors can leverage these insights to make informed decisions in the Dubai real estate market.

The paper aims to utilize an integral transform, specifically the Khalouta transform, an abstraction of various integral transforms, to address fractional differential equations using both Riemann-Liouville and Caputo fractional derivative. We discuss some results and the existence of this integral transform. In addition, we also discuss the duality between Shehu transform and Khalouta transform. The numerical examples are provided to confirm the applicability and correctness of the proposed method for solving fractional differential equations.2010 Mathematics ClassificationPrimary 92B05, 92C60; Secondary 26A33.

In the past few decades, multi-linear algebra also known as tensor algebra has been adapted and employed as a tool for various engineering applications. Recent developments in tensor algebra have indicated that several well-known concepts from linear algebra can be extended to a multi-linear setting with the help of a special form of tensor contracted product, known as the Einstein product. Thus, the tensor contracted product and its properties can be harnessed to define the notions of multi-linear system theory where the input, output signals, and the system are inherently multi-domain or multi-modal. This study provides an overview of tensor algebra tools which can be seen as an extension of linear algebra, at the same time highlighting the differences and advantages that the multi-linear setting brings forth. In particular, the notions of tensor inversion, tensor singular value, and tensor eigenvalue decomposition using the Einstein product are explained. In addition, this study also introduces the notion of contracted convolution for both discrete and continuous multi-linear system tensors. Tensor network representation of various tensor operations is also presented. In addition, application of tensor tools in developing transceiver schemes for multi-domain communication systems, with an example of MIMO CDMA system, is presented. This study provides a foundation for professionals whose research involves multi-domain or multi-modal signals and systems.

IntroductionAgriculture emerges as one of the most dangerous industries in the world, considering injury and illness rates. After the service sector in Turkey, the next large-scale sector is the agricultural sector, which constitutes 20% of the general employment. The exposure of farmers to pesticides, used to increase the quality and productivity of agricultural products, causes health risks via the mouth, respiration, skin, and eyes. Pesticide use in Turkey is increasing; the annual average increase is estimated at 1.2%. Exposure to pesticides can be reduced by wearing personal protective equipment to protect against health and safety hazards.ObjectiveThis study aimed to determine the importance of personal protective equipment using the multi-criteria decision-making method to prevent the risk of injury and disease resulting from pesticide use.Materials and methodsThe Analytical Hierarchy Process (AHP) method was used to find the weights of the criteria determined by expert opinion and a literature review. The Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) was used to rank personal protective equipment.ResultsPersonal protective equipment includes masks, gloves, overalls, safety shoes, glasses, and hats. The use of multi-criteria decision-making methods in health and safety in the agricultural sector will contribute to the literature.ConclusionEmphasizing the use of personal protective equipment, especially when using pesticides, will increase the rate of use of protective measures.

Tuberculosis (TB), a disease caused by bacteria Mycobacterium tuberculosis (Mtb), remains one of the major infectious diseases of humans with 10 million TB cases and 1.5 million deaths due to TB worldwide yearly. Upon exposure of a new host to Mtb, bacteria typically infect one local site in the lung, but over time, Mtb disseminates in the lung and in some cases to extrapulmonary sites. The contribution of various host components such as immune cells to Mtb dynamics in the lung, its dissemination in the lung and outside of the lung, remains incompletely understood. Here we overview different types of mathematical models used to gain insights in within-host dynamics of Mtb; these include models based on ordinary or partial differential equations (ODEs and PDEs), stochastic simulation models based on ODEs, agent-based models (ABMs), and hybrid models (ODE-based models linked to ABMs). We illustrate results from several of such models and identify areas for future resesarch.

Mathematical modeling is a powerful method to understand how biological systems work. By creating a mathematical model of a given phenomenon one can investigate which model assumptions are needed to explain the phenomenon and which assumptions can be omitted. Creating an appropriate mathematical model (or a set of models) for a given biological system is an art, and classical textbooks on mathematical modeling in biology go into great detail in discussing how mathematical models can be understood via analytical and numerical analyses. In the last few decades mathematical modeling in biology has grown in size and complexity, and along with this growth new tools for the analysis of mathematical models and/or comparing models to data have been proposed. Examples of tools include methods of sensitivity analyses, methods for comparing alternative models to data (based on AIC/BIC/etc.), and mixed-effect-based fitting of models to data. I argue that the use of many of these “toolbox” approaches for the analysis of mathematical models has negatively impacted the basic philosophical principle of the modeling—to understand what the model does and why it does what it does. I provide several examples of limitations of these toolbox-based approaches and how they hamper generation of insights about the system in question. I also argue that while we should learn new ways to automate mathematical modeling-based analyses of biological phenomena, we should aim beyond a mechanical use of such methods and bring back intuitive insights into model functioning, by remembering that after all, modeling is an art and not simply engineering. “Getting something for nothing is impossible; there is always a price to pay.” Louis Gross.“There is not such a thing as a free lunch.”

