Chaos analysis and traveling wave solutions for fractional (3+1)-dimensional Wazwaz Kaur Boussinesq equation with beta derivative.

Wazwaz Kaur Boussinesq (WKB) equation can effectively simulate the behavior of water waves in shallow water, including the nonlinear effect and dispersion phenomenon of waves, which is of great significance for understanding the dynamic process of ocean, river and other water bodies. To enrich the wave equation theory, the (3+1)-dimensional integer order derivative of WKB equation is changed to the fractional one with beta derivative. The current work deals with the fractional (3+1)-dimensional WKB equation for discussing its chaotic behavior and establishing some new analytic solutions. The chaotic properties of the equation are verified by the trend of evolution along with time, Lyapunov exponents and initial sensitivity analysis. And then complete discrimination system for polynomial method is applied to derive some trigonometric, hyperbolic, Jacobi elliptic and other solutions. The graphical demonstrations are provided for part of these solutions. From these visualized graphs, the solitary, periodic and quasi-periodic wave are shown and the effect of fractional derivatives on the equation can be seen intuitively.

Optimization of drug solubility inside the supercritical CO2 system via numerical simulation based on artificial intelligence approach.

In this research paper, we explored the predictive capabilities of three different models of Polynomial Regression (PR), Extreme Gradient Boosting (XGB), and LASSO to estimate the density of supercritical carbon dioxide (SC-CO2) and the solubility of niflumic acid as functions of the input variables of temperature and pressure. The optimization of hyperparameters for these models is achieved using the innovative Barnacles Mating Optimizer (BMO) algorithm. For SC-CO2 density estimation, PR exhibits remarkable accuracy, showing an R-squared value of 0.99207 for data fitting. XGB performs admirably with an R2 of 0.92673, while LASSO model demonstrates good predictive ability, showing an R2 of 0.81917. Furthermore, we assess the models' performance in predicting the solubility of niflumic acid. PR exhibits excellent predictive capabilities with an R2 of 0.96949. XGB also delivers strong performance, yielding an R-squared score of 0.92961. LASSO performs well, achieving an R-squared score of 0.82094. The results indicated promising performance of machine learning models and optimizer in estimating drug solubility in supercritical CO2 as the solvent applicable for pharmaceutical industry.

Leveraging Quadratic Polynomials in Python for Advanced Data Analysis.

This research explores the application of quadratic polynomials in Python for advanced data analysis. The study demonstrates how quadratic models can effectively capture nonlinear relationships in complex datasets by leveraging Python libraries such as NumPy, Matplotlib, scikit-learn, and Pandas. The methodology involves fitting quadratic polynomials to the data using least-squares regression and evaluating the model fit using the coefficient of determination (R-squared). The results highlight the strong performance of the quadratic polynomial fit, as evidenced by high R-squared values, indicating the model's ability to explain a substantial proportion of the data variability. Comparisons with linear and cubic models further underscore the quadratic model's balance between simplicity and precision for many practical applications. The study also acknowledges the limitations of quadratic polynomials and proposes future research directions to enhance their accuracy and efficiency for diverse data analysis tasks. This research bridges the gap between theoretical concepts and practical implementation, providing an accessible Python-based tool for leveraging quadratic polynomials in data analysis.

This study examines how quadratic polynomials, which are mathematical equations used to model and understand patterns in data, can be effectively applied using Python, a versatile programming language with libraries suited for mathematical and visual analysis. Researchers have focused on the adaptability of these polynomials in various fields, from software analytics to materials science, in order to provide practical Python code examples. They also discussed the predictive accuracy of the method, confirmed through a statistical measure called R-squared, and acknowledged the need for future research to integrate more complex models for richer data interpretation.

A Self-Attention Legendre Graph Convolution Network for Rotating Machinery Fault Diagnosis.

