Chain Equation Research Articles

Time fractional (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation: its Lie symmetries, exact solutions and conservation laws

Abstract In this paper, Lie symmetry analysis method is applied to (2+1)-dimensional time-fractional Heisenberg ferromagnetic spin chain equation. We obtain all the Lie symmetries admitted by the governing equation and reduce the corresponding (2+1)-dimensional fractional partial differential equations with Riemann-Liouville fractional derivative to (1+1)-dimensional counterparts with Erd'{e}lyi-Kober fractional derivative. Then we obtain the power series solutions of the reduced equations, prove their convergence and analyze their dynamic behavior graphically. In addition, the conservation laws for all the obtained Lie symmetries are constructed by the new conservation theorem and the generalization of Noether operators.

Evaluation of the cross sections and photoelectron angular distribution parameters following atomic photoionization under extreme conditions

In this manuscript, we report on a theoretical study of the atomic structures, cross sections, and photoelectron angular distribution parameters following the atomic photoionization under extreme conditions. To achieve this goal, a relativistic approach using the Dirac-Coulomb Hamiltonian within the framework of relativistic configuration interaction, taking advantage of independent particle basis wave functions, is proposed. To describe the interaction of charged particles in the ideal and non-ideal plasmas, the Debye potential and the pseudopotential are implemented, the latter being derived from a progressive resolution of the Bogolyubov chain equations. Both bound and continuous state wave functions, essential for a comprehensive understanding of quantum systems, are determined from the modified local central potential, which is obtained in a self-consistent manner to represent the electronic shielding effect on the nuclear potential. The photoionization processes are evaluated using the relativistic distorted wave approach, which is consistent with the principles of relativistic Dirac theory and thus provides an accurate description of the dynamics. As a test desk, the present method is applied to the evaluation of the energies, ionization potentials, wave functions, cross sections, and photoelectron angular distribution parameters, using the single photon ionization of the Li-like Fe XXIV ions as the basis for analysis. Our results demonstrate that the plasma environment effect not only decreases the ionization potentials and increases the cross sections but also affects the photoelectron angular distribution parameters across different shells, leading to a more balanced and symmetrical photoelectron distribution pattern. A detailed comparison is made between our results, and the available well-established theoretical predictions and experimental data of the unshielded case in the literature shows a good agreement. The present work provides novel insights and theoretical models that not only help us to better understand the fundamental properties of the complex systems but are also beneficial for innovative applications in the study of astrophysical and laboratory plasmas.

309. COMPARATIVE OUTCOMES OF OPEN VS. MINIMALLY INVASIVE ESOPHAGECTOMY FOR ESOPHAGEAL AND GASTRO-ESOPHAGEAL JUNCTION TUMORS: INSIGHTS FROM A THORACO-ABDOMINAL STRATIFICATION MODEL

Abstract Background Minimally invasive esophagectomy (MIE) has demonstrated improved outcomes for fit patients with esophageal/gastro-esophageal junction tumors. However, challenges arise in patients less tolerant of prolonged anesthesia or harboring extensive advanced-stage tumors, which limit the utilization of MIE, increasing the risk of referral to nonsurgical strategies. To date, the criteria for considering left thoraco-abdominal esophagectomy (TAE) and the corresponding outcomes in this specific patient population remain unclear. Therefore, our institutional study aimed to identify clinical characteristics for the consideration of TAE, offering insights into treatment selection strategies for esophageal cancer patients. Additionally, we compared the short-term outcomes between TAE and MIE. Methods We included all consecutive patients who underwent esophagectomy with gastric conduit reconstruction for stage I-IVa esophageal and gastro-esophageal junction tumors at a tertiary referral center from 2015 to 2023. Predictors for considering TAE were identified through a multivariable regression model utilizing multivariate imputation by chain equation for missing data of pulmonary and cardiac function, using the predicted mean matching method. Significant variables were used to develop a stratification model, evaluated through the receiver-operating curve. Differences in outcome were assessed using the Kruskal-Wallis rank sum for continuous and Pearson’s chi-squared or Fischer’s exact test for categorical variables. Results This study included 744 patients; 317 (43%) underwent TAE and 427 (57%) had MIE. Patient characteristics were significantly different. Following multivariable analysis, age (1.04 [1.02-1.06]; p<0.001), ECOG-status (1.43 [1.09-1.87]; p=0.009), comorbidity index (1.26 [1.10-1.46]; p<0.001), DLCO (0.98 [0.97-0.99]; p<0.001), ejection fraction (0.97 [0.94-1.00]; p=0.021), tumor location (GEJ: 1.58 [1.10-2.27], Middle: 0.38 [0.18-0.79]; p<0.001), cStage (II: 2.03 [1.02-4.19], III: 3.29 [1.78-6.33], IVa: 3.42 [1.74-6.97]; p<0.001) and adenocarcinoma (2.44 [1.39-4.55]; p=0.002) were identified as predictors for TAE. The stratification model demonstrated an area-under-the-curve of 0.76 [0.73-0.80]. Leave-one-out-cross-validation demonstrated a 70% accuracy. The short-term outcomes were comparable between TAE and MIE (Table 1). Conclusion Our study demonstrated that age, ECOG status, comorbidity index, diffusion capacity, ejection fraction, tumor location, stage and histology were independent predictors for the consideration of thoraco-abdominal esophagectomy. In this context, our stratification model demonstrated a robust predictive value. Moreover, our model suggests considering MIE below a probability threshold of 30% and TAE above 60%, demonstrating an 85% sensitivity and 90% specificity at these thresholds, respectively. Decisions within the 30% to 60% range should be individualized and based on specific patient and tumor characteristics. Short-term outcomes were comparable between TAE and MIE, emphasizing the significance of adequate stratification before surgery.

