Kumlachew Wubale Tesfaw, Ayele Taye Goshu, Tsegaye Simon Lachamo
This study examines how tourism influences the ecological balance of a protected natural park where two interacting wildlife species follow Lotka–Volterra-type prey–predator dynamics. Tourists’ decisions to visit the park depend on environmental fluctuations, species visibility, and time-varying preferences toward prey and predator populations. To capture these complex interactions, we develop a coupled deterministic–stochastic model that includes seasonal variations in tourist carrying capacity and attraction rates and models’ environmental noise using the Beta-Exponential-Gaussian (BExG) probability distribution by developing a local R package called BExGaussian for the first time, which accounts for skewed and heavy-tailed disturbances. Qualitative analysis confirms the model’s well-posedness, positivity, existence, and boundedness and identifies a bifurcation at a net tourist effect of η,γ=0.5, separating destabilizing from coexistence-promoting regimes. The numerical simulations using MATLAB and the Euler–Maruyama scheme show that deterministic thresholds accurately predict persistence boundaries under stochastic forcing and align with the analytical results clearly. The ex-Gaussian noise induces extreme oscillations useful for stress testing, while BExG noise produces realistic, moderate variability. Sensitivity analysis highlights predator recovery rate, conversion efficiency, probability distribution types, tourist net effect, and tourist turnover as key factors sustaining persistence, whereas strong predation and negative tourist effects increase extinction risk. Ecologically, the results suggest that maintaining a neutral-to-positive tourist effect η,γ>0.5 and promoting moderate tourist departure rates can stabilize population cycles, balancing ecological resilience with tourism-driven socioeconomic benefits.
Muhammad Rifki Nisardi, Nur Rahmi, Muhammad Arkam Arifuddin
et al.
Aluminum 5083 is one of the materials used for the construction of ship hulls due to its classification as a material with good corrosion resistance. Despite its high corrosion resistance, Aluminum 5083 remains susceptible to galvanic corrosion and pitting corrosion caused by marine environmental conditions. This study develops a mathematical model by adding chloride and passivation effects using fractional differential equations to describe the corrosion rate of Aluminum 5083. The model construction using a Fractional Differential Equation System (FDES) aims to capture memory effects to represent the complex corrosion dynamics accurately. Stability analysis of the fractional model shows that the system is locally asymptotically stable, with all eigenvalues satisfying the condition . Furthermore, a numerical solution approach using the PECE-PI method is employed to solve the model, demonstrating agreement between the simulation results and real-world corrosion phenomena. Involvement of different fractional orders α reveals an effect on the rates of increase and decrease in concentration for each variable. The smaller the value of fractional order α, the slower the concentration change process occurs.
Bivariate Poisson regression is a method for modeling two correlated count response variables. However, standard Poisson models often assume equidispersion, which is frequently violated in real-world data due to overdispersion. To address this issue, the Bivariate Poisson Log-Normal Regression (BPLNR) model is employed, which incorporates random effects to account for variability beyond that captured by the Poisson distribution. This study applies the BPLNR model to analyze the number of leprosy cases in Indonesia in 2021, categorized by the World Health Organization (WHO) into Paucibacillary (PB) and Multibacillary (MB). These two types are known to be correlated and exhibit overdispersion, rendering standard Bivariate Poisson models inadequate. This research contributes by applying BPLNR to leprosy data in Indonesia—an area that has been underexplored in prior studies, which largely employed univariate or standard Poisson approaches and ignored the correlation and overdispersion structure. Data were obtained from the 2021 Indonesian Health Profile and the Central Statistics Agency. Parameter estimation was conducted using Maximum Likelihood Estimation (MLE) with the Newton-Raphson algorithm, and hypothesis testing was performed using the Maximum Likelihood Ratio Test (MLRT). The results confirm that BPLNR effectively models the joint distribution of PB and MB cases while accounting for overdispersion. Key factors influencing both types of leprosy include population density, poverty rate, access to proper sanitation and drinking water, and availability of medical personnel and health facilities. A limitation of this study is the use of aggregate provincial-level data, which may obscure local variation and spatial effects. Future research could integrate spatial modeling techniques or individual-level data to enhance inference.
A min-plus algebra is a set , where is the set of all real numbers equipped with two binary operations, namely minimum and addition . Every square matrix in min-plus algebra can always be calculated as a permanent and dominant matrix. The min-plus algebra can be extended to an interval min-plus algebra, where the elements are closed intervals denoted with two binary operations, minimum and addition . Min-plus interval algebra can be defined in a square matrix. This research will discuss the permanent and dominant a matrix over min-plus interval algebra, the relationship between permanent and dominant matrix, and bideterminant matrix over min-plus interval algebra. From the research results obtained, permanent and dominant formulas, it found that the dominant is greater than or equal to the permanent and the bideterminant formulas.