Rotating machinery is widely used in modern industrial systems, and its health status can directly impact the operation of the entire system. Timely and accurate diagnosis of rotating machinery faults is crucial for ensuring production safety, reducing economic losses, and improving efficiency. Traditional deep learning methods can only extract features from the vertices of the input data, thereby overlooking the information contained in the relationships between vertices. This paper proposes a Legendre graph convolutional network (LGCN) integrated with a self-attention graph pooling method, which is applied to fault diagnosis of rotating machinery. The SA-LGCN model converts vibration signals from Euclidean space into graph signals in non-Euclidean space, employing a fast local spectral filter based on Legendre polynomials and a self-attention graph pooling method, significantly improving the model's stability and computational efficiency. By applying the proposed method to 10 different planetary gearbox fault tasks, we verify that it offers significant advantages in fault diagnosis accuracy and load adaptability under various working conditions.

Kekulé Counts, Clar Numbers, and ZZ Polynomials for All Isomers of (5,6)-Fullerenes C52-C70.

We report an extensive tabulation of several important topological invariants for all the isomers of carbon (5,6)-fullerenes Cn with n = 52-70. The topological invariants (including Kekulé count, Clar count, and Clar number) are computed and reported in the form of the corresponding Zhang-Zhang (ZZ) polynomials. The ZZ polynomials appear to be distinct for each isomer cage, providing a unique label that allows for differentiation between various isomers. Several chemical applications of the computed invariants are reported. The results suggest rather weak correlation between the Kekulé count, Clar count, Clar number invariants, and isomer stability, calling into doubt the predictive power of these topological invariants in discriminating the most stable isomer of a given fullerene. The only exception is the Clar count/Kekulé count ratio, which seems to be the most important diagnostic discovered from our analysis. Stronger correlations are detected between Pauling bond orders computed from Kekulé structures (or Clar covers) and the corresponding equilibrium bond lengths determined from the optimized DFTB geometries of all 30,579 isomers of C20-C70.

Cost-effectiveness analysis of immune checkpoint inhibitors as first-line therapy in advanced biliary tract cancer.

Aim: To assess the cost-effectiveness of immune checkpoint inhibitors as first-line treatments for advanced biliary tract cancer (BTC).Methods: This pharmacoeconomic evaluation employed the fractional polynomial network meta-analysis and partitioned survival model. Costs and utilities were collected from the literature and databases. Sensitivity analyses were used to examine uncertainties.Results: The incremental cost-effectiveness ratios (ICERs) of first-line treatment strategies were $761,371.37 per quality-adjusted life-year (QALY) or $206,222.53/QALY in the US and $354,678.79 /QALY or $213,874.22/QALY in China, respectively. The sensitivity analysis results were largely consistent with the base case.Conclusion: From the US and Chinese payer perspectives, adding durvalumab or pembrolizumab to chemotherapy is unlikely to be cost effective in the first-line setting for advanced BTC.

[Box: see text].

On degree-based operators and topological descriptors of molecular graphs and their applications to QSPR analysis of carbon derivatives.

This work initiates a concept of reduced reverse degree based RR D M -Polynomial for a graph, and differential and integral operators by using this RR D M -Polynomial. In this study twelve reduced reverse degree-based topological descriptors are formulated using the RR D M -Polynomial. The topological descriptors, denoted as T D 's, are numerical invariants that offer significant insights into the molecular topology of a molecular graph. These descriptors are essential for conducting QSPR investigations and accurately estimating physicochemical attributes. The structural and algebraic characteristics of the graphene and graphdiyne are studied to apply this methodology. The study involves the analysis and estimation of Reduced reverse degree-based topological descriptors and physicochemical features of graphene derivatives using best-fit quadratic regression models. This work opens up new directions for scientists and researchers to pursue, taking them into new fields of study.

Polynomial-SHAP analysis of liver disease markers for capturing of complex feature interactions in machine learning models.

Liver disease diagnosis is pivotal for effective patient management, and machine learning techniques have shown promise in this domain. In this study, we investigate the impact of Polynomial-SHapley Additive exPlanations analysis on enhancing the performance and interpretability of machine learning models for liver disease classification. Our results demonstrate significant improvements in accuracy, precision, recall, F1_score, and Matthews correlation coefficient across various algorithms when polynomial- SHapley Additive exPlanations analysis is applied. Specifically, the Light Gradient Boosting Machine model achieves exceptional performance with 100 % accuracy in both scenarios. Furthermore, by comparing the results obtained with and without the approach, we observe substantial differences in the performance, highlighting the importance of incorporating Polynomial-SHapley Additive exPlanations analysis for improved model performance. The Polynomial features and SHapley Additive exPlanations values also enhance the interpretability of machine learning models by capturing complex feature interactions, enabling users to gain deeper insights into the underlying mechanisms driving the diagnosis. Moreover, data rebalancing using Synthetic Minority Over-sampling Technique and parameter tuning were employed to optimize the performance of the models. These findings underscore the significance of employing this analytical approach in machine-learning-based diagnostic systems for liver diseases, offering superior performance and enhanced interpretability for informed decision-making in clinical practice.

