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We consider degenerate Kolmogorov-Fokker-Planck operators ℒu=∑i,j=1qaij(x,t)uxixj+∑k,j=1Nbjkxkuxj−ut,{\mathcal{ {\mathcal L} }}u=\mathop{\sum }\limits_{i,j=1}^{q}{a}_{ij}\left(x,t){u}_{{x}_{i}{x}_{j}}+\mathop{\sum }\limits_{k,j=1}^{N}{b}_{jk}{x}_{k}{u}_{{x}_{j}}-{u}_{t}, such that the corresponding model operator having constant aij{a}_{ij} is hypoelliptic, translation invariant w.r.t. a Lie group operation in RN+1{{\mathbb{R}}}^{N+1} and 2-homogeneous w.r.t. a family of nonisotropic dilations. We assume that the aij{a}_{ij}’s are globally bounded and Hölder continuous in xx (w.r.t. some intrinsic distance induced by ℒ{\mathcal{ {\mathcal L} }}); the matrix {aij}i,j=1q{\{{a}_{ij}\}}_{i,j=1}^{q} is symmetric and uniformly positive on Rq{{\mathbb{R}}}^{q}. We prove “partial Schauder a priori estimates” on a bounded open set Ω⊂RN+1\Omega \subset {{\mathbb{R}}}^{N+1}, of the kind ∑i,j=1q([uxixj]∗,α,2x+[uxixj]∗,2)≤c{[ℒu]∗,α,2x+[ℒu]∗,2+supΩ∣u∣}\mathop{\sum }\limits_{i,j=1}^{q}({\left[{u}_{{x}_{i}{x}_{j}}]}_{\ast ,\alpha ,2}^{x}+{\left[{u}_{{x}_{i}{x}_{j}}]}_{\ast ,2})\le c\left\{{\left[{\mathcal{ {\mathcal L} }}u]}_{\ast ,\alpha ,2}^{x}+{\left[{\mathcal{ {\mathcal L} }}u]}_{\ast ,2}+\mathop{\sup }\limits_{\Omega }| u| \right\} for suitable functions uu, where [u]∗,α,2x=sup(x,t)≠(y,t)∈Ωd(x,t),(y,t)2+α∣u(x,t)−u(y,t)∣‖x−y‖α[u]∗,2=supξ∈Ωdξ2∣u(ξ)∣.\begin{array}{rcl}{\left[u]}_{\ast ,\alpha ,2}^{x}& =& \mathop{\sup }\limits_{\left(x,t)\ne (y,t)\in \Omega }{d}_{\left(x,t),(y,t)}^{2+\alpha }\frac{| u\left(x,t)-u(y,t)| }{\Vert x-y{\Vert }^{\alpha }}\\ {{[}u]}_{\ast ,2}& =& \mathop{\sup }\limits_{\xi \in \Omega }{d}_{\xi }^{2}| u\left(\xi )| .\end{array} Here ‖⋅‖\Vert \cdot \Vert is a homogeneous norm in RN{{\mathbb{R}}}^{N}, while dξ=dist(ξ,∂Ω){d}_{\xi }={\rm{dist}}\left(\xi ,\partial \Omega ) and dξ,η=min{dξ,dη}{d}_{\xi ,\eta }=\min \left\{{d}_{\xi },{d}_{\eta }\right\}. We also prove that the derivatives uxixj{u}_{{x}_{i}{x}_{j}} are locally Hölder continuous in space and time.

Our review of Liouville theorems includes a special focus on nonlinear partial differential equations and inequalities.

This paper shows how resilience-based measurements, Industrial Resilience Index (IRI), is able to indicate the performance trend of general manufacturing, measured in Gross Domestic Product (GDP), impacted by shocks represented by the value drops of the Rupiah to the US Dollar. This paper argues that IRI is able to measure not only the resilience of the Metal Product Manufacturing Sector (MPMS) but also the performance dynamic of the general manufacturing industry. This study evaluates the IRI performance by using the cross-correlation method. The cross-correlation process consists of a comparison between IRI and the GDP of the manufacturing industry, as well as a comparison to other indices related to manufacturing sectors, such as the Purchasing Manager Index (PMI), the Production Index of Large and Medium Manufacturing Industry (PII), the Competitiveness Industrial Performance (CIP), and the Global Competitiveness Index (GCI). The positive and high value of the correlations in this study shows IRI’s ability to reflect the sector resilience and the GDP of the general manufacturing industry trend. The result of this study suggests that IRI can be utilized as a dynamic indicator of the general manufacturing industry. Through its data series and trend analysis, decision or policymakers may employ IRI to forecast how resilient MPMS, as well as the general manufacturing industry trend, is when the sector faces shocks in the future. The result of the study shows that cross-correlation coefficient of IRI is 0.74. The coefficient value indicates that IRI is a coincident indicator within the business cycles of the general manufacturing industry. Therefore, as an alternative of resilience-based measurement, the study suggests that IRI is able to demonstrate its significance in predicting the resilience of MPMS and the general manufacturing industry, in anticipating a dynamic shock is in the future.

Abstract Purpose The objective of this research is to explore the applicability of machine learning and fully homomorphic encryption (FHE) in the private pathological assessment, with a focus on the inference phase of support vector machines (SVM) for the classification of confidential medical data. Methods A framework is introduced that utilizes the Cheon-Kim-Kim-Song (CKKS) FHE scheme, facilitating the execution of SVM inference on encrypted datasets. This framework ensures the privacy of patient data and negates the necessity of decryption during the analytical process. Additionally, an efficient feature extraction technique is presented for the transformation of medical imagery into vectorial representations. Results The system’s evaluation across various datasets substantiates its practicality and efficacy. The proposed method delivers classification accuracy and performance on par with traditional, non-encrypted SVM inference, while upholding a 128-bit security level against established cryptographic attacks targeting the CKKS scheme. The secure inference process is executed within a temporal span of mere seconds. Conclusion The findings of this study underscore the viability of FHE in enhancing the security and efficiency of bioinformatics analyses, potentially benefiting fields such as cardiology, oncology, and medical imagery. The implications of this research are significant for the future of privacy-preserving machine learning, promoting progress in diagnostic procedures, tailored medical treatments, and clinical investigations.

