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Abstract This paper presents a systematic approach to investigating the existence of solutions for fractional integro-differential equation systems incorporating delay and relaxation impulsive terms. By employing suitable definitions of fractional derivatives, we establish physically interpretable boundary conditions. To account for abrupt state changes, impulsive conditions are integrated into the model. The system is transformed into an equivalent integral equation, facilitating the application of Banach and Schaefer fixed-point theorems to prove the existence and uniqueness of solutions. The practical applicability of our findings is demonstrated through an illustrative example.

Abstract Objective Studies looking into patient and institutional variables linked to extended hospital stays have arisen as a result of the increased focus on severe maternal morbidity and mortality. Understanding the length of hospitalization of patients after delivery is important to gain insights into when hospitals will reach capacity and to predict corresponding staffing or equipment requirements. In Sudan, the distribution of the length of stay during delivery hospitalizations is heavily skewed, with the average length of stay of 2 to 3 days. This study aimed to investigate the use of non-parametric random effect model with Gamma distributed response for analyzing skewed hospital length of stay data in Sudan in neonatal and maternal unit. Methods We applied Gamma regression models with unknown random effects, estimated using the non-parametric maximum likelihood (NPML) technique [5]. The NPML reduces the heterogeneity in the distribution of the response and produce a robust estimation since it does not require any assumptions on the distribution. The same applies to the log–Gamma link that does not require any transformation for the data distribution and it can handle the outliers in the data points. In this study, the models are fitted with and without covariates and compared using AIC and BIC values. Results The findings imply that in the context of health care database investigations, Gamma regression models with non–parametric random effect consistently reduce heterogeneity and improve model accuracy. The generalized linear model with covariates and random effect (k = 4) had the best fit, indicating that Sudanese hospital length of stay data could be classified into four groups with varying average stays influenced by maternal, neonatal, and obstetrics data. Conclusion Identifying factors contributing to longer stays allows hospitals to implement strategies for improvement. Non-parametric random effect model with Gamma distributed response effectively accounts for unobserved heterogeneity and individual-level variability, leading to more accurate inferences and improved patient care. Including random effects can significantly affect variable significance in statistical models, emphasizing the need to consider unobserved heterogeneity when analyzing data containing potential individual-level variability. The findings emphasise the importance of making robust methodological choices in healthcare research in order to inform accurate policy decisions.

The essence of the research is the search for geometric, material and technological limits of the new concept of spinning spindles. Considering the trend of introducing new generation electric drives into the segment of high-speed spinning spindles (over 120,000 rpm), it is necessary to map and describe the basic physical connections, to find the necessary dependencies and correlations of individual design parameters and their limits for the design of a new generation of spindles. Due to the design limitations of the original and years-used spindle drive concept with a belt and the requirement for the production and development of a new generation of spun fibers, it is necessary to expand the basic knowledge for the design of spindles of the new concept, the design of which will be based on the knowledge and dependencies obtained by measuring and examining the basic principles and determining parameters for the design of spindle structures of a new progressive concept.

Analysing a company's or a group of companies' activities is becoming increasingly attractive in the current period. The events sector is dynamic and exhibits specific characteristics we wish to highlight. We will refer to companies that organise large-scale events. In practical terms, there are also certain companies with only one employee who still participates in organising major events. These companies can pose a risk to the market, as they may fail to make payments to suppliers. The analysis of activities is not based solely on the trial balance. A series of documents, such as the purchase journal, sales journal, bank statements, etc., are required to assess a company's financial stability and security. We will research the activity of a company in the area of cinematographic, video and television program production for the year 2023 in order to establish some risks regarding the registered purchase invoices. The risks refer to the potential existence of fictitious invoices, which are recorded in the accounting and for which payments were made, but the services did not exist. Also, we researched the evolution of the company's profitability. The results were concretized in the fact that there must be a concrete control system regarding purchase invoices and payments made through the bank and cashier.

Previous articles in this series have looked at various aspects of planning, designing, conducting and interpreting biomedical research. In this article, we offer an overview of some tools and resources available to health and biomedical researchers, to help them with their research.

Background: As physical inactivity is presently a global concern, encouraging people to engage in physical activity (PA) is a public health policy priority. This study was conducted to analyze the process of change in the adoption of policies which aim at promoting PA in setting the policy agenda.Methods: This qualitative study was conducted using document reviews and semi-structured interviews. A total of 23 key informants from different sections of the policymaking process for PA promotion programs in Iran participated in the study. Purposeful sampling with a maximum variation was used to identify the key informants. Analysis of documents and interviews was conducted on the basis of Kingdon’s multiple streams Framework (MSF): problems, policies, and political streams. The MAXQDA-10 software was used to manage the data analysis process.Results: The problem stream was found to be “the high prevalence of physical inactivity, perceived subjective barriers, and contextual factors for PA” throughout the country. The policy stream focused on integrating PA services into primary health care, scheduling national and global calendar campaigns and events, and using the existing legal structures to promote PA in communities. At the political stream, support for policy documents and various legislative and governing authorities, as well as international support, particularly the World Health Organization 2018–2030 agenda, provided a favorable environment for this issue.Conclusion: Despite the opening of a policy window for developing policies to promote PA, several challenges may hinder the policy implementation process, including a lack of health promotion approach in the health system, lack of inter-sectoral cooperation, COVID-19 pandemic-associated restrictions, and management and structural issues. As the policy window is not being used appropriately, the policymakers must review the policies, with particular attention to the feasibility of policies, the organizational culture of the different ministries, and the mediating and advocating roles of the health sector in operationalizing the policies.