Spectral integrated neural networks (SINNs) for solving forward and inverse dynamic problems.

This study introduces an innovative neural network framework named spectral integrated neural networks (SINNs) to address both forward and inverse dynamic problems in three-dimensional space. In the SINNs, the spectral integration technique is utilized for temporal discretization, followed by the application of a fully connected neural network to solve the resulting partial differential equations in the spatial domain. Furthermore, the polynomial basis functions are employed to expand the unknown function, with the goal of improving the performance of SINNs in tackling inverse problems. The performance of the developed framework is evaluated through several dynamic benchmark examples encompassing linear and nonlinear heat conduction problems, linear and nonlinear wave propagation problems, inverse problem of heat conduction, and long-time heat conduction problem. The numerical results demonstrate that the SINNs can effectively and accurately solve forward and inverse problems involving heat conduction and wave propagation. Additionally, the SINNs provide precise and stable solutions for dynamic problems with extended time durations. Compared to commonly used physics-informed neural networks, the SINNs exhibit superior performance with enhanced convergence speed, computational accuracy, and efficiency.

Exploring physicochemical characteristics of cyclodextrin through M-polynomial indices.

Cyclodextrin, a potent anti-tumor medication utilized predominantly in ovarian and breast cancer treatments, encounters significant challenges such as poor solubility, potential side effects, and resistance from tumor cells. Combining cyclodextrin with biocompatible substrates offers a promising strategy to address these obstacles. Understanding the atomic structure and physicochemical properties of cyclodextrin and its derivatives is essential for enhancing drug solubility, modification, targeted delivery, and controlled release. In this study, we investigate the topological indices of cyclodextrin using algebraic polynomials, specifically the degree-based M-polynomial and neighbor degree-based M-polynomial. By computing degree-based and neighbor degree-based topological indices, we aim to elucidate the structural characteristics of cyclodextrin and provide insights into its physicochemical behavior. The computed indices serve as predictive tools for assessing the health benefits and therapeutic efficacy of cyclodextrin-based formulations. In addition, we examined that the computed indices showed a significant relationship with the physicochemical characteristics of antiviral drugs. Graphical representations of the computed results further facilitate the visualization and interpretation of cyclodextrin's molecular structure, aiding researchers in designing novel drug delivery systems with improved pharmacological properties.

Modeling the horizontal distribution of tree crown biomass from terrestrial laser scanning data.

Tree crown biomass is rarely assessed individually in forest monitoring, but when it is to be reported, standard conversion factors are commonly used for predicting crown biomass as a function of stem biomass. Further, in the conventional methods, the predicted total tree biomass is assigned exclusively to the stem position. In reality, however, tree and in particular crown biomass is spatially distributed over the entire crown projection area. In this study, we investigated the "Horizontal Biomass Distribution (HBD)" model, which serves to depict this biomass as a spatial distribution over the crown projection area: here, the individual tree crown biomass is modeled as a continuous distribution within the area defined by the crown projection. We examined two empirical HBD prediction models: (1) Weibull distribution; and (2) Segmented polynomial regression; which describe the biomass contained up to a given crown radius on the horizontal projection of individual trees, i.e., spatial distribution of crown biomass as a function of the horizontal distance from the stem. The approach was demonstrated using terrestrial laser scanning (TLS) on a sample of 33 urban trees from eight species. We found that (1) the segmented polynomial regression model revealed better performance in defining the HBD for various tree species; (2) a certain variability in HBD patterns was observed between the sample trees, with the variability being more pronounced between species groups than within species; and (3) the methodological approaches using TLS proxies are suitable and convenient to non-destructively assess the HBD, which would be otherwise impractical by direct measurements.

Operational stability study of lactate biosensors: modeling, parameter identification, and stability analysis.