Pioneering the plethora of soliton for the (3+1)-dimensional fractional heisenberg ferromagnetic spin chain equation

Abstract In this scholarly article, we investigate the complex structured (3+1)-dimensional Fractional Heisenberg Ferromagnetic Spin Chain equation (FHFSCE) with conformable fractional derivatives. We develop a diverse glut of soliton solutions using an improved version of the G ′ G -expansion method, namely the r + G ′ G -expansion method. The constraints for the existence of these solutions are painstakingly explained. Our findings are clearly communicated through a number of 3D and 2D graphical representations displaying periodic, multiple periodic, kink, and shock soliton solutions. These soliton solutions are expressed in several mathematical function forms, such as hyperbolic, trigonometric, and rational functions. Our findings support the suggested method’s efficacy as a powerful symbolic algorithm for discovering innovative soliton solutions within nonlinear evolution systems.

Forecasting potential invaders to prevent future biological invasions worldwide.

The ever-increasing and expanding globalisation of trade and transport underpins the escalating global problem of biological invasions. Developing biosecurity infrastructures is crucial to anticipate and prevent the transport and introduction of invasive alien species. Still, robust and defensible forecasts of potential invaders are rare, especially for species without known invasion history. Here, we aim to support decision-making by developing a quantitative invasion risk assessment tool based on invasion syndromes (i.e., generalising typical attributes of invasive alien species). We implemented a workflow based on 'Multiple Imputation with Chain Equation' to estimate invasion syndromes from imputed datasets of species' life-history and ecological traits and macroecological patterns. Importantly, our models disentangle the factors explaining (i) transport and introduction and (ii) establishment. We showcase our tool by modelling the invasion syndromes of 466 amphibians and reptile species with invasion history. Then, we project these models to amphibians and reptiles worldwide (16,236 species [c.76% global coverage]) to identify species with a risk of being unintentionally transported and introduced, and risk of establishing alien populations. Our invasion syndrome models showed high predictive accuracy with a good balance between specificity and generality. Unintentionally transported and introduced species tend to be common and thrive well in human-disturbed habitats. In contrast, those with established alien populations tend to be large-sized, are habitat generalists, thrive well in human-disturbed habitats, and have large native geographic ranges. We forecast that 160 amphibians and reptiles without known invasion history could be unintentionally transported and introduced in the future. Among them, 57 species have a high risk of establishing alien populations. Our reliable, reproducible, transferable, statistically robust and scientifically defensible quantitative invasion risk assessment tool is a significant new addition to the suite of decision-support tools needed for developing a future-proof preventative biosecurity globally.

Analytical solutions and soliton behaviors in the space fractional Heisenberg ferromagnetic spin chain equation

This study investigates soliton solutions to the (2 + 1)-dimensional space fractional Heisenberg ferromagnetic spin chain equation incorporating beta fractional derivatives that explain the nonlinear propagation of spin wave in the ferromagnetic material with magnetic interactions including the both classical and semi-classical frameworks. This model has applications in spintronics, plasma physics, magnet theory, and condensed matter physics. Employing the two-potential extended Kudryashov and (G′/G, 1/G)-expansion methods, we derive some original and generic solutions composed of trigonometric functions, hyperbolic functions, and their rational forms. For particular values of the parameters, these solutions offer V-shaped, bell-shaped, kink, periodic, flat kink, and singular periodic solitons. The physical behavior of these solitons is demonstrated through three-dimensional, contour, and two-dimensional plots. The results are important in the study of phase transitions in ferromagnetic materials, lattice vibrations in condensed matter, and the propagation of shock waves in plasma. This study also demonstrates the potential and reliability of the employed strategies.