Abstract The use of prior knowledge in the machine learning framework has been considered a potential tool to handle the curse of dimensionality in genetic and genomics data. Although random forest (RF) represents a flexible non-parametric approach with several advantages, it can provide poor accuracy in high-dimensional settings, mainly in scenarios with small sample sizes. We propose a knowledge-slanted RF that integrates biological networks as prior knowledge into the model to improve its performance and explainability, exemplifying its use for selecting and identifying relevant genes. knowledge-slanted RF is a combination of two stages. First, prior knowledge represented by graphs is translated by running a random walk with restart algorithm to determine the relevance of each gene based on its connection and localization on a protein-protein interaction network. Then, each relevance is used to modify the selection probability to draw a gene as a candidate split-feature in the conventional RF. Experiments in simulated datasets with very small sample sizes $$(n \le 30)$$ ( n ≤ 30 ) comparing knowledge-slanted RF against conventional RF and logistic lasso regression, suggest an improved precision in outcome prediction compared to the other methods. The knowledge-slanted RF was completed with the introduction of a modified version of the Boruta feature selection algorithm. Finally, knowledge-slanted RF identified more relevant biological genes, offering a higher level of explainability for users than conventional RF. These findings were corroborated in one real case to identify relevant genes to calcific aortic valve stenosis.

Abstract Background Hospitalizations for exacerbations of congestive heart failure (CHF), chronic obstructive pulmonary disease (COPD) and diabetic ketoacidosis (DKA) are costly in the United States. The purpose of this study was to predict in-hospital charges for each condition using machine learning (ML) models. Results We conducted a retrospective cohort study on national discharge records of hospitalized adult patients from January 1st, 2016, to December 31st, 2019. We constructed six ML models (linear regression, ridge regression, support vector machine, random forest, gradient boosting and extreme gradient boosting) to predict total in-hospital cost for admission for each condition. Our models had good predictive performance, with testing R-squared values of 0.701-0.750 (mean of 0.713) for CHF; 0.694-0.724 (mean 0.709) for COPD; and 0.615-0.729 (mean 0.694) for DKA. We identified important key features driving costs, including patient age, length of stay, number of procedures, and elective/nonelective admission. Conclusions ML methods may be used to accurately predict costs and identify drivers of high cost for COPD exacerbations, CHF exacerbations and DKA. Overall, our findings may inform future studies that seek to decrease the underlying high patient costs for these conditions.

Abstract In this paper, the fractional-order Chelyshkov functions (FCHFs) and Riemann-Liouville fractional integrals are utilized to find numerical solutions to fractional delay differential equations, by transforming the problem into a system of algebraic equations with unknown FCHFs coefficients. An error bound of FCHFs approximation is estimated and its convergence is also demonstrated. The effectiveness and accuracy of the presented method are established through several examples. The resulting solution is accurate and agrees with the exact solution, even if the exact solution is not a polynomial. Moreover, comparisons between the obtained numerical results and those recently reported in the literature are shown.

Abstract In this paper, we establish the existence and stability of periodic solutions for neutral-type differential equations with piecewise impulses on time scales. We first obtain some sufficient conditions for the existence of a unique periodic solution by using the Banach contraction mapping principle. We also prove the existence of at least one periodic solution using the Schauder fixed point theorem. In addition, we establish the stability results based on the existence of periodic solutions. It is worth noting that the results of this paper are based on time scales, so that they are applicable to continuous, discrete, and other types of systems.

Abstract In this study, an ordinary-deterministic equation system modeling the spread dynamics of malware under mutation is analyzed with fractional derivatives and random variables. The original model is transformed into a system of fractional-random differential equations (FRDEs) using Caputo fractional derivatives. Normally distributed random variables are defined for the parameters of the original system that are related to the mutations and infections of the nodes in the network. The resulting system of FRDEs is simulated using the predictor-corrector method based fde12 algorithm and the forward fractional Euler method (ffEm) for various values of the model components such as the standard deviations, orders of derivation, and repetition numbers. Additionally, the sensitivity analysis of the original model is investigated in relation to the random nature of the components and the basic reproduction number ( R 0 $R_{0}$ ) to underline the correspondence of random dynamics and sensitivity indices. Both the normalized forward sensitivity indices (NFSI) and the standard deviation of R 0 $R_{0}$ with random components give matching results for analyzing the changes in the spread rate. Theoretical results are backed by the simulation outputs on the numerical characteristics of the fractional-random model for the expected number of infections and mutations, expected timing of the removal of mutations from the network, and measurement of the variability in the results such as the coefficients of variation. Comparison of the results from the original model and the fractional-random model shows that the fractional-random analysis provides a more generalized perspective while facilitating a versatile investigation with ease and can be used on different models as well.

Abstract The primary objective of this manuscript is to investigate the existence and uniqueness of solutions for the Langevin ( k , φ ) $(\mathtt{k},\varphi )$ -Hilfer fractional differential equation of different orders with multipoint nonlocal fractional integral boundary conditions. We consider the generalized version of the Hilfer fractional diferential equation called as ( k , φ ) $(\mathtt{k},\varphi )$ -Hilfer fractional differential equation. We provide some significant outcomes about ( k , φ ) $(\mathtt{k},\varphi )$ -Hilfer fractional Langevin differential equation that requires deriving equivalent fractional integral equation to ( k , φ ) $(\mathtt{k},\varphi )$ -Hilfer Langevin fractional differential equation. The existence result is established using the Krasnoselskii’s fixed-point theorem, while the uniqueness is addressed with the help of Banach contraction principle. Additionally, we investigate the different forms of Ulam stability for the solution of the mentioned problem, under specific conditions. To validate our main outcomes, we present a detailed example at the end of the manuscript.