The fields of medicine and neuroscience often face challenges in obtaining a sufficient amount of diverse data for training machine learning models. Data augmentation can alleviate this issue by artificially synthesizing new data from existing data. Generative adversarial networks (GANs) provide a promising approach for data augmentation in the context of images and biomarkers. GANs can synthesize high-quality, diverse, and realistic data that can supplement real data in the training process. This study provides an overview of the use of GANs for data augmentation in medicine and neuroscience. The strengths and weaknesses of various GAN models, including deep convolutional GANs (DCGANs) and Wasserstein GANs (WGANs), are discussed. This study also explores the challenges and ways to address them when using GANs for data augmentation in the field of medicine and neuroscience. Future works on this topic are also discussed.
Andrey Kovtanyuk, Andrey Kovtanyuk, Alexander Chebotarev
et al.
A non-linear model of oxygen transport from a capillary to tissue is considered. The model takes into account the convection of oxygen in the blood, its diffusion transfer through the capillary wall, and the diffusion and consumption of oxygen in tissue. In the current work, a boundary value problem for the oxygen transport model is studied. The existence theorem is proved and a numerical algorithm is constructed and implemented. The numerical experiments studying the effect of low hematocrit and reduced blood flow rate on cerebral hypoxia in preterm infants are conducted.
In this paper, we consider a boundary value problem in a rectangular domain for a fourth-order homogeneous partial differential equation containing the third derivative with respect to time. The uniqueness of the solution of the stated problem is proved by the method of energy integrals. Using the method of separation of variables, the solution of the considered problem is sought as a multiplication of two functions X (x) and Y (y). To determine X (x),we obtain a fourth-order ordinary differential equation with four boundary conditions at the segment boundary [0,p], and for a Y (y) – third-order ordinary differential equation with three boundary conditions at the boundary of the segment [0,q]. Imposing conditions on the given functions, we prove the existence theorem for a regular solution of the problem. The solution of the problem is constructed in the form of an infinite series, and the possibility of term-by-term differentiation of the series with respect to all variables is substantiated. When substantiating the uniform convergence, it is shown that the “small denominator” is different from zero.
After conducting a survey of several Moroccan university institutions, we generally observed the absence or rarity of a Methodology course, dedicated to providing students with tools to prepare their master's theses, or their end of studies projects (PFE). The purpose of this article is to take stock of the situation concerning the teaching of this course in Morocco, to explain the purpose and objectives of this course for students and to suggest content axes for the course. A pedagogical approach, which emanates from our experience of teaching this course, at the School of Information Sciences, will be discussed at the end of the article.
Colnet Bénédicte, Josse Julie, Varoquaux Gaël
et al.
Randomized controlled trials (RCTs) are often considered the gold standard for estimating causal effect, but they may lack external validity when the population eligible to the RCT is substantially different from the target population. Having at hand a sample of the target population of interest allows us to generalize the causal effect. Identifying the treatment effect in the target population requires covariates to capture all treatment effect modifiers that are shifted between the two sets. Standard estimators then use either weighting (IPSW), outcome modeling (G-formula), or combine the two in doubly robust approaches (AIPSW). However, such covariates are often not available in both sets. In this article, after proving L1{L}^{1}-consistency of these three estimators, we compute the expected bias induced by a missing covariate, assuming a Gaussian distribution, a continuous outcome, and a semi-parametric model. Under this setting, we perform a sensitivity analysis for each missing covariate pattern and compute the sign of the expected bias. We also show that there is no gain in linearly imputing a partially unobserved covariate. Finally, we study the substitution of a missing covariate by a proxy. We illustrate all these results on simulations, as well as semi-synthetic benchmarks using data from the Tennessee student/teacher achievement ratio (STAR), and a real-world example from critical care medicine.
This paper provides a number of examples of relatively weakly compact sets in Orlicz spaces. We show some results arising from these examples. Particularly, we provide a criterion which ensures that some Orlicz function is increasing more rapidly than another (in a sense of T. Ando). In addition, we point out that if a bounded subset K of the Orlicz space L Φ is not bounded by the modular Φ, then it is possible for a set K to remain unbounded under any modular Ψ increasing more rapidly than Φ.
Isotropic positive definite functions on spheres play important roles in spatial statistics, where they occur as the correlation functions of homogeneous random fields and star-shaped random particles. In approximation theory, strictly positive definite functions serve as radial basis functions for interpolating scattered data on spherical domains. We review characterizations of positive definite functions on spheres in terms of Gegenbauer expansions and apply them to dimension walks, where monotonicity properties of the Gegenbauer coefficients guarantee positive definiteness in higher dimensions. Subject to a natural support condition, isotropic positive definite functions on the Euclidean space $\mathbb{R}^3$, such as Askey's and Wendland's functions, allow for the direct substitution of the Euclidean distance by the great circle distance on a one-, two- or three-dimensional sphere, as opposed to the traditional approach, where the distances are transformed into each other. Completely monotone functions are positive definite on spheres of any dimension and provide rich parametric classes of such functions, including members of the powered exponential, Mat\'{e}rn, generalized Cauchy and Dagum families. The sine power family permits a continuous parameterization of the roughness of the sample paths of a Gaussian process. A collection of research problems provides challenges for future work in mathematical analysis, probability theory and spatial statistics.