Introduction: This paper investigates the operational stability of lactate biosensors, crucial devices in various biomedical and biotechnological applications. We detail the construction of an amperometric transducer tailored for lactate measurement and outline the experimental setup used for empirical validation. Methods: The modeling framework incorporates Brown and Michaelis-Menten kinetics, integrating both distributed and discrete delays to capture the intricate dynamics of lactate sensing. To ascertain model parameters, we propose a nonlinear optimization method, leveraging initial approximations from the Brown model's delay values for the subsequent model with discrete delays. Results: Stability analysis forms a cornerstone of our investigation, centering on linearization around equilibrium states and scrutinizing the real parts of quasi-polynomials. Notably, our findings reveal that the discrete delay model manifests marginal stability, occupying a delicate balance between asymptotic stability and instability. We introduce criteria for verifying marginal stability based on characteristic quasi-polynomial roots, offering practical insights into system behavior. Discussion: Qalitative examination of the model elucidates the influence of delay on dynamic behavior. We observe a transition from stable focus to limit cycle and period-doubling phenomena with increasing delay values, as evidenced by phase plots and bifurcation diagrams employing Poincaré sections. Additionally, we identify limitations in model applicability, notably the loss of solution positivity with growing delays, underscoring the necessity for cautious interpretation when employing delayed exponential function formulations. This comprehensive study provides valuable insights into the design and operational characteristics of lactate biosensors, offering a robust framework for understanding and optimizing their performance in diverse settings.

Variation of temperature increase rate in the Northern Hemisphere according to latitude, longitude and altitude: the Turkey example.

Global climate change notably influences meteorological variables such as temperature, affecting regions and countries worldwide. In this study, monthly average temperature data spanning 73 years (1950-2022) were analyzed for 28 stations in the city centers across seven regions of Turkey. The station warming rates (SWR) were calculated for selected stations and the overall country using Singular Spectrum Analysis (SSA) and Least Square Polynomial Fit (LSPF) methods. The temperature trend in Turkey exhibited a decline until the late 1970s, followed by a continuous rise due to global warming. Between 1980 and 2022, the average SWR in Turkey was found to be 0.52 °C/decade. The SWR was determined to be the lowest in Antakya (0.28 °C/decade) and the highest in Erzincan (0.69 °C/decade). The relationship between SWR and latitude, longitude, altitude, and distance to Null Island (D2NI) was explored through linear regression analysis. Altitude and D2NI were found to be the most significant variables, influencing the SWR. For altitude, the correlation coefficient (R) was 0.39 with a statistically significant value (p) of 0.039. For D2NI, R, and p values were 0.39 and 0.038, respectively. Furthermore, in the multiple regression analysis involving altitude and D2NI, R and p values were determined to be 0.50 and 0.029, respectively. Furthermore, the collinearity analysis indicates no collinearity between altitude and D2NI, suggesting that their effects are separated in the multiple regression.

A Method for Reducing Training Time of ML-Based Cascade Scheme for Large-Volume Data Analysis.

We live in the era of large data analysis, where processing vast datasets has become essential for uncovering valuable insights across various domains of our lives. Machine learning (ML) algorithms offer powerful tools for processing and analyzing this abundance of information. However, the considerable time and computational resources needed for training ML models pose significant challenges, especially within cascade schemes, due to the iterative nature of training algorithms, the complexity of feature extraction and transformation processes, and the large sizes of the datasets involved. This paper proposes a modification to the existing ML-based cascade scheme for analyzing large biomedical datasets by incorporating principal component analysis (PCA) at each level of the cascade. We selected the number of principal components to replace the initial inputs so that it ensured 95% variance retention. Furthermore, we enhanced the training and application algorithms and demonstrated the effectiveness of the modified cascade scheme through comparative analysis, which showcased a significant reduction in training time while improving the generalization properties of the method and the accuracy of the large data analysis. The improved enhanced generalization properties of the scheme stemmed from the reduction in nonsignificant independent attributes in the dataset, which further enhanced its performance in intelligent large data analysis.

Computation of differential and integral operators using M -polynomials of gold crystal.