Abstract In this paper, we prove that under weak assumptions on the reaction terms and diffusion coefficients, a positive solution exists for a one-dimensional case and a positive radial solution to a multidimensional case of a nonlocal elliptic problem. Additionally, we establish the uniqueness of the solution, with the fixed point theorem being the primary tool employed. Our results are new and generalize several existing results.

Abstract The paper focuses on establishing sufficient conditions for the existence of the solutions in some functional q-integral equations, particularly in Banach spaces. In this method, the technique of measures of noncompactness and Petryshyn’s fixed point theorem in Banach space is used. We provide some examples of equations, which confirm that our result is applicable to a wide class of integral equations.

Abstract The current paper undertakes an in-depth exploration of the dynamics of nonlinear waves governed by a 3D-modified nonlinear wave equation, a significant model in the study of complex wave phenomena. To this end, the study employs both classical and nonclassical Lie symmetries for rigorously deriving invariant solutions of the governing equation. These symmetries enable the formal construction of exact solutions, which are crucial for understanding the complex behavior of the model. Furthermore, the research extends into the realm of bifurcation analysis through the application of planar dynamical system theory. Such an analysis reveals the conditions under which the 3D-modified nonlinear wave equation admits Jacobi elliptic function solutions. The study also delves into the impact of the nonlinear parameter on the physical characteristics of bright and kink solitary waves as well as continuous periodic waves using Maple. Overall, the comprehensive analysis presented not only enhances the understanding of complex nonlinear wave dynamics but also sets the stage for future advancements in vast areas of fluid dynamics and plasma physics.

Abstract We investigate the interior regularity to nonlinear subelliptic systems in divergence form with drift term for the case of superquadratic controllable structure conditions in the Heisenberg group. On the basis of a generalization of the A $\mathcal{A}$ -harmonic approximation technique, C 1 $C^{1}$ -regularity is established for horizontal gradients of vector-valued solutions to the subelliptic systems with drift term. Specially, our result is optimal in the sense that in the case of Hölder continuous coefficients we directly attain the optimal Hölder exponent for the horizontal gradients of weak solutions on the regular set.

Abstract Let Ω be a nonempty closed convex subset of a real Hilbert space H $\mathfrak{H}$ . Let ℑ be a nonspreading mapping from Ω into itself. Define two sequences { ψ n } n = 1 ∞ $\{\psi _{{n}}\}_{n=1}^{\infty}$ and { ϕ n } n = 1 ∞ $\{\phi _{{n}}\}_{n=1}^{\infty}$ as follows: { ψ n + 1 = π n ψ n + ( 1 − π n ) ℑ ψ n , ϕ n = 1 n ∑ n t = 1 ψ t , $$\begin{aligned} \textstyle\begin{cases} \psi _{n+1}=\pi _{n}\psi _{{n}}+(1-\pi _{n})\Im \psi _{{n}}, \\ \phi _{{n}}=\dfrac{1}{n}\underset{t=1}{\overset{n}{\sum}}\psi _{t}, \end{cases}\displaystyle \end{aligned}$$ for n ∈ N $n\in \mathit{N}$ , where 0 ≤ π n ≤ 1 $0\leq \pi _{n}\leq 1$ , and π n → 0 $\pi _{n} \rightarrow 0$ . In 2010, Kurokawa and Takahashi established weak and strong convergence theorems of the sequences developed from the above Baillion-type iteration method (Nonlinear Anal. 73:1562–1568, 2010). In this paper, we prove weak and strong convergence theorems for a new class of ( η , β ) $(\eta ,\beta )$ -enriched strictly pseudononspreading ( ( η , β ) $(\eta ,\beta )$ -ESPN) maps, more general than that studied by Kurokawa and W. Takahashi in the setup of real Hilbert spaces. Further, by means of a robust auxiliary map incorporated in our theorems, the strong convergence of the sequence generated by Halpern-type iterative algorithm is proved thereby resolving in the affirmative the open problem raised by Kurokawa and Takahashi in their concluding remark for the case in which the map ℑ is averaged. Some nontrivial examples are given, and the results obtained extend, improve, and generalize several well-known results in the current literature.

We prove that any Lipschitz map that satisfies a condition inspired by the work of G. David may be decomposed into countably many bi-Lipschitz pieces.

This article is concerned with the qualitative properties for the Cauchy problem of a non-Newtonian filtration equation with a reaction source term and volumetric moisture content. On the basis of the slowly decaying behavior of volumetric moisture content, we establish new critical exponents that depend on the ratio of coefficients and exponent of volumetric moisture content. Meantime, under appropriate conditions, we show that the solution globally exists for small enough initial data and blows up in finite time for large enough or any nontrivial initial datum.

In this article, we study the following fractional Kirchhoff-type problems with critical and sublinear nonlinearities: a+b∬RN×RN∣u(x)−u(y)∣2∣x−y∣N+2sdxdy(−Δ)su=λuq−1+u2s*−1,u>0,inΩ,u=0,inRN\Ω,∫RNu2dx=c2,\left\{\begin{array}{l}\left(a+b\mathop{\iint }\limits_{{{\mathbb{R}}}^{N}\times {{\mathbb{R}}}^{N}}\frac{{| u\left(x)-u(y)| }^{2}}{{| x-y| }^{N+2s}}{\rm{d}}x{\rm{d}}y\right){\left(-\Delta )}^{s}u=\lambda {u}^{q-1}+{u}^{{2}_{s}^{* }-1},\hspace{1em}u\gt 0,\hspace{1em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}\Omega ,\\ u=0\left,\hspace{1em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{N}\backslash \Omega \right,\\ \mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{N}}{u}^{2}{\rm{d}}x={c}^{2},\end{array}\right. where (−Δ)s{\left(-\Delta )}^{s} is the fractional Laplacian, Ω⊂RN\Omega \subset {{\mathbb{R}}}^{N} is a bounded domain with Lipschitz boundary, 00,a>0,b>0,c>0\lambda \gt 0,a\gt 0,b\gt 0,c\gt 0. First, we prove that the bounded Palais-Smale sequence has a profile decomposition in the fractional Laplacian setting. Then, by utilizing decomposition techniques and variational methods, we acquire that there are two positive normalized solutions for the aforementioned problems.