Abstract Background Cutaneous melanoma is the most aggressive form of skin cancer, responsible for most skin cancer-related deaths. Recent advances in artificial intelligence, jointly with the availability of public dermoscopy image datasets, have allowed to assist dermatologists in melanoma identification. While image feature extraction holds potential for melanoma detection, it often leads to high-dimensional data. Furthermore, most image datasets present the class imbalance problem, where a few classes have numerous samples, whereas others are under-represented. Methods In this paper, we propose to combine ensemble feature selection (FS) methods and data augmentation with the conditional tabular generative adversarial networks (CTGAN) to enhance melanoma identification in imbalanced datasets. We employed dermoscopy images from two public datasets, PH2 and Derm7pt, which contain melanoma and not-melanoma lesions. To capture intrinsic information from skin lesions, we conduct two feature extraction (FE) approaches, including handcrafted and embedding features. For the former, color, geometric and first-, second-, and higher-order texture features were extracted, whereas for the latter, embeddings were obtained using ResNet-based models. To alleviate the high-dimensionality in the FE, ensemble FS with filter methods were used and evaluated. For data augmentation, we conducted a progressive analysis of the imbalance ratio (IR), related to the amount of synthetic samples created, and evaluated the impact on the predictive results. To gain interpretability on predictive models, we used SHAP, bootstrap resampling statistical tests and UMAP visualizations. Results The combination of ensemble FS, CTGAN, and linear models achieved the best predictive results, achieving AUCROC values of 87% (with support vector machine and IR=0.9) and 76% (with LASSO and IR=1.0) for the PH2 and Derm7pt, respectively. We also identified that melanoma lesions were mainly characterized by features related to color, while not-melanoma lesions were characterized by texture features. Conclusions Our results demonstrate the effectiveness of ensemble FS and synthetic data in the development of models that accurately identify melanoma. This research advances skin lesion analysis, contributing to both melanoma detection and the interpretation of main features for its identification.

Abstract Background High-dimensional omics data integration has emerged as a prominent avenue within the healthcare industry, presenting substantial potential to improve predictive models. However, the data integration process faces several challenges, including data heterogeneity, priority sequence in which data blocks are prioritized for rendering predictive information contained in multiple blocks, assessing the flow of information from one omics level to the other and multicollinearity. Methods We propose the Priority-Elastic net algorithm, a hierarchical regression method extending Priority-Lasso for the binary logistic regression model by incorporating a priority order for blocks of variables while fitting Elastic-net models sequentially for each block. The fitted values from each step are then used as an offset in the subsequent step. Additionally, we considered the adaptive elastic-net penalty within our priority framework to compare the results. Results The Priority-Elastic net and Priority-Adaptive Elastic net algorithms were evaluated on a brain tumor dataset available from The Cancer Genome Atlas (TCGA), accounting for transcriptomics, proteomics, and clinical information measured over two glioma types: Lower-grade glioma (LGG) and glioblastoma (GBM). Conclusion Our findings suggest that the Priority-Elastic net is a highly advantageous choice for a wide range of applications. It offers moderate computational complexity, flexibility in integrating prior knowledge while introducing a hierarchical modeling perspective, and, importantly, improved stability and accuracy in predictions, making it superior to the other methods discussed. This evolution marks a significant step forward in predictive modeling, offering a sophisticated tool for navigating the complexities of multi-omics datasets in pursuit of precision medicine’s ultimate goal: personalized treatment optimization based on a comprehensive array of patient-specific data. This framework can be generalized to time-to-event, Cox proportional hazards regression and multicategorical outcomes. A practical implementation of this method is available upon request in R script, complete with an example to facilitate its application.

Abstract In this work, we solve a system of fractional differential equations utilizing a Mittag-Leffler type kernel through a fractal fractional operator with two fractal and fractional orders. A six-chamber model with a single source of chlamydia is studied using the concept of fractal fractional derivatives with nonsingular and nonlocal fading memory. The fractal fractional model of the Chlamydia system can be solved by using the characteristics of a non-decreasing and compact mapping. A suggested model with the Lipschitz criteria and linear growth is studied both qualitatively and quantitatively, taking into account boundedness, uniqueness, and positive solutions at equilibrium points with Leray-Schauder results under time scale concepts. We examined the framework of local and global stability and insight into Lyapunov function properties for the infectious disease model. Chaos Control will employ the regulate for linear responses approach to stabilize the system following its equilibrium points. This will take into consideration a fractional order framework with a managed design, where solutions are bounded in the feasible domain and have a greater impact at the lower minimum infectious rate. To illustrate the implications of fractional and fractal dimensions with varying interest rate values through simulations with Newton’s polynomial method under the Mittag-Lefller kernel. Additionally, a comparative analysis of results is also derived by employing power and exponential decay kernels at various fractional orders.

Abstract In this paper, we consider the existence of a normalized ground-state solution for the Choquard–Kirchhoff equation: { − ( a + b ∫ R 3 | ∇ u | 2 d x ) Δ u = λ u + μ ( I α ∗ | u | p ) | u | p − 2 u + ω | u | 4 u , in R 3 , u > 0 , ∫ R 3 | u | 2 = m 2 , in R 3 , $$ \left \{ \textstyle\begin{array}{l@{\quad}r} -(a+b\int _{\mathbb{R}^{3}}|\nabla u|^{2}dx)\Delta{u}=\lambda u+\mu (I_{ \alpha}\ast |u|^{p})|u|^{p-2}u+\omega |u|^{4}u,\ \ &\text{in}\, \mathbb{R}^{3}, \\ u>0,\quad \int _{\mathbb{R}^{3}}|u|^{2}=m^{2},\,&\text{in}\, \mathbb{R}^{3}, \end{array}\displaystyle \right . $$ where a, b, m, μ, ω > 0 $\omega >0$ , p ∈ ( 2 , 7 + α 3 ) $p\in (2,\frac{7+\alpha}{3})$ , λ ∈ R $\lambda \in \mathbb{R}$ , α ∈ ( 0 , 3 ) $\alpha \in (0,3)$ , and I α $I_{\alpha}$ is a Riesz potential. Utilizing approximation methods and Schwartz symmetrization rearrangements, we establish the existence of normalized ground states for these kinds of mass-constrained Choquard–Kirchhoff problems.

Abstract The present paper investigates a new method for computationally solving the time-fractional coupled Korteweg–de Vries equations (TFCKdVEs) with initial boundary conditions (IBCs). The method utilizes a set of generalized shifted Jacobi polynomials (GSJPs) that adhere to the specified initial and boundary conditions (IBCs). Our approach involves constructing operational matrices (OMs) for both ordinary derivatives (ODs) and fractional derivatives (FDs) of the GSJPs we employ. We subsequently employ the collocation spectral method using these OMs. This method successfully converts the TFCKdVEs into a set of algebraic equations, greatly simplifying the task. In order to assess the efficiency and precision of the proposed numerical technique, we utilized it to solve two distinct numerical instances.