Gold is generally considered a noble metal since it is inherently inert in its bulk state. However, gold demonstrates reactivity when it is in its ionic state. The inherent inertness of bulk gold has resulted in its widespread recognition as a vital raw material in various biomedical processes. The applications of these technologies include drug delivery microchips, dental prostheses, reconstructive surgery, culinary additives, and cardiovascular stents. Gold can also exist in molecules or ions, particularly gold ions, which facilitates the production of gold nanomaterials. In this paper, we have computed differential and integral operators by using the M -Polynomial of gold crystals and by utilizing this polynomial, we have also computed eleven topological indices like 1 s t Zagreb, 2 n d Zagreb, Hyper, Sigma, Second Modified, General Randic, General Reciprocal Randic, 3 r d Redefined Zagreb, Symmetric Division Degree, Harmonic, Inverse Sum indices for the structure of Gold crystal.

Manager-Team (Dis)agreement on Stress-Preventive Behaviours: Relationship with Psychosocial Work Environment and Employees' Well-Being.

The "Management Competencies to Prevent and Reduce Stress at Work" (MCPARS) approach focuses on identifying the stress-preventive managers' competencies able to optimise the employees' well-being through the management of the psychosocial work environment. Considering leadership as contextualised in complex social dynamics, the self-other agreement (SOA) investigation of the MCPARS may enhance previous findings, as it allows for exploring the manager-team perceptions' (dis)agreement and its potential implications. However, no studies have tested the MCPARS using the SOA and multisource data. Grounded in Yammarino and Atwater's SOA reference theory, we conducted an in-depth investigation on the MCPARS's theoretical framework by examining the implications of manager-team (dis)agreement, regarding managers' competencies, on employees' psychosocial environment (H1-H2) and affective well-being (H3). Data from 36 managers and 475 employees were analysed by performing several polynomial regressions, response surface, and mediation analyses. The results reveal a significant relationship between SOA on MCPARS and employees' perceptions of the psychosocial environment (H1). Employees report better perceptions when supervised by in-agreement good or under-estimator managers, while lower ratings occur under over-estimator or in-agreement poor managers (H2). Moreover, the psychosocial environment significantly mediated the relationship between SOA on MCPARS and employees' well-being (H3). The MCPARS theoretical model's soundness is supported, and its implications are discussed.

Stability and passivity analysis of delayed neural networks via an improved matrix-valued polynomial inequality.

The stability and passivity of delayed neural networks are addressed in this paper. A novel Lyapunov-Krasovskii functional (LKF) without multiple integrals is constructed. By using an improved matrix-valued polynomial inequality (MVPI), the previous constraint involving skew-symmetric matrices within the MVPI is removed. Then, the stability and passivity criteria for delayed neural networks that are less conservative than the existing ones are proposed. Finally, three examples are employed to demonstrate the meliority and feasibility of the obtained results.

Towards Design Optimization of Compliant Mechanisms: A Hybrid Pseudo-Rigid-Body Model-Finite Element Method Approach and an Accurate Empirical Compliance Equation for Circular Flexure Hinges.

Innovative designs such as morphing wings and terrain adaptive landing systems are examples of biomimicry and innovations inspired by nature, which are actively being investigated by aerospace designers. Morphing wing designs based on Variable Geometry Truss Manipulators (VGTMs) and articulated helicopter robotic landing gear (RLG) have drawn a great deal of attention from industry. Compliant mechanisms have become increasingly popular due to their advantages over conventional rigid-body systems, and the research team led by the second author at Toronto Metropolitan University (TMU) has set their long-term goal to be exploiting these systems in the above aerospace applications. To gain a deeper insight into the design and optimization of compliant mechanisms and their potential application as alternatives to VGTM and RLG systems, this study conducted a thorough analysis of the design of flexible hinges, and single-, four-, and multi-bar configurations as a part of more complex, flexible mechanisms. The investigation highlighted the flexibility and compliance of mechanisms incorporating circular flexure hinges (CFHs), showcasing their capacity to withstand forces and moments. Despite a discrepancy between the results obtained from previously published Pseudo-Rigid-Body Model (PRBM) equations and FEM-based analyses, the mechanisms exhibited predictable linear behavior and acceptable fatigue testing results, affirming their suitability for diverse applications. While including additional linkages perpendicular to the applied force direction in a compliant mechanism with N vertical linkages led to improved factors of safety, the associated increase in system weight necessitates careful consideration. It is shown herein that, in this case, adding one vertical bar increased the safety factor by 100N percent. The present study also addressed solutions for the precise modeling of CFHs through the derivation of an empirical polynomial torsional stiffness/compliance equation related to geometric dimensions and material properties. The effectiveness of the presented empirical polynomial compliance equation was validated against FEA results, revealing a generally accurate prediction with an average error of 1.74%. It is expected that the present investigation will open new avenues to higher precision in the design of CFHs, ensuring reliability and efficiency in various practical applications, and enhancing the optimization design of compliant mechanisms comprised of such hinges. A specific focus was put on ABS plastic and aluminum alloy 7075, as they are the materials of choice for non-load-bearing and load-bearing structural components, respectively.