Abstract 3429: Using metabolomics to identify biomarkers mediating the associations of adiposity in childhood and early adulthood with mammographic breast density in premenopausal women

Abstract Introduction: Mammographic breast density (MBD), a strong predictor of breast cancer risk, is highly influenced by body mass index (BMI) in childhood and early adulthood, but the mechanisms elucidating this relationship are undetermined. To our knowledge, no study has explored the mediating role of biomarkers on the relationship between early-life adiposity and MBD. The goal of this study is to discover metabolites that mediate the relationship between BMI at ages 10 and 18 with MBD in premenopausal women. Methods: This study includes premenopausal women who had their screening mammogram at Washington University in St. Louis, MO, and provided a fasting blood sample. Metabolon performed untargeted metabolomic profiling, detecting 1,074 metabolites. Metabolites missing >300 observations were excluded, leaving 828 metabolites; the other missing values were imputed using the nearest neighbor method. To mitigate batch effect, we normalized the metabolite peak area data using ComBat. Volumetric percent density (VPD) was calculated in 700 women using Volpara software. BMI at age 10 was estimated using the Stunkard pictogram, and BMI at age 18 was calculated from self-reported weight at 18 and height at study initiation. To assess the mediating role of the 828 metabolites, we performed high dimensional mediation analysis using the hima R package adjusting for potential confounders. Missing values in the covariates and BMI measures included in the mediation analysis were imputed using multivariate imputation by chain equations. Associations were considered significant if FDR p-value <0.1. Results: Four metabolites (glutamate, beta-cryptoxanthin, phytanate, and cortolone glucuronide (1)) mediated the relationship between BMI at age 10 and VPD; and 2 metabolites (glutamate, beta-cryptoxanthin) mediated the relationship between BMI at age 18 and VPD. Glutamate and beta-cryptoxanthin significantly mediated the relationship between both BMI measures and VPD, but glutamate was the strongest mediator across both time points. Glutamate mediated 6.7% (FDR p-value=0.06) and 9.3% (FDR p-value=0.008) of the total effect between BMI at age 10 and 18, respectively, on VPD. Beta-cryptoxanthin mediated 4.1% (FDR p-value=0.06) and 6.3% (FDR p-value=0.04), of the total effect between BMI at age 10 and 18, respectively, on VPD. Additionally, phytanate mediated 2.6% (FDR p-value=0.06) and cortolone glucuronide (1) mediated 2.0% (FDR p-value=0.07) of the total effect between BMI at age 10 and VPD. Conclusion: Amino acid, lipid, cofactor/vitamin, and xenobiotic metabolites mediated the associations of BMI in early-life and VPD in premenopausal women. This innovative study offers insight into the biological mechanisms underlying the link between early-life adiposity and MBD, which can support future research into breast cancer prevention. Citation Format: Kayla R. Getz, Myung Sik Jeon, Lili Liu, Lei Liu, Chongliang Luo, Jingqin Luo, Adetunji T. Toriola. Using metabolomics to identify biomarkers mediating the associations of adiposity in childhood and early adulthood with mammographic breast density in premenopausal women [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 3429.

Rogue wave excitations and hybrid wave structures of the Heisenberg ferromagnet equation with time-dependent inhomogeneous bilinear interaction and spin-transfer torque.

In this paper, we focus on the localized rational waves of the variable-coefficient Heisenberg spin chain equation, which models the local magnetization in ferromagnet with time-dependent inhomogeneous bilinear interaction and spin-transfer torque. First, we establish the iterative generalized (m,N-m)-fold Darboux transformation of the Heisenberg spin chain equation. Then, the novel localized rational solutions (LRSs), rogue waves (RWs), periodic waves, and hybrid wave structures on the periodic, zero, and nonzero constant backgrounds with the time-dependent coefficients α(t) and β(t) are obtained explicitly. Additionally, we provide the trajectory curves of magnetization and the variation of the magnetization direction for the obtained nonlinear waves at different times. These phenomena imply that the LRSs and RWs play the crucial roles in changing the circular motion of the magnetization. Finally, we also numerically simulate the wave propagations of some localized semi-rational solutions and RWs.

Using Diverse Data Sources to Impute Missing Air Quality Data Collected in a Resource-Limited Setting

The sustainable operation of ambient air quality monitoring stations in developing countries is not always possible. Intermittent failures and breakdowns at air quality monitoring stations often affect the continuous measurement of data as required. These failures and breakdowns result in missing data. This study aimed to impute NO2, SO2, O3, and PM 10 to produce complete data sets of daily average exposures from 2010 to 2017. Models were built for (a) an individual pollutant at a monitoring station, (b) a combined model for the same pollutant from different stations, and (c) a data set with all the pollutants from all the monitoring stations. This study sought to evaluate the efficacy of the Multiple Imputation by Chain Equations (MICE) algorithm in successfully imputing air quality data