Abstract This study is concerned with a nonlinear viscoelastic wave equation with logarithmic source term. By considering the nonlinear distributed delay feedback influenced by acoustic and fractional boundary conditions at the boundary coupling, we establish the global existence and general decay results under appropriate assumptions, even in the case of a general kernel. This result extends and complements some previous results.

Abstract In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p-Laplacian type involving a singularity and a critical Sobolev exponent { − Δ p u = u p ∗ − 1 + λ | u | γ − 1 u , in Ω , u = 0 , on ∂ Ω , $$ \textstyle\begin{cases} -\Delta _{p}u=u^{p^{*}-1}+\frac{\lambda}{|u|^{\gamma -1}u}, & \text{in} ~\Omega , \\ u=0, &\text{on}~\partial \Omega , \end{cases} $$ where Ω is a bounded domain, p ∗ = N p N − p $p^{\ast}=\frac{Np}{N-p}$ ( N ≥ 3 $N \geq 3$ ) is the critical Sobolev exponent and λ > 0 $\lambda > 0$ . Based on the cutoff technique, we prove that the above problem possesses infinitely many positive solutions with 0 < γ < 1 , 1 < p < N $0 < \gamma 0 $\lambda > 0$ small enough.

Abstract This study establishes Newton-type inequalities for third differentiable and s-convex functions that use the Riemann integral. New Newton-type inequalities are also introduced using a summation parameter p ≥ 1 $p\geq 1$ for various convexity cases.

Abstract The outbreak of emerging infectious diseases poses significant challenges to global public health. Accurate early forecasting is crucial for effective resource allocation and emergency response planning. This study aims to develop a comprehensive predictive model for emerging infectious diseases, integrating the blending framework, transfer learning, incremental learning, and the biological feature Rt to increase prediction accuracy and practicality. By transferring features from a COVID-19 dataset to a monkeypox dataset and introducing dynamically updated incremental learning techniques, the model's predictive capability in data-scarce scenarios was significantly improved. The research findings demonstrate that the blending framework performs exceptionally well in short-term (7-day) predictions. Furthermore, the combination of transfer learning and incremental learning techniques significantly enhanced the adaptability and precision, with a 91.41% improvement in the RMSE and an 89.13% improvement in the MAE. In particular, the inclusion of the Rt feature enabled the model to more accurately reflect the dynamics of disease spread, further improving the RMSE by 1.91% and the MAE by 2.17%. This study underscores the significant application potential of multimodel fusion and real-time data updates in infectious disease prediction, offering new theoretical perspectives and technical support. This research not only enriches the theoretical foundation of infectious disease prediction models but also provides reliable technical support for public health emergency responses. Future research should continue to explore integrating data from multiple sources and enhancing model generalization capabilities to further enhance the practicality and reliability of predictive tools.

Abstract Background In medical device validation and verification studies, the area under the receiver operating characteristic curve (AUROC) is often used as a primary endpoint despite multiple reports showing its limitations. Hence, researchers are encouraged to consider alternative metrics as primary endpoints. A new metric called G4 is presented, which is the geometric mean of sensitivity, specificity, the positive predictive value, and the negative predictive value. G4 is part of a balanced metric family which includes the Unified Performance Measure (also known as P4) and the Matthews’ Correlation Coefficient (MCC). The purpose of this manuscript is to unveil the benefits of using G4 together with the balanced metric family when analyzing the overall performance of binary classifiers. Results Simulated datasets encompassing different prevalence rates of the minority class were analyzed under a multi-reader-multi-case study design. In addition, data from an independently published study that tested the performance of a unique ultrasound artificial intelligence algorithm in the context of breast cancer detection was also considered. Within each dataset, AUROC was reported alongside the balanced metric family for comparison. When the dataset prevalence and bias of the minority class approached 50%, all three balanced metrics provided equivalent interpretations of an AI’s performance. As the prevalence rate increased / decreased and the data became more imbalanced, AUROC tended to overvalue / undervalue the true classifier performance, while the balanced metric family was resistant to such imbalance. Under certain circumstances where data imbalance was strong (minority-class prevalence

Abstract Background Associated with high-dimensional omics data there are often “meta-features” such as biological pathways and functional annotations, summary statistics from similar studies that can be informative for predicting an outcome of interest. We introduce a regularized hierarchical framework for integrating meta-features, with the goal of improving prediction and feature selection performance with time-to-event outcomes. Methods A hierarchical framework is deployed to incorporate meta-features. Regularization is applied to the omic features as well as the meta-features so that high-dimensional data can be handled at both levels. The proposed hierarchical Cox model can be efficiently fitted by a combination of iterative reweighted least squares and cyclic coordinate descent. Results In a simulation study we show that when the external meta-features are informative, the regularized hierarchical model can substantially improve prediction performance over standard regularized Cox regression. We illustrate the proposed model with applications to breast cancer and melanoma survival based on gene expression profiles, which show the improvement in prediction performance by applying meta-features, as well as the discovery of important omic feature sets with sparse regularization at meta-feature level. Conclusions The proposed hierarchical regularized regression model enables integration of external meta-feature information directly into the modeling process for time-to-event outcomes, improves prediction performance when the external meta-feature data is informative. Importantly, when the external meta-features are uninformative, the prediction performance based on the regularized hierarchical model is on par with standard regularized Cox regression, indicating robustness of the framework. In addition to developing predictive signatures, the model can also be deployed in discovery applications where the main goal is to identify important features associated with the outcome rather than developing a predictive model.