Extreme Mass Ratio Inspirals (EMRIs) are one of the key sources for future space-based gravitational wave interferometers. Measurements of EMRI gravitational waves are expected to determine the characteristics of their sources with sub-percent precision. However, their waveform generation is challenging due to the long duration of the signal and the high harmonic content. Here, we present the first ready-to-use Schwarzschild eccentric EMRI waveform implementation in the frequency domain for use with either graphics processing units (GPUs) or central processing units (CPUs). We present the overall waveform implementation and test the accuracy and performance of the frequency domain waveforms against the time domain implementation. On GPUs, the frequency domain waveform takes in median 0.044 s to generate and is twice as fast to compute as its time domain counterpart when considering massive black hole masses ≥2×106M⊙ and initial eccentricities e0 > 0.2. On CPUs, the median waveform evaluation time is 5 s, and it is five times faster in the frequency domain than in the time domain. Using a sparser frequency array can further speed up the waveform generation, reaching up to 0.3 s. This enables us to perform, for the first time, EMRI parameter inference with fully relativistic waveforms on CPUs. Future EMRI models, which encompass wider source characteristics (particularly black hole spin and generic orbit geometries), will require significantly more harmonics. Frequency domain models will be essential analysis tools for these astrophysically realistic and important signals.

Gap junctions are channels in cell membranes allowing ions to pass directly between cells. They are found throughout the body, including heart myocytes, neurons, and astrocytes. In cardiac tissue and throughout the nervous system, an action potential (AP) in one cell can trigger APs in neighboring cells connected by gap junctions. It is known experimentally that there is an ideal gap junction conductance for AP propagation—lower or higher conductance can lead to propagation failure. We explain this phenomenon geometrically in branching networks by analyzing an idealized model that focuses exclusively on gap junction and AP-generating currents. As expected, the gap junction conductance must be high enough for AP propagation to occur. However, if the gap junction conductance is too high, then it dominates the cell's intrinsic firing conductance and disrupts AP generation. We also identify conditions for semi-active propagation, where cells in the network are not individually excitable but still propagate action potentials.

This study deals with a fitted third-degree B-spline collocation method for two parametric singularly perturbed parabolic problems with a time lag. The proposed method comprises the Cranck-Nicolson method for time discretization and the third-degree B-spline method spatial variable discretization. Rigorous numerical experimentations were carried out on some test examples. The obtained numerical results depict that the proposed scheme is more accurate than some methods existing in the literature. Parameter convergence analysis of the scheme is carried out and shows the present scheme is (ε−μ)−uniform convergent with the order of convergence ((Δt)2 + ℓ2).

The study sought to compare two-item response theory (IRT) models, the Rasch and 2PL models, and to uncover insights on COVID-19 knowledge and attitude item difficulty and discrimination among university students. We premise this study on ITM to argue that logical flow, degree of difficulty, and discrimination of items for the constructs among respondents contribute to the validity and quality of statistical inferences. The developed Rasch and 2PL models are compared to determine the difficulty and discrimination of knowledge and attitude items, with an application to COVID-19. Our results show that although the Rasch and 2PL models provide rich diagnostic tools to understand multiple traits, the 2PL model provides more robust results for the assessment of knowledge and attitude of students about the COVID-19 epidemic. Moreover, of the two constructs, the items for the attitude construct recieved more reliable responses than the knowledge construct items. Accordingly, under any pandemic, the lack of proper and evolving knowledge could have dire consequences; hence, strict efforts should be made while designing knowledge items.

Risk management has emerged as a critical element across several economic sectors, with particular significance in the banking industry. The governing bodies of these industries encounter a multitude of threats stemming from the escalation of an unpredictable economic environment, the intricacy of transactions and big data, and several other concealed factors. The primary aim of the present research is to investigate the impact of certain financial risks, including capital risk, liquidity risk, and operational risk, on the financial performance of both commercial and Islamic banks operating within the banking sector of the United Arab Emirates. The study will focus on the time frame spanning from 2015 to 2022. The data used in this study was sourced from the annual reports of banks, which were acquired from the official websites of the Abu Dhabi Securities Exchange and the Dubai stock market. The most prevalent indicators used to assess a bank's financial performance are Return on Assets (ROA) and Return on Equity (ROE). In contrast, the financial risk metrics included three distinct categories of risk: capital risk, liquidity risk, and operational risk. The findings indicate that there is a statistically significant positive relationship between capital risk and both return on assets (ROA) and return on equity (ROE). However, it was observed that neither liquidity risk nor operational risk had a statistically significant impact on either of the financial performance metrics. Moreover, the size of a bank has a notable and favorable impact on both return on assets (ROA) and return on equity (ROE). The ramifications of the study's conclusions have significant importance for regulators, bank management, and investors. IPolicymakers need to prioritize the enhancement of the regulatory framework pertaining to caboutements in order to the financial stability of banks. Bank managers should give priority to the management of capital risk and the size of the bank in order to their financial performance. In order to optimize profits, it is important for investors to carefully evaluate and take into account the many risk considerations associated with their investment selections.JEL:G20, G21