Objectives: This study aims to explore the health services and their spatial and functional efficiency in the countryside of Al-Qaim District for the year 2021, and to investigate to investigate the extent of their conformity with local standards by the relevant authorities in the governorate.Methodology: The research relied on the (functional) and analytical approach in studies of health services in the countryside of Al-Qaim District, with the help of some quantitative and statistical methods and techniques using modern technologies (GIS) in spatial and statistical analysis and discovering spatial relationships between variables and standards subject to the research in addition to field workResults: The results of the field research showed that (42%) could reach the health services walking, (27%) arriving by private cars, (17%) using public transportations, (8%) using bicycles, and (6%) using motorcycles. The results also showed a shortage in health centers for some administrative units, as well as a shortage in doctors, dentists, pharmacists and health professionals. Therefore, the study recommends that the Anbar Health Directorate should provide medical staff for the study area in line with local standards for specialist doctors, dentists, pharmacists and health professionals, as the area suffers from a severe shortage of medical staff to treat the population and provide treatments and laboratory equipment for the study area.Conclusion: The health centers in the study area provide therapeutic services such as vaccinations, school health, promotion and supervision, in addition to some simple surgical operations such as bandaging and others. Therefore, most of the population goes to the cities to obtain better therapeutic services. The field study, through the use of human standards and indicators and health services, showed their negativity in terms of the numbers of doctors, pharmacists, dentists and health professionals

In this article, we first introduce a new fractional gg-Laplacian Monge-Ampère operator: Fgsv(x)≔infP.V.∫Rngv(z)−v(x)∣C−1(z−x)∣sdz∣C−1(z−x)∣n+s∣C∈C,{F}_{g}^{s}v\left(x):= \inf \left\{\hspace{0.1em}\text{P.V.}\hspace{0.1em}\mathop{\int }\limits_{{{\mathbb{R}}}^{n}}g\left(\frac{v\left(z)-v\left(x)}{{| {C}^{-1}\left(z-x)| }^{s}}\right)\frac{{\rm{d}}z}{{| {C}^{-1}\left(z-x)| }^{n+s}}| C\in {\mathcal{C}}\right\}, where gg is the derivative of a Young function and the diagonal matrix C{\mathcal{C}} is positive definite, which has a determinant equal to 1. First, we establish some crucial maximum principles for equations involving the fractional gg-Laplacian Monge-Ampère operator. Based on the maximum principles, the direct method of moving planes is applied to study the equation involving the fractional gg-Laplacian Monge-Ampère operator. As a result, the nonexistence of the positive solutions, symmetry, monotonicity, and asymptotic property of solutions are obtained in bounded/unbounded domains.

Abstract Objectives This study aims to develop an innovative approach for monitoring and assessing labor pain through ECG waveform analysis, utilizing machine learning techniques to monitor pain resulting from uterine contractions. Methods The study was conducted at National Taiwan University Hospital between January and July 2020. We collected a dataset of 6010 ECG samples from women preparing for natural spontaneous delivery (NSD). The ECG data was used to develop an ECG waveform-based Nociception Monitoring Index (NoM). The dataset was divided into training (80%) and validation (20%) sets. Multiple machine learning models, including LightGBM, XGBoost, SnapLogisticRegression, and SnapDecisionTree, were developed and evaluated. Hyperparameter optimization was performed using grid search and five-fold cross-validation to enhance model performance. Results The LightGBM model demonstrated superior performance with an AUC of 0.96 and an accuracy of 90%, making it the optimal model for monitoring labor pain based on ECG data. Other models, such as XGBoost and SnapLogisticRegression, also showed strong performance, with AUC values ranging from 0.88 to 0.95. Conclusions This study demonstrates that the integration of machine learning algorithms with ECG data significantly enhances the accuracy and reliability of labor pain monitoring. Specifically, the LightGBM model exhibits exceptional precision and robustness in continuous pain monitoring during labor, with potential applicability extending to broader healthcare settings. Trial registration ClinicalTrials.gov Identifier: NCT04461704.

Abstract Genome-wide association studies (GWAS) have revolutionized our understanding of the genetic architecture of complex traits and diseases. GWAS summary statistics have become essential tools for various genetic analyses, including meta-analysis, fine-mapping, and risk prediction. However, the increasing number of GWAS summary statistics and the diversity of software tools available for their analysis can make it challenging for researchers to select the most appropriate tools for their specific needs. This systematic review aims to provide a comprehensive overview of the currently available software tools and databases for GWAS summary statistics analysis. We conducted a comprehensive literature search to identify relevant software tools and databases. We categorized the tools and databases by their functionality, including data management, quality control, single-trait analysis, and multiple-trait analysis. We also compared the tools and databases based on their features, limitations, and user-friendliness. Our review identified a total of 305 functioning software tools and databases dedicated to GWAS summary statistics, each with unique strengths and limitations. We provide descriptions of the key features of each tool and database, including their input/output formats, data types, and computational requirements. We also discuss the overall usability and applicability of each tool for different research scenarios. This comprehensive review will serve as a valuable resource for researchers who are interested in using GWAS summary statistics to investigate the genetic basis of complex traits and diseases. By providing a detailed overview of the available tools and databases, we aim to facilitate informed tool selection and maximize the effectiveness of GWAS summary statistics analysis.