Abstract We consider the following anisotropic sinh-Poisson type equation with a Hardy or Hénon term: 0.1 { − div ( a ( x ) ∇ u ) + a ( x ) u = ε 2 a ( x ) | x − q | 2 α ( e u − e − u ) in Ω , ∂ u ∂ n = 0 , on Ω , $$ \left \{ \textstyle\begin{array}{l@{\quad}l} -\mathrm{div}(a(x)\nabla u)+ a(x)u=\varepsilon ^{2}a(x)|x-q|^{2\alpha}(e^{u}-e^{-u}) &\text{in $\Omega $,} \\ \frac{\partial u}{\partial n}=0, &\text{on $\Omega $,} \end{array}\displaystyle \right . $$ where ε > 0 $\varepsilon >0$ , q ∈ Ω ¯ ⊂ R 2 $q\in \bar{\Omega}\subset \mathbb{R}^{2}$ , α ∈ ( − 1 , ∞ ) ∖ N $\alpha \in (-1,\infty )\backslash \mathbb{N}$ , Ω ⊂ R 2 $\Omega \subset \mathbb{R}^{2}$ is a smooth bounded domain, n is the unit outward normal vector of ∂Ω, and anisotropic coefficient a ( x ) $a(x)$ is a smooth positive function defined on Ω̄. From the finite-dimensional reduction method, we proved that the problem (0.1) has a sequence of sign-changing solutions with arbitrarily many interior spikes accumulating to q, provided q ∈ Ω $q\in \Omega $ is a strict local maximizer of a ( x ) $a(x)$ . However, if q ∈ ∂ Ω $q\in \partial \Omega $ is a strict local maximum point of a ( x ) $a(x)$ and satisfies 〈 ∇ a ( q ) , n 〉 = 0 $\langle \nabla a(q),n \rangle =0$ , we proved that (0.1) has a family of sign-changing solutions with arbitrarily many mixed interior and boundary spikes accumulating to q. Under the same condition, we could also construct a sequence of blow-up solutions to the following problem { − div ( a ( x ) ∇ u ) + a ( x ) u = ε 2 a ( x ) | x − q | 2 α e u in Ω , ∂ u ∂ n = 0 , on ∂ Ω . $$ \left \{ \textstyle\begin{array}{l@{\quad}l} -\mathrm{div}(a(x)\nabla u)+ a(x)u=\varepsilon ^{2}a(x)|x-q|^{2\alpha}e^{u} &\text{in $\Omega $,} \\ \frac{\partial u}{\partial n}=0, &\text{on $\partial \Omega $.} \end{array}\displaystyle \right . $$

Abstract In life important applications are modeled mathematically by nonlinear partial differential equations. Primarily, the objective is to transform such equations into a system of algebraic equations to get their solutions. The Legendre collocation method is demonstrated by the differentiation operational matrix via shifted Legendre polynomials in such a transformation. The validity and effectiveness of the prospective method are manifested by illustrative examples, an error analysis, residual analysis, and comparison with others.

Abstract With b belonging to a new B M O θ ( ρ ) $BMO_{\theta}(\rho )$ space, L = − △ + V $L=-\triangle +V$ is a Schrödinger operator on R n ${\mathbb{R}^{n}}$ with nonnegative potential V belonging to the reverse Hölder class R H n / 2 $RH_{n/2}$ . The fractional integral operator associated with L is denoted by I β L ${\mathcal{I}}_{\beta}^{L}$ . We investigate the boundedness of I β L ${\mathcal{I}}_{\beta}^{L}$ and [ b , I β L ] $[b,{\mathcal{I}}_{\beta}^{L}]$ , which are its commutators with b θ ( ρ ) $b_{\theta}(\rho )$ on vanishing generalized mixed Morrey spaces V M p → , φ α , V $VM_{\vec{p},\varphi}^{\alpha ,V}$ related to Schrödinger operation and generalized mixed Morrey spaces M p → , φ α , V $M_{\vec{p},\varphi}^{\alpha ,V}$ . The boundedness of the operator I β L ${\mathcal{I}}_{\beta}^{L}$ is ensured by finding sufficient conditions on the pair ( φ 1 , φ 2 ) $(\varphi _{1},\varphi _{2})$ , which goes from M p → , φ 1 α , V $M_{\vec{p},\varphi _{1}}^{\alpha ,V}$ to M q → , φ 2 α , V $M_{\vec{q},\varphi _{2}}^{\alpha ,V}$ , and from V M p → , φ 1 α , V $VM_{\vec{p},\varphi _{1}}^{\alpha ,V}$ to V M q → , φ 2 α , V $VM_{\vec{q},\varphi _{2}}^{\alpha ,V}$ , ∑ i = 1 n 1 p i − ∑ i = 1 n 1 q i = β $\sum \limits _{i=1}^{n}\frac{1}{p_{i}}-\sum \limits _{i=1}^{n}\frac{1}{q_{i}}=\beta $ . When b belongs to B M O θ ( ρ ) $BMO_{\theta}(\rho )$ and ( φ 1 , φ 2 ) $(\varphi _{1},\varphi _{2})$ satisfies some conditions, we also show that the commutator operator [ b , I β L ] $[b,{\mathcal{I}}_{\beta}^{L}]$ is bounded from M p → , φ 1 α , V $M_{\vec{p},\varphi _{1}}^{\alpha ,V}$ to M q → , φ 2 α , V $M_{\vec{q},\varphi _{2}}^{\alpha ,V}$ and from V M p → , φ 1 α , V $VM_{\vec{p},\varphi _{1}}^{\alpha ,V}$ to V M q → , φ 2 α , V $VM_{\vec{q},\varphi _{2}}^{\alpha ,V}$ .

Abstract This paper considers the double diffusive Brinkman flow in a semi-infinite pipe. By establishing a priori estimates of the solutions and setting an appropriate “energy” function, we not only obtain the continuous dependence and convergence of the solution on the Soret coefficient but also prove that the solutions decay exponentially with the distance from the finite end of the cylinder.

Abstract The nonlinear Markov branching process with immigration and resurrection (NMBPIR) is considered in this paper. We give the criteria for regularity and uniqueness of NMBPIR, and then investigate the extinction probability and the mean extinction time. Furthermore, we give a condition for the Feller minimal NMBPIR to be recurrence, and provide an example to illustrate our results.