In this study, we present a nonlinear deterministic mathematical model for co-infection of pneumonia and COVID-19 transmission dynamics. To understand the dynamics of the co-infection of COVID-19 and pneumonia sickness, we developed and examined a compartmental based ordinary differential equation type mathematical model. Firstly, we showed the limited region and non-negativity of the solution, which demonstrate that the model is biologically relevant and mathematically well-posed. Secondly, the Jacobian matrix and the Lyapunov function are used to illustrate the local and global stability of the equilibrium locations. If the related reproduction numbers R0c, R0p, and R0 are smaller than unity, then pneumonia, COVID-19, and their co-infection have disease-free equilibrium points that are both locally and globally asymptotically stable otherwise the endemic equilibrium points are stable. Sensitivity analysis is used to determine how each parameter affects the spread or control of the illnesses. Moreover, we applied the optimal control theory to describe the optimal control model that incorporates four controls, namely, prevention of pneumonia, prevention of COVID-19, treatment of infected pneumonia and treatment of infected COVID-19. Then the Pontryagin's maximum principle is introduced to obtain the necessary condition for the optimal control problem. Finally, the numerical simulation of optimality system reveals that the combination of treatment and prevention is the most optimal to minimize the diseases.

In the era of advancing artificial intelligence (AI), its application in agriculture has become increasingly pivotal. This study explores the integration of AI for the discriminative classification of corn diseases, addressing the need for efficient agricultural practices. Leveraging a comprehensive dataset, the study encompasses 21,662 images categorized into four classes: Broken, Discolored, Silk cut, and Pure. The proposed model, an enhanced iteration of MobileNetV2, strategically incorporates additional layers—Average Pooling, Flatten, Dense, Dropout, and softmax—augmenting its feature extraction capabilities. Model tuning techniques, including data augmentation, adaptive learning rate, model checkpointing, dropout, and transfer learning, fortify the model's efficiency. Results showcase the proposed model's exceptional performance, achieving an accuracy of ~96% across the four classes. Precision, recall, and F1-score metrics underscore the model's proficiency, with precision values ranging from 0.949 to 0.975 and recall values from 0.957 to 0.963. In a comparative analysis with state-of-the-art (SOTA) models, the proposed model outshines counterparts in terms of precision, recall, F1-score, and accuracy. Notably, MobileNetV2, the base model for the proposed architecture, achieves the highest values, affirming its superiority in accurately classifying instances within the corn disease dataset. This study not only contributes to the growing body of AI applications in agriculture but also presents a novel and effective model for corn disease classification. The proposed model's robust performance, combined with its competitive edge against SOTA models, positions it as a promising solution for advancing precision agriculture and crop management.

A retrospective view of the “subprime mortgage” crisis enables us to assess the actions of banks, both those prompting the genesis of the crisis and those resulting from subsequent actions aimed at resolving it and rebooting the economy. However, given the fact that the crisis is framed by the sudden appearance of another outside the established parameters of the post-recession boom, we are able to analyze whether the actions adopted by regulators were as effective as initially thought. Solvency and profitability are two of the most important factors that reveals the quality of banking management. From the numerous parameters described in the literature reviewed, fourth banking ratios were selected to evaluate the relationship between solvency and profitability from 2011 to 2021, a period between the two economic-financial crises of the 21st century. Using a representative sample of Spanish banking and applying a descriptive and explicative methodology, the results show a complementarity between solvency and profitability. This evidence provides to bank managers more knowledge about the behavior of banking during crisis periods.

This article analyzes the impact of tax policy on income inequality in the European Union (EU). Each EU member-state has adopted a distinct set of fiscal policies. Although most member-states have coordinated their tax systems to promote economic growth, EU countries hold politically divergent views about income inequality and the power of taxation to redress inequality. This research applies linear regression methods incorporating regularization as well as fixed and random effects. Stacking generalization produces a composite model that dramatically improves predictive accuracy while aggregating causal inferences from simpler models. Social contributions, income taxes, and consumption taxes ameliorate inequality. Government spending, however, exacerbates inequality.