Abstract Objective Data imbalance is a pervasive issue in medical data mining, often leading to biased and unreliable predictive models. This study aims to address the urgent need for effective strategies to mitigate the impact of data imbalance on classification models. We focus on quantifying the effects of different imbalance degrees and sample sizes on model performance, identifying optimal cut-off values, and evaluating the efficacy of various methods to enhance model accuracy in highly imbalanced and small sample size scenarios. Methods We collected medical records of patients receiving assisted reproductive treatment in a reproductive medicine center. Random forest was used to screen the key variables for the prediction target. Various datasets with different imbalance degrees and sample sizes were constructed to compare the classification performance of logistic regression models. Metrics such as AUC, G-mean, F1-Score, Accuracy, Recall, and Precision were used for evaluation. Four imbalance treatment methods (SMOTE, ADASYN, OSS, and CNN) were applied to datasets with low positive rates and small sample sizes to assess their effectiveness. Results The logistic model’s performance was low when the positive rate was below 10% but stabilized beyond this threshold. Similarly, sample sizes below 1200 yielded poor results, with improvement seen above this threshold. For robustness, the optimal cut-offs for positive rate and sample size were identified as 15% and 1500, respectively. SMOTE and ADASYN oversampling significantly improved classification performance in datasets with low positive rates and small sample sizes. Conclusions The study identifies a positive rate of 15% and a sample size of 1500 as optimal cut-offs for stable logistic model performance. For datasets with low positive rates and small sample sizes, SMOTE and ADASYN are recommended to improve balance and model accuracy.

Abstract Pangenomics is a relatively new scientific field which investigates the union of all the genomes of a clade. The word pan means everything in ancient Greek; the term pangenomics originally regarded genomes of bacteria and was later intended to refer to human genomes as well. Modern bioinformatics offers several tools to analyze pangenomics data, paving the way to an emerging field that we can call computational pangenomics. Current computational power available for the bioinformatics community has made computational pangenomic analyses easy to perform, but this higher accessibility to pangenomics analysis also increases the chances to make mistakes and to produce misleading or inflated results, especially by beginners. To handle this problem, we present here a few quick tips for efficient and correct computational pangenomic analyses with a focus on bacterial pangenomics, by describing common mistakes to avoid and experienced best practices to follow in this field. We believe our recommendations can help the readers perform more robust and sound pangenomic analyses and to generate more reliable results.

Abstract Background Identifying critical genes is important for understanding the pathogenesis of complex diseases. Traditional studies typically comparing the change of biomecules between normal and disease samples or detecting important vertices from a single static biomolecular network, which often overlook the dynamic changes that occur between different disease stages. However, investigating temporal changes in biomolecular networks and identifying critical genes is critical for understanding the occurrence and development of diseases. Methods A novel method called Quantifying Importance of Genes with Tensor Decomposition (QIGTD) was proposed in this study. It first constructs a time series network by integrating both the intra and inter temporal network information, which preserving connections between networks at adjacent stages according to the local similarities. A tensor is employed to describe the connections of this time series network, and a 3-order tensor decomposition method was proposed to capture both the topological information of each network snapshot and the time series characteristics of the whole network. QIGTD is also a learning-free and efficient method that can be applied to datasets with a small number of samples. Results The effectiveness of QIGTD was evaluated using lung adenocarcinoma (LUAD) datasets and three state-of-the-art methods: T-degree, T-closeness, and T-betweenness were employed as benchmark methods. Numerical experimental results demonstrate that QIGTD outperforms these methods in terms of the indices of both precision and mAP. Notably, out of the top 50 genes, 29 have been verified to be highly related to LUAD according to the DisGeNET Database, and 36 are significantly enriched in LUAD related Gene Ontology (GO) terms, including nuclear division, mitotic nuclear division, chromosome segregation, organelle fission, and mitotic sister chromatid segregation. Conclusion In conclusion, QIGTD effectively captures the temporal changes in gene networks and identifies critical genes. It provides a valuable tool for studying temporal dynamics in biological networks and can aid in understanding the underlying mechanisms of diseases such as LUAD.

Abstract The main purpose of this paper is to consider the multiple birth properties for multi-type Markov branching processes. We first construct a new multi-dimensional Markov process based on the multi-type Markov branching process, which can reveal the multiple birth characteristics. Then the joint probability distribution of multiple birth of multi-type Markov branching process until any time t is obtained by using the new process. Furthermore, the probability distribution of multiple birth until the extinction of the process is also given.

Abstract In this article, a new numerical algorithm for solving a 1-dimensional (1D) and 2-dimensional (2D) time-fractional diffusion equation is proposed. The Sinc-Galerkin scheme is considered for spatial discretization, and a higher-order finite difference formula is considered for temporal discretization. The convergence behavior of the methods is analyzed, and the error bounds are provided. The main objective of this paper is to propose the error bounds for 2D problems by using the Sinc-Galerkin method. The proposed method in terms of convergence is studied by using the characteristics of the Sinc function in detail with optimal rates of exponential convergence for 2D problems. Some numerical experiments validate the theoretical results and present the efficiency of the proposed schemes.

The present work presents a series of experimental distortion analysis of square shipbuilding steel plates with an attached stiffener. Two approved fillet welding configurations are applied to attach the stiffener using shielded metal arc welding at Port Said Shipyard. The specimens are welded using continuous and intermittent chain fillet welding for variant plating thicknesses with constant stiffener geometrical configurations, where two welding passes are applied. The effect of different fillet welding geometry on the induced initial imperfection amplitudes for different base plating thicknesses is investigated. The imperfection shapes are tracked, and the amplitudes are measured during and after the welding process. The imperfection amplitudes for each plating thickness and welding geometry are analyzed considering both preheat after the first pass and heat relief. Several relationships considering the welding time and the amount consumed electrodes are performed for different plating thicknesses and welding geometries. A comparison between existing empirical formulations and the observed results is performed in the form of plate slenderness, showing reasonable conclusions.