This article reviews the present condition and future possibilities of walnut growing in the Republic of Uzbekistan. It is stated that the recent decrees and resolutions of the President of the Republic of Uzbekistan and the Government have led to the expansion of the area dedicated to fruit crops, particularly walnuts. The establishment of the "Association of Producers and Exporters of Walnuts" has enabled the creation of modern plantations in Uzbekistan consisting of high-yielding walnut varieties that are well-suited to the local natural and climatic conditions. The association also aims to promote the adoption of science-based methods and resource-saving technologies for walnut growing. Furthermore, it aims to increase walnut production in different regions of the Republic, conduct market research to expand the sales market, develop strategies to boost walnut exports and carry out research to implement innovative technologies in walnut production processes. Since one of the products of walnuts in Uzbekistan is walnut jam, the paper also presents the results of experimental studies on the chemical composition of jam made from unripe walnuts. The studies show that the primary macronutrients in unripe walnut jam are sodium, potassium, magnesium, calcium, and iron. Additionally, it contains trace elements such as iodine, zinc, cadmium, nickel, and cobalt. Due to the diverse macro- and micro-elemental composition of unripe walnut jam, this product can be used as both a food item and a preventive material against various diseases, particularly iodine deficiency in the human body.

LLDikti Region III is a unit operating under the Ministry of Education, Culture, Research, and Technology, responsible for promoting the enhancement of higher education quality in Jakarta. One of the media used by LLDikti Region III to serve stakeholders is through its website; therefore, the quality of services on the website must be continuously enhanced. The aim of this research is to determine whether the LLDikti Region III website meets user expectations, measured using the Webqual 4.0 method and Importance-Performance Analysis (IPA). Usability, information quality, and service interaction quality that will be used to evaluate the quality of this website. The respondents consist of members of the academic community from universities within the LLDikti Region III. Data was collected through an online questionnaire using stratified sampling techniques with 165 respondents. The results of this study show that 54.9% of the website's quality affects user satisfaction, while the remainder is influenced by variables not tested in this study. Based on the analysis conducted using the IPA method, several indicators in quadrant I still require significant attention, as they are considered important by users but have low performance. From these findings, the researcher suggests developing the website in areas where performance is low, particularly for indicators in quadrant I.

In this article, we study the following Kirchhoff equation with combined nonlinearities: −a+b∫R4∣∇u∣2dxΔu+λu=μ∣u∣q−2u+∣u∣2u,inR4,∫R4∣u∣2dx=c2,\left\{\begin{array}{l}-\left(a+b\mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{4}}{| \nabla u| }^{2}{\rm{d}}x\right)\Delta u+\lambda u=\mu {| u| }^{q-2}u+{| u| }^{2}u,\hspace{1.0em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{4},\\ \mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{4}}{| u| }^{2}{\rm{d}}x={c}^{2},\end{array}\right. where a,b,c>0a,b,c\gt 0, μ,λ∈R\mu ,\lambda \in {\mathbb{R}}, 20b,c\gt 0 and μ∈R\mu \in {\mathbb{R}}, we prove some existence, nonexistence, and asymptotic behavior of the obtained normalized solutions. When μ>0\mu \gt 0:(i) for 2

Compressible Euler equations with space-dependent damping in high dimensions Rn(n=2,3){{\bf{R}}}^{n}\hspace{0.33em}\hspace{0.33em}\left(n=2,3) are considered in this article. Assuming that the small initial velocity and small perturbation of the initial density have compact support, we establish finite-time blow-up results for the Euler system, by combining energy estimate and new test functions constructed by the solutions of the following linear elliptic partial differential equations system: −G1(x)+∇⋅G2→(x)=0,−G2→(x)+∇G1(x)=μG2→(x)(1+∣x∣)λ.\left\{\begin{array}{l}-{G}_{1}\left(x)+\nabla \cdot \overrightarrow{{G}_{2}}\left(x)=0,\\ -\overrightarrow{{G}_{2}}\left(x)+\nabla {G}_{1}\left(x)=\frac{\mu \overrightarrow{{G}_{2}}\left(x)}{{(1+| x| )}^{\lambda }}.\end{array}\right. This result generalizes the one in the literature from 1−D1-D to high dimension Rn(n=2,3){{\bf{R}}}^{n}\hspace{0.33em}\hspace{0.33em}\left(n=2,3).

Our purpose is to establish nonexistence results concerning complete noncompact mean curvature flow solitons with polynomial volume growth immersed in certain semi-Riemannian warped products, under mild constraints on the warping and soliton functions. Applications to self-shrinkers in the Euclidean space, as well as to mean curvature flow solitons in other important warped product models such as the Schwarzschild and Reissner-Nordström spaces, and Robertson-Walker spacetimes such as the Einstein-de Sitter spacetime, are also given. Furthermore, we study the nonexistence of entire solutions to the mean curvature flow equation. Our approach is based on a suitable conformal change of metric jointly with a maximum principle for complete noncompact Riemannian manifolds with polynomial volume growth due to Alías et al.

This study proposed and analyzed a vector-borne reaction–diffusion–advection model with vector-bias mechanism and heterogeneous parameters in one-dimensional habitat. The basic reproduction number R0{{\mathfrak{R}}}_{0} in connection with principal eigenvalue of elliptic eigenvalue problem is characterized as the role of determining the threshold dynamics of the system. The main objective of this study is to investigate the asymptotic profiles and monotonicity of R0{{\mathfrak{R}}}_{0} with respect to diffusion rates and advection rates under certain conditions. Through exploring the level set of R0{{\mathfrak{R}}}_{0}, we also find that there exists a unique surface separating the dynamics. Our results also reveal that the infected hosts and vectors will aggregate at the downstream end if the ratio of advection rates and diffusion rates is sufficiently large.