Moisture Sorption Isotherms of Polydextrose and Its Gelling Efficiency in Inhibiting the Retrogradation of Rice Starch.

As an anti-staling agent in bread, the desorption isotherm of polydextrose has not been studied due to a very long equilibrium time. The adsorption and desorption isotherms of five Chinese polydextrose products were measured in the range of 0.1-0.9 aw and 20-35 °C by a dynamic moisture sorption analyzer. The results show that the shape of adsorption and desorption isotherms was similar to that of amorphous lactose. In the range of 0.1-0.8 aw, the hysteresis between desorption and adsorption of polydextrose was significant. The sorption isotherms of polydextrose can be fitted by seven commonly used models, and our developed seven-parameter polynomial, the adsorption equations of generalized D'Arcy and Watt (GDW) and Ferro-Fontan, and desorption equations of polynomial and Peleg, performed well in the range of 0.1-0.9 aw. The hysteresis curves of polydextrose at four temperatures quickly decreased with aw increase at aw ˂ 0.5, andthereafter slowly decreased when aw ≥ 0.5. The polynomial fitting hysteresis curves of polydextrose were divided into three regions: ˂0.2, 0.2-0.7, and 0.71-0.9 aw. The addition of 0-10% polydextrose to rice starch decreased the surface adsorption and bulk absorption during the adsorption and desorption of rice starch, while it increased the water adsorption value at aw ≥ 0.7 due to polydextrose dissolution. DSC analysis showed that polydextrose as a gelling agent inhibited the retrogradation of rice starch, which could be used to maintain the quality of cooked rice.

A probabilistic evaluation of the Dutch robustness and model-based selection protocols for Head-and-Neck IMPT: A multi-institutional study.

BACKGROUND AND PURPOSE: In the Netherlands, 2 protocols have been standardized for PT among the 3 proton centers: a robustness evaluation (RE) to ensure adequate CTV dose and a model-based selection (MBS) approach for IMPT patient-selection. This multi-institutional study investigates (i) inter-patient and inter-center variation of target dose from the RE protocol and (ii) the robustness of the MBS protocol against treatment errors for a cohort of head-and-neck cancer (HNC) patients treated in the 3 Dutch proton centers. MATERIALS AND METHODS: Clinical treatment plans of 100 HNC patients were evaluated. Polynomial Chaos Expansion (PCE) was used to perform a comprehensive robustness evaluation per plan, enabling the probabilistic evaluation of 100,000 complete fractionated treatments. PCE allowed to derive scenario distributions of clinically relevant dosimetric parameters to assess CTV dose (D99.8%/D0.2%, based on a prior photon plan calibration) and tumour control probabilities (TCP) as well as the evaluation of the dose to OARs and normal tissue complication probabilities (NTCP) per center. RESULTS: For the CTV70.00, doses from the RE protocol were consistent with the clinical plan evaluation metrics used in the 3 centers. For the CTV54.25, D99.8% were consistent with the clinical plan evaluation metrics at center 1 and 2 while, for center 3, a reduction of 1 GyRBE was found on average. This difference did not impact modelled TCP at center 3. Differences between expected and nominal NTCP were below 0.3 percentage point for most patients. CONCLUSION: The standardization of the RE and MBS protocol lead to comparable results in terms of TCP and the NTCPs. Still, significant inter-patient and inter-center variation in dosimetric parameters remained due to clinical practice differences at each institution. The MBS approach is a robust protocol to qualify patients for PT.