The agrarian business in Bulgaria has the potential for development by applying a marketing approach to its management. Agricultural production can be developed by satisfying the needs of the market. The supply of Bulgarian agricultural products faces many market challenges, which forces farmers to look for means to improve the market image of their products. The purpose of the article is to determine guidelines for improving the management of Bulgarian agricultural holdings. Implementation of strategic marketing activities by farmers can improve their economic performance based on better market performance. The correct implementation of these activities requires that they be considered as part of a systemic process that affects all elements of the production and marketing system. This requires that the management functions related to planning, execution, and control of marketing activities are performed in the context of the market environment for each particular business.

The study examined Undergraduates’ awareness of the use of technological tools for information collection and analysis. Specifically, the study is focused on: (i) examining how often final-year undergraduates have heard about the different methods used to collect information about a respondent or participants (ii) investigating how commonly final-year undergraduates believe technological tools are used to collect information (iii) examining how frequently final-year undergraduates have heard about technological tools used to analyze information collected. The sample of the study comprised 100 undergraduates selected using Krejcie and Morgan sample size determination table. The results revealed that the respondents are aware of the common methods (questionnaire, experiment, and interview) used to collect information, except for focused group discussion, which is occasionally used as a method to collect information. Also, it was revealed that the use of computer-assisted tools, social media, and audio-visual tools are common technological tools used to collect information, with low awareness of the use of Google Forms and email. The use of SPSS and Microsoft Excel for information analysis is common amongst undergraduates, which showed high awareness whereas, the use of ACTIVITY INSIGHT, STATA, and NVIVO is not frequent, which showed low awareness. Awareness and practical teachings be organized for undergraduates on the different methods as well as technological tools that can be to collect and analyze information respectively.

This work is concerned with the following Klein-Gordon-Maxwell system: −Δu+V(x)u−(2ω+ϕ)ϕu=f(u),x∈R2,Δϕ=(ω+ϕ)u2,x∈R2,\left\{\begin{array}{ll}-\Delta u+V\left(x)u-\left(2\omega +\phi )\phi u=f\left(u),\hspace{1.0em}& x\in {{\mathbb{R}}}^{2},\\ \Delta \phi =\left(\omega +\phi ){u}^{2},\hspace{1.0em}& x\in {{\mathbb{R}}}^{2},\end{array}\right. where ω>0\omega \gt 0 is a constant, u,ϕ:R2→Ru,\phi :{{\mathbb{R}}}^{2}\to {\mathbb{R}}, V∈C(R2,R)V\in {\mathcal{C}}\left({{\mathbb{R}}}^{2},{\mathbb{R}}), and f∈C(R,R)f\in {\mathcal{C}}\left({\mathbb{R}},{\mathbb{R}}) obeys exponential critical growth in the sense of the Trudinger-Moser inequality. We give some new sufficient conditions on ff, specifically related to exponential growth, to obtain the existence of nontrivial solutions. Our results improve and extend the previous results. In particular, we give a more precise estimation than the ones in the existing literature about the minimax level.

This article is devoted to the study of a critical Choquard-Kirchhoff pp-sub-Laplacian equation on the entire Heisenberg group Hn{{\mathbb{H}}}^{n}, where the Kirchhoff function KK can be zero at zero, i.e., the equation can be degenerate, and involving a nonlinearity, which is critical in the sense of the Hardy-Littlewood-Sobolev inequality. We first establish the concentration-compactness principle for the pp-sub-Laplacian Choquard equation on the Heisenberg group, and we then prove existence results.

We provide bounds for the sequence of eigenvalues {λi(Ω)}i{\left\{{\lambda }_{i}\left(\Omega )\right\}}_{i} of the Dirichlet problem (I−Δ)lnu=λuinΩ,u=0inRN\Ω,{\left(I-\Delta )}^{\mathrm{ln}}u=\lambda u\hspace{1em}{\rm{in}}\hspace{0.33em}\Omega ,\hspace{1.0em}u=0\hspace{1em}{\rm{in}}\hspace{0.33em}{{\mathbb{R}}}^{N}\setminus \Omega , where (I−Δ)ln{\left(I-\Delta )}^{\mathrm{ln}} is the Klein-Gordon operator with Fourier transform symbol ln(1+∣ξ∣2)\mathrm{ln}\left(1+{| \xi | }^{2}). The purpose of this study is to obtain the upper and lower bounds for the sum of the first k-eigenvalues by extending the Li-Yau’s method and Kröger’s method, respectively.

This article is devoted to study a class of new p(x)p\left(x)-Kirchhoff equation. By means of perturbation technique, variational method, and the method invariant sets for the descending flow, the existence and multiplicity of solutions to this problem are obtained.

In this article, we aim to establish the optimal time decay rates of strong solutions to a two-phase flow model derived from a type of coupled fluid-kinetic equation. It is proved that the strong solutions converge to the given constant states with algebraic time decay rates under some additional assumptions on the initial data.