Abstract This paper presents a novel spectral algorithm for the numerical solution of multi-dimensional fractional-order telegraph equations, a critical model used to capture the combined effects of diffusion and wave propagation. The core innovation of this work is the application of Jacobi-Romanovski polynomials as the basis functions for spectral discretization. These polynomials offer unique advantages, including the ability to handle nonstandard domains and boundary conditions, making them particularly suitable for partial differential equation (PDE) applications. A comprehensive error analysis is conducted, providing deep insights into the convergence rates and factors affecting the accuracy of the numerical solutions. Extensive numerical experiments further demonstrate the superior performance of the proposed spectral algorithm in solving a wide range of multi-dimensional fractional-order telegraph equation models. The results show a significant improvement in accuracy and computational efficiency compared to traditional numerical methods, such as finite difference or finite element techniques. This research advances the field of computational science by offering a robust, efficient, and versatile numerical framework for the precise solution of complex multi-dimensional PDEs.

Abstract By using the well-known mountain-pass theorem and Ekeland’s variational principle, we prove that there exist at least two fully nontrivial solutions for a ( p , q ) $(p,q)$ -Kirchhoff elliptic system with the Dirichlet boundary conditions and perturbation terms on a locally weighted and connected finite graph G = ( V , E ) $G=(V,E)$ . We also present a necessary condition of the existence of semitrivial solutions for the system. Moreover, by using Ekeland’s variational principle and Clark’s Theorem, respectively, we prove that the system has at least one or multiple semitrivial solutions when the perturbation terms satisfy different assumptions. Finally, we present a nonexistence result of solutions.

Abstract In this work, we examine a third-order nonlinear neutral integro-differential equation with constant delay. By building a Lyapunov functional, we obtain some sufficient criteria that ensure the asymptotic stability and boundedness of solutions for an analyzed equation. We present two examples to demonstrate the applicability of our conclusions, which extend and improve several well-known results in the literature.

Abstract The nonlinear fractional Langevin equation is an important equation used in various areas of physics and mathematics. In this article, we focus on the singular-hybrid case of the generalized Langevin equations and prove the existence of a solution using fixed point theory. We also provide numerical and graphical simulations to demonstrate the convergence and existence of a solution for this singular problem. Finally, we present numerical examples in the form of tables and graphs to examine the accuracy of the method.

Abstract The purpose of this paper is to study the split feasibility problem with multiple output sets and fixed point problem in the class of demicontractive mappings and propose relaxed inertial self-adaptive algorithms that do not use the least squares method. Under some appropriate assumptions, we establish a strong convergence result for the sequence generated by the proposed algorithm. Our result generalizes and extends several results existing in the literature. Finally, we illustrate the convergence of the proposed algorithm by using a numerical example.

Objective. Currently, the task of increasing the spectral solvability of a video stream using modern frame filtering methods is urgent. Various methods of frame filtering are considered and analyzed in the work, and their detailed comparative analysis is carried out. The obtained data contribute to the further development of various materials to increase the spectral resolution of the video stream. Method. A large number of different approaches have been developed in the scientific literature to increase the spectral resolution of a video stream using modern frame filtering methods, and the most basic ones are analyzed in this paper: linear spatial filtering; nonlinear spatial filtering; spatial frequency filtering; filtering using Fourier analysis; filtering based on wavelet analysis. Result. A preliminary systematization of the characteristics of the methods under consideration has been carried out in order to develop new algorithms and implement them to improve image quality, increase detail and clarity of the video stream; various frame filtering methods have been analyzed, contributing to an increase in the spectral resolution of the video stream, and their impact on the quality of video content has been considered; during the analysis, it was found that in order to increase the spectral solvability of the video stream, it is necessary to use a combined filter. The above facts will allow us to further develop methodological recommendations for increasing the spectral solvability of the video stream. Conclusion. The considered approaches to increasing the spectral resolution of a video stream using modern frame filtering methods are preferable when increasing the spectral resolution of images, since they use all the positive aspects of linear, nonlinear and spatial frequency filtering.

Objective. This paper presents a study of object tracking algorithms for analyzing sports competitions with a minimum permissible number of frames per second without critical loss of quality of operational systems. The purpose of the study is to determine the optimal tracking method and reidentification model with an increase in the time interval between frames. Method. The study used the Re-Identification MSMT17, Market1501, DukeMTMCreID datasets; specialized neural networks OsNet, ResNet and MobileNet. Tracking algorithms BotSort, Bytetrack, OcSort, DeepOcSort, StrongSort. The NOTA and IDF1 quality metrics were used. Result. The metrics of the experiments are generally quite low, which is due to the nonlinearity of athletes' movement, unlike pedestrians' movement, and a large number of changes in their posture. Conclusion. Depending on the degree of information compression, the optimal tracking methods when using pre-trained reidentification models are ByteTrack and OcSort.

The city of Togliatti, which has been leading its history since 1737 and is currently the first in terms of population among Russian so-called «single-industry towns», has accumulated a significant amount of its own literature. At the same time, the historiography of Stavropol-Togliatti began to develop widely only from the second half of the XX century, it still has an eclectic character and continues to progress. The author of the article when using the method of historical periodization, comparative-historical and analytical methods analyzed the literature on the history of the city, its systematization was carried out, six historiographic groups on the topic were allocated, the authors who made the greatest contribution to the study of the city of Stavropol-Togliatti were named.

The aim of this article is to consider a three-dimensional Cauchy problem for the parabolic-elliptic system arising from biological transport networks. For such problem, we first establish the global existence, uniqueness, and uniform boundedness of the strong solution by estimating the derivative of the diagonal permeability tensor with respect to time variable. Moreover, for the diffusion coefficient appropriately large, we demonstrate that the corresponding stationary problem admits a strong solution and that the solution of the Cauchy problem will stabilize to its stationary counterpart in infinite time with a time-decay rate.

In this study, we consider the initial boundary value problem of the planar magnetohydrodynamics (MHD) system when the viscous coefficients and heat conductivity depend on the temperature, which are assumed to be proportional to θα{\theta }^{\alpha }, α≥0\alpha \ge 0, and θβ{\theta }^{\beta }, β≥0\beta \ge 0, respectively, and magnetic diffusivity coefficient depends on the specific volume. We prove the existence and uniqueness of the global-in-time classical solution with general large initial data provided that α\alpha is sufficiently small and there is no restriction on the parameter β\beta . Moreover, the nonlinearly exponential stability of the solution is obtained. As a result, we extend the works given by Sun et al. for the full compressible Navier-Stokes equations and by Li and Shang for the full compressible MHD equations.