<p>In this paper, I use the edge design analysis, contrast method analysis and regression analysis to study the actual reasons that led to the housing crisis. Also, applications of the housing crisis in KSA have been obtained, for example, the extent of this phenomenon with two levels (+, -).</p>
Norziana Yahya, Ernie Mazuin Mohd Yusof, Ruzita Hj Ahmad
et al.
The rapid development of information technology has affected various aspects of life including education at the school level. However, conventional teaching and learning methods are still used in secondary schools, especially for Islamic subjects. One of the ways to help students learn better in Islamic subjects is by implementing a web-based content platform in the context of Islamic education. This is a learning tool to support the teaching and learning process using various media such as educational video materials for secondary school students, because multimedia elements will make learning more interesting especially for Islamic subjects that require memorization, reading, and comprehension. Another desired goal is for teachers to be able to manage their Islamic lessons online. In developing web applications, appropriate development methodologies have been implemented using Waterfall Model as a guideline. The waterfall model has different development phases such as analysis, design, implementation, testing and finally documentation. The web-based Islamic Education Content Platform (IECP) was designed and developed using Visual Studio Code with PHP and MySQL databases. It was assessed by obtaining Expert Review (ER) through a set of questionnaires given to four experts and fifteen respondents through User Acceptance Test (UAT). The results of ER indicate that web-based IECP is suitable for use and currently need to be refined and improved. Meanwhile, the UAT results show that web-based IECP is generally accepted and believed to be beneficial, especially to secondary school students and teachers.
The traditional estimation of Mixture regression models is based on the normal assumption of component errors and thus is sensitive to outliers and heavy-tailed errors. In this paper, we propose a robust Mixture regression models in which a mixture of slash distributions is assumed for the errors. Using the fact that the slash distribution can be written as a scale mixture of a normal and a latent distribution, we also estimate model parameters an expectation-maximization (EM) algorithm. The results of our simulation show that based on AIC and BIC criterion, the proposed robust regression model mixture on slash distribution dominates the robust regression based the normal and the t distribution. Finally, the proposed model is compared with other procedures, based on a real data set.
Syadatul Saeda binti Mat Saleh, Najihan Awang@Ali, Nurul Husna Jamian
Nowadays, it is more important to be as efficient as possible. Most of the teaching institutions, one of the essential tasks that is carried out every year or every semester are to allocate teaching workload. Teaching workload allocation refers to the teaching staff teaches which subject and group classes. The task is a time-consuming process. The best allocation will be one of the contributing factors to the teaching quality. In current practice to this department, the teaching load allocates manually through a trial-and-error manner using Microsoft Excel. This may lead to unfavourable results. In this study, we aim to propose an innovative approach to allocate teaching load to group courses using integer programming which able to optimize the teaching allocation while satisfying the teaching staff preferences and based on department policies as constraints. Primary data were gathered using google form among 12 lecturers with 8 courses and 45 group classes considered. A feasible solution will be solved using LINGO unlimited software and the model serves as the best tool to assist the head of the department to allocate teaching workload. It found that the model proposes as a suitable tool to be employed for teaching allocation.
Risks are evolving and risk management too. As a part of this evolution, many professional bodies had released their own methodology, tool, and techniques to deal with uncertainty. From the early 1990s, a growing number of national and international standards risk management have emerged. These publications concern both private and public organizations. They aim to present guidelines and best practices to implement and to support a risk management policy. The purpose of this paper is to provide a review of risk management standards. In order to do that, we compared nine national and international standards. The results show convergences and divergences.
This article is concerned with the effect of slip boundary condition on two-dimensional creeping movement of a Newtonian fluid in the existence of pervious medium with wall features and heterogeneoushomogeneous chemical responses. The objective of this paper is to measure the performance of slip and wall feature constraints through graphs. It is observed that diffusion ascends with an increase in slip and wall constraints. The effective diffusion coefficient has been computed through long wavelength supposition and Taylor’s condition for chemical responses.
One of the main features of statistical systems out of equilibrium is the currents they exhibit in their stationary state: microscopic currents of probability between configurations, which translate into macroscopic currents of mass, charge, etc. Understanding the general behaviour of these currents is an important step towards building a universal framework for non-equilibrium steady states akin to the Gibbs–Boltzmann distribution for equilibrium systems. In this review, we consider one-dimensional bulk-driven particle gases, and in particular the asymmetric simple exclusion process (ASEP) with open boundaries, which is one of the most popular models of one-dimensional transport. We focus, in particular, on the current of particles flowing through the system in its steady state, and on its fluctuations. We show how one can obtain the complete statistics of that current, through its large deviation function, by combining results from various methods: exact calculation of the cumulants of the current, using the integrability of the model; direct diagonalization of a biased process in the limits of very high or low current; hydrodynamic description of the model in the continuous limit using the macroscopic fluctuation theory. We give a pedagogical account of these techniques, starting with a quick introduction to the necessary mathematical tools, as well as a short overview of the existing works relating to the ASEP. We conclude by drawing the complete dynamical phase diagram of the current. We also remark on a few possible generalizations of these results.