The information paradigms defining contemporary society call for the character of plurivalence through their omnipresence in multiple areas of activity. Their ubiquitous character provides the basis of the accounting-computer science interdependence, the undeniable reality being marked by the computer indispensability in the professional accountant’s life. In this way, specialized literature becomes allencompassing by the approaches marked by complexity and density regarding the issues of modernizing the accounting by its massive computerization. The cloud accounting phenomenon is a component part of the innovative changes that accounting has undergone lately. The research paper aims to outline the bibliometric universe of the cloud accounting concept based on the methods, tools and techniques subscribed to bibliometrics in view of reflecting its representativeness through the lens of specialized literature. The results thus obtained consolidate the emblematic character of the cloud accounting issue in light of the massive interest manifested for its thoroughness and exploration equally by researchers, theoreticians, and practitioners. The study also stands out for its originality, being currently the only one dealing with issues of cloud accounting concept bibliometrics. The attribute of uniqueness of this paper is defined by shaping the research universe assigned to the phenomenon based on specialized literature, identifying the manner to reshape the profession and the field by changing the digital paradigm and illustrating the representativeness of technology in the academic community through the perspective of the bibliometrics tool. Likewise, an element of novelty is given by highlighting the definition of cloud accounting from the author’s perspective based on the image provided by the literature review.

Abstract Cardiovascular diseases are the main cause of death in the world and cardiovascular imaging techniques are the mainstay of noninvasive diagnosis. Aortic stenosis is a lethal cardiac disease preceded by aortic valve calcification for several years. Data-driven tools developed with Deep Learning (DL) algorithms can process and categorize medical images data, providing fast diagnoses with considered reliability, to improve healthcare effectiveness. A systematic review of DL applications on medical images for pathologic calcium detection concluded that there are established techniques in this field, using primarily CT scans, at the expense of radiation exposure. Echocardiography is an unexplored alternative to detect calcium, but still needs technological developments. In this article, a fully automated method based on Convolutional Neural Networks (CNNs) was developed to detect Aortic Calcification in Echocardiography images, consisting of two essential processes: (1) an object detector to locate aortic valve – achieving 95% of precision and 100% of recall; and (2) a classifier to identify calcium structures in the valve – which achieved 92% of precision and 100% of recall. The outcome of this work is the possibility of automation of the detection with Echocardiography of Aortic Valve Calcification, a lethal and prevalent disease.

Abstract Background In recent years, significant morbidity and mortality in patients with severe inflammatory bowel disease (IBD) and cytomegalovirus (CMV) have drawn considerable attention to the status of CMV infection in the intestinal mucosa of IBD patients and its role in disease progression. However, there is currently no high-throughput sequencing data for ulcerative colitis patients with CMV infection (CMV + UC), and the immune microenvironment in CMV + UC patients have yet to be explored. Method The xCell algorithm was used for evaluate the immune microenvironment of CMV + UC patients. Then, WGCNA analysis was explored to obtain the co-expression modules between abnormal immune cells and gene level or protein level. Next, three machine learning approach include Random Forest, SVM-rfe, and Lasso were used to filter candidate biomarkers. Finally, Best Subset Selection algorithms was performed to construct the diagnostic model. Results In this study, we performed transcriptomic and proteomic sequencing on CMV + UC patients to establish a comprehensive immune microenvironment profile and found 11 specific abnormal immune cells in CMV + UC group. After using multi-omics integration algorithms, we identified seven co-expression gene modules and five co-expression protein modules. Subsequently, we utilized various machine learning algorithms to identify key biomarkers with diagnostic efficacy and constructed an early diagnostic model. We identified a total of eight biomarkers (PPP1R12B, CIRBP, CSNK2A2, DNAJB11, PIK3R4, RRBP1, STX5, TMEM214) that play crucial roles in the immune microenvironment of CMV + UC and exhibit superior diagnostic performance for CMV + UC. Conclusion This 8 biomarkers model offers a new paradigm for the diagnosis and treatment of IBD patients post-CMV infection. Further research into this model will be significant for understanding the changes in the host immune microenvironment following CMV infection.

Abstract The second-order periodic system with p-Laplacian and unbounded time-dependent perturbation terms is investigated. Using the principle integral method, it is shown that under certain assumptions on the unbounded and periodic terms, all solutions to the equation possess boundedness.

The article provides a comparative assessment of domestic and foreign scientists’ and economists’ works, who studied theoretical approaches to sustainable economic development. Countries are increasingly integrating with each other, labor productivity is higher, but at the same time natural resources are used too intensively, which leads to environmental pollution. In this regard, it is necessary to pay more attention and even be unable to influence the processes aimed at ensuring stable economic growth. In the conditions of world economic relations transformation, economic systems activity sustainability is a key element of development and growth of national economies of states. The introduction and use of theoretical approaches in the process of studying the sustainable development of the economy makes it possible to systematize various properties of economic systems in the process of analyzing its development prospects. The obtained results of the conducted research can be used in theoretical frameworks evaluation aimed at studying the sustainable development of economy.

The relevance of the study is conditioned by the fact that in recent years the level of regional socio-economic systems development has been significantly affected by various negative factors, and it is necessary to carry out an operational analysis that will help to identify them in a timely manner. Uneven development of regions is characteristic of many countries and is determined by the peculiarities of historical traditions, current economic potential and interrelations with international communities, as well as by state regional policy. The level of innovative development and society digitalization creates conditions for the transition of Russia from a resource-based economy to an investment and innovation economy in order to improve and maintain competitiveness. As a result of the research and study of the scientists’ materials, who have investigated the ways and mechanisms of analyzing regional socio-economic systems formation and development, as well as their impact on the Russian economy development, which at the present stage is reaching a new level in the conditions of sanctions, we have conducted an assessment of regional socio-economic systems and various methods of its implementation.

The article provides a comparative analysis of the scientists’ and economists’ works, who studied the approaches to the methods of comprehensive assessment of latent reserves of innovation potential of the industrial complex. In the conditions of global economic relations transformation, the complex analysis of latent reserves of innovation potential development acts as one of the main elements of development and strategic growth of enterprises’ innovation potential. The conducted research has a significant impact on further study of the complex analysis of latent reserves of innovation potential development, contributing to the effective development of the industrial complex. The obtained results of the study can be used in the assessment and comprehensive analysis of latent reserves formation aimed at the enterprises’ innovative potential growth.