The issues and prospects of sustainable development of the Republic of Bashkortostan with a focus on innovation aspects have been considered in order to develop recommendations to ensure the long-term progress of the region. The research methodology is based on the analysis and comparison of economic, social, and environmental factors of sustainable development, assessment of the role of innovation in each sphere, study of successes and experience of other constituent entities of the Russian Federation and foreign countries, as well as on the proposals for creating regional centers for assessing and monitoring sustainable development that in their activities will be focused on comprehensive research in regional socio-economic systems, considering the innovation component. The main spheres and components of ensuring sustainable development of the region have been defined and presented. The main study results are: identification of key aspects of sustainable development of the Republic of Bashkortostan; identification of issues and prospects in developing the economy and social and environmental spheres; analysis of the role of innovation in ensuring sustainable development; recommendations development for creating regional centers for assessing and monitoring sustainable development. Sustainable development of the territory is one of the main strategic objectives of the constituent entity. In order to achieve it, it is necessary to continue the work, as well as to increase attention to innovations, education and management systems. The centers creation can contribute to the system analysis and assessment of sustainable development processes, as well as the development of recommendations and strategies to improve the economic, social, and environmental condition of the territory.

Delinquent behavior and objective factors influencing it have been considered. It should be noted that crime is a complex phenomenon, which is influenced by many factors. Modern scientists combine these factors into two large groups such as subjective (or socio-cultural) and objective (or socio-economic). In order to study the latter and establish the existence of a relationship between them and youth crime, we have selected the most common criminal acts committed in the youth environment such as theft and robbery, as well as the most numerous crimes committed by young people against life and health such as infliction of minor and moderate harm to health. Among objective factors, we have chosen the indicators that can have the strongest impact on youth crime as a whole and on its individual categories such as ­average monthly accrued wages in the region, cash income per capita, and average per capita consumer spending. According to the conducted simple statistical analysis results, an inverse correlation between the number of criminals committing property crimes and the selected socio-economic factors has been revealed. Due to the use of a simple research method, it was not possible to establish any dependence of the number of young people committing crimes against property on the selected objective (socio-economic) factors.

Abstract Background The additive model of inheritance assumes that heterozygotes (Aa) are exactly intermediate in respect to homozygotes (AA and aa). While this model is commonly used in single-locus genetic association studies, significant deviations from additivity are well-documented and contribute to phenotypic variance across many traits and systems. This assumption can introduce type I and type II errors by overestimating or underestimating the effects of variants that deviate from additivity. Alternative genotype encoding strategies have been explored to account for different inheritance patterns, but they often incur significant computational or methodological costs. To address these challenges, we introduce PAGER (Phenotype Adjusted Genotype Encoding and Ranking), an efficient pre-processing method that encodes each genetic variant based on normalized mean phenotypic differences between diallelic genotype classes (AA, Aa, and aa). This approach more accurately reflects each variant’s true inheritance model, improving model precision while minimizing the costs associated with alternative encoding strategies. Results Through extensive benchmarking on SNPs simulated with both binary and continuous phenotypes, we demonstrate that PAGER accurately represents various inheritance patterns (including additive, dominant, recessive, and heterosis), achieves levels of statistical power that meet or exceed other encoding strategies, and attains computation speeds up to 55 times faster than a similar method, EDGE. We also apply PAGER to publicly available real-world data and identify a novel, relevant putative QTL associated with body mass index in rats (Rattus norvegicus) that is not detected with the additive model. Conclusions Overall, we show that PAGER is an efficient genotype encoding approach that can uncover sources of missing heritability and reveal novel insights in the study of complex traits while incurring minimal costs.

Abstract Alzheimer's disease (AD) has emerged as the most prevalent and complex neurodegenerative disorder among the elderly population. However, the genetic comorbidity etiology for AD remains poorly understood. In this study, we conducted pleiotropic analysis for 41 AD phenotypic comorbidities, identifying ten genetic comorbidities with 16 pleiotropy genes associated with AD. Through biological functional and network analysis, we elucidated the molecular and functional landscape of AD genetic comorbidities. Furthermore, leveraging the pleiotropic genes and reported biomarkers for AD genetic comorbidities, we identified 50 potential biomarkers for AD diagnosis. Our findings deepen the understanding of the occurrence of AD genetic comorbidities and provide new insights for the search for AD diagnostic markers. Graphical Abstract Study pipeline.

Abstract Background Modifiers significantly impact disease phenotypes by modulating the effects of disease-causing variants, resulting in varying disease manifestations among individuals. However, identifying genetic interactions between modifier and disease-causing variants is challenging. Results We developed MDVarP, an ensemble model comprising 1000 random forest predictors, to identify modifier ~ disease-causing variant combinations. MDVarP achieves high accuracy and precision, as verified using an independent dataset with published evidence of genetic interactions. We identified 25 novel modifier ~ disease-causing variant combinations and obtained supporting evidence for these associations. MDVarP outputs a class label ("Associated-pair" or "Nonrelevant-pair") and two prediction scores indicating the probability of a true association. Conclusions MDVarP prioritizes variant pairs associated with phenotypic modulations, enabling more effective mapping of functional contributions from disease-causing and modifier variants. This framework interprets genetic interactions underlying phenotypic variations in human diseases, with potential applications in personalized medicine and disease prevention.

Abstract This paper studies the existence and uniqueness of solutions for a new kind of mixed fractional differential systems with slit-strips conditions, containing Caputo-type fractional derivatives. The first result on the existence and uniqueness is based on Banach’s fixed point theorem, and the second result on the existence and uniqueness of the solution is proved by using a Schaefer-type fixed point theorem. The applicability of our primary results is finally illustrated by some examples.

Abstract This paper aims to obtain solutions in terms of the complex potential structure for the plain strain problem of an elastic micropolar and isotropic body with pores. The constitutive equations on which the method is applied and is useful are the well-known equations of the elasticity theory for the above-mentioned body. We intend to solve the Kirch problem using the procedure of complex variables.