Abstract This study utilizes a spectral tau method to acquire an accurate numerical solution of the time-fractional diffusion equation. The central point of this approach is to use double basis functions in terms of certain Chebyshev polynomials, namely Chebyshev polynomials of the seventh-kind and their shifted ones. Some new formulas concerned with these polynomials are derived in this study. A rigorous error analysis of the proposed double expansion further corroborates our research. This analysis is based on establishing some inequalities regarding the selected basis functions. Several numerical examples validate the precision and effectiveness of the suggested method.

Abstract This study explores the extension of Milne-type inequalities to the realm of Katugampola fractional integrals, aiming to broaden the analytical tools available in fractional calculus. By introducing a novel integral identity, we establish a series of Milne-type inequalities for functions possessing extended s-convex first-order derivatives. Subsequently, we present an illustrative example complete with graphical representations to validate our theoretical findings. The paper concludes with practical applications of these inequalities, demonstrating their potential impact across various fields of mathematical and applied sciences.

Abstract In this paper, a class of fractional Sturm–Liouville advection–dispersion equations with instantaneous and noninstantaneous impulses is considered, in particular, the nonlinearities discussed here include Caputo fractional derivatives. Since the nonlinear terms contain fractional derivatives, this problem does not directly have variational structure, we need to combine critical point theory and an iterative method to deal with such problems. Finally, the existence of at least one nontrivial solution is proved by the mountain pass theorem and the iterative method. At the same time, an example is given to illustrate the main result.

Abstract A convex fair partition of a convex polygonal region is defined as a partition on which all regions are convex and have equal area and equal perimeter. The existence of such a partition for any number of regions remains an open question. In this paper, we address this issue by developing an algorithm to find such a convex fair partition without restrictions on the number of regions. Our approach utilizes the normal flow algorithm (a generalization of Newton’s method) to find a zero for the excess areas and perimeters of the convex hulls of the regions. The initial partition is generated by applying Lloyd’s algorithm to a randomly selected set of points within the polygon, after appropriate scaling. We performed extensive experimentation, and our algorithm can find a convex fair partition for 100% of the tested problem. Our findings support the conjecture that a convex fair partition always exists.

In this article, we consider the global and local well-posedness of the mild solutions to the Cauchy problem of fractional drift diffusion system with higher-order nonlinearity. The main difficulty comes from the higher-order nonlinearity. Instead of the convention that people always focus on the properties of the solution in critical spaces, here we are interested in non-critical spaces such as supercritical Sobolev spaces and subcritical Lebesgue spaces. For the initial data in these non-critical spaces, using the properties of fractional heat semigroup and the classical Hardy-Littlewood-Sobolev inequality, we obtain the existence and uniqueness of the mild solution, together with the decaying rate estimates in terms of time variable.

Abstract We study the bifurcation curve and exact multiplicity of positive solutions in the space C 2 ( ( − L , L ) ) ∩ C ( [ − L , L ] ) $C^{2}\left ( (-L,L)\right ) \cap C\left ( [-L,L]\right ) $ for the Minkowski-curvature equation { − ( u ′ ( x ) 1 − ( u ′ ( x ) ) 2 ) ′ = λ f ( u ) , − L < x < L , u ( − L ) = u ( L ) = 0 . $$ \left \{ \textstyle\begin{array}{l} -\left ( \dfrac{u^{\prime }(x)}{\sqrt{1-\left ( {u^{\prime }(x)}\right ) ^{2}}}\right ) ^{\prime }=\lambda f(u),\text{\ \ }-L< x< L, \\ u(-L)=u(L)=0.\end{array}\displaystyle \right . $$ where λ > 0 $\lambda >0$ is a bifurcation parameter, f ∈ C [ 0 , ∞ ) ∩ C 2 ( 0 , ∞ ) $f\in C[0,\infty )\cap C^{2}(0,\infty )$ satisfies f ( u ) > 0 $f(u)>0$ for u > 0 $u>0$ and f is either concave or geometrically concave on ( 0 , ∞ ) $(0,\infty )$ . If f is a concave function, we prove that the bifurcation curve is monotone increasing on the ( λ , ∥ u ∥ ∞ ) $(\lambda ,\left \Vert u\right \Vert _{\infty })$ -plane. If f is a geometrically concave function, we prove that the bifurcation curve is either ⊂-shaped or monotone increasing on the ( λ , ∥ u ∥ ∞ ) $(\lambda ,\left \Vert u\right \Vert _{\infty })$ -plane under a mild condition. Some interesting applications are given.

Abstract This paper deals with the following nonlinear elliptic equation: − Δ u = Q ( | y ′ | , y ″ ) u N + 2 N − 2 , u > 0 , in R N , u ∈ D 1 , 2 ( R N ) , $$ -\Delta u=Q(|y'|,y'')u^{\frac{N+2}{N-2}},\,\,u>0,\,\,\text{in}\,{ \mathbb{R}}^{N},\,\,u\in D^{1,2}({\mathbb{R}}^{N}), $$ where ( y ′ , y ″ ) ∈ R 2 × R N − 2 $(y',y'')\in {\mathbb{R}}^{2}\times {\mathbb{R}}^{N-2}$ , N ≥ 5 $N\geq 5$ , Q ( | y ′ | , y ″ ) $Q(|y'|,y'')$ is a bounded nonnegative function in R 2 × R N − 2 $\mathbb{R}^{2}\times {\mathbb{R}}^{N-2}$ . By using the local Pohozaev identities we prove a nondegeneracy result for the positive solutions constructed in (Peng et al. in J. Differ. Equ. 267:2503–2530, 2019).

Abstract This article is devoted to proving the uniqueness of positive solutions for p-Laplacian equations with Caputo and Riemann-Liouville fractional derivative. The uniqueness result and the dependence of the solution on a parameter are established based on the fixed point point theorem of mixed monotone operators. In the end, a numerical simulation is given to verify the main results.