Abstract This manuscript is concerned with obtaining results for fixed points that arise from new contractive mappings on controlled metric spaces. These mappings are a mixture of Wardowski’s contractions with both multivalued, nonlinear mappings and auxiliary functions. It is also proved that the obtained fixed-point outcomes are well-posed. Additionally, a data-dependence result for fixed points is given. To aid with understanding, several illustrative examples are also provided. Numerous findings that are currently in the literature are specific instances of the findings that were made.

This study is concerned with the existence of normalized solutions for the Choquard equations with critical nonlinearities −Δu+λu=f(u)+(Iα∗∣u∣2α*)∣u∣2α*−2u,inRN,∫RN∣u∣2dx=a2,\left\{\begin{array}{l}-\Delta u+\lambda u=f\left(u)+\left({I}_{\alpha }\ast {| u| }^{{2}_{\alpha }^{* }}){| u| }^{{2}_{\alpha }^{* }-2}u,\hspace{1em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{N},\hspace{1.0em}\\ \mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{N}}{| u| }^{2}{\rm{d}}x={a}^{2},\hspace{1.0em}\end{array}\right. where N>2N\gt 2, α∈(0,N)\alpha \in \left(0,N), a>0a\gt 0, and Iα(x){I}_{\alpha }\left(x) is the Riesz potential given by Iα(x)=Aα∣x∣N−αwithAα=ΓN−α22απN2Γα2,{I}_{\alpha }\left(x)=\frac{{A}_{\alpha }}{{| x| }^{N-\alpha }}\hspace{1em}\hspace{0.1em}\text{with}\hspace{0.1em}\hspace{0.33em}{A}_{\alpha }=\frac{\Gamma \left(\phantom{\rule[-0.68em]{}{0ex}},\frac{N-\alpha }{2}\right)}{{2}^{\alpha }{\pi }^{\tfrac{N}{2}}\Gamma \left(\phantom{\rule[-0.68em]{}{0ex}},\frac{\alpha }{2}\right)}, and 2α*=N+αN−2{2}_{\alpha }^{* }=\frac{N+\alpha }{N-2} is the Hardy-Littlewood-Sobolev critical exponent and ff is a subcritical nonlinearity. In the case that ff is L2{L}^{2}-supercritical growth, by means of the Pohozaev manifold method and mountain pass theorem, we obtain a couple of the normalized solution; while in the case f(u)=μ∣u∣q−2uf\left(u)=\mu {| u| }^{q-2}u with 20\mu \gt 0 a parameter, we employ the truncation technique and the genus theory to prove the multiplicity of normalized solutions.

Abstract Background The rapid growth of deep learning, as well as the vast and ever-growing amount of available data, have provided ample opportunity for advances in fusion and analysis of complex and heterogeneous data types. Different data modalities provide complementary information that can be leveraged to gain a more complete understanding of each subject. In the biomedical domain, multi-omics data includes molecular (genomics, transcriptomics, proteomics, epigenomics, metabolomics, etc.) and imaging (radiomics, pathomics) modalities which, when combined, have the potential to improve performance on prediction, classification, clustering and other tasks. Deep learning encompasses a wide variety of methods, each of which have certain strengths and weaknesses for multi-omics integration. Method In this review, we categorize recent deep learning-based approaches by their basic architectures and discuss their unique capabilities in relation to one another. We also discuss some emerging themes advancing the field of multi-omics integration. Results Deep learning-based multi-omics integration methods were categorized broadly into non-generative (feedforward neural networks, graph convolutional neural networks, and autoencoders) and generative (variational methods, generative adversarial models, and a generative pretrained model). Generative methods have the advantage of being able to impose constraints on the shared representations to enforce certain properties or incorporate prior knowledge. They can also be used to generate or impute missing modalities. Recent advances achieved by these methods include the ability to handle incomplete data as well as going beyond the traditional molecular omics data types to integrate other modalities such as imaging data. Conclusion We expect to see further growth in methods that can handle missingness, as this is a common challenge in working with complex and heterogeneous data. Additionally, methods that integrate more data types are expected to improve performance on downstream tasks by capturing a comprehensive view of each sample.

Abstract Background Epistasis, the interaction between genetic loci where the effect of one locus is influenced by one or more other loci, plays a crucial role in the genetic architecture of complex traits. However, as the number of loci considered increases, the investigation of epistasis becomes exponentially more complex, making the selection of key features vital for effective downstream analyses. Relief-Based Algorithms (RBAs) are often employed for this purpose due to their reputation as “interaction-sensitive” algorithms and uniquely non-exhaustive approach. However, the limitations of RBAs in detecting interactions, particularly those involving multiple loci, have not been thoroughly defined. This study seeks to address this gap by evaluating the efficiency of RBAs in detecting higher-order epistatic interactions. Motivated by previous findings that suggest some RBAs may rank predictive features involved in higher-order epistasis negatively, we explore the potential of absolute value ranking of RBA feature weights as an alternative approach for capturing complex interactions. In this study, we assess the performance of ReliefF, MultiSURF, and MultiSURFstar on simulated genetic datasets that model various patterns of genotype-phenotype associations, including 2-way to 5-way genetic interactions, and compare their performance to two control methods: a random shuffle and mutual information. Results Our findings indicate that while RBAs effectively identify lower-order (2 to 3-way) interactions, their capability to detect higher-order interactions is significantly limited, primarily by large feature count but also by signal noise. Specifically, we observe that RBAs are successful in detecting fully penetrant 4-way XOR interactions using an absolute value ranking approach, but this is restricted to datasets with only 20 total features. Conclusions These results highlight the inherent limitations of current RBAs and underscore the need for the development of Relief-based approaches with enhanced detection capabilities for the investigation of epistasis, particularly in datasets with large feature counts and complex higher-order interactions.

Abstract In this paper, we examine the existence, uniqueness, and stability of solutions for a Caputo variable order ϑ-initial value problem (ϑ-IVP) with multi-point initial conditions. The proofs for uniqueness and existence leverage Sadovski’s and Banach’s fixed point theorems, along with the Kuratowski measure of noncompactness. Furthermore, we explore the Ulam–Hyers–Rassias (UHR) stability of the solution. To validate our findings, we present a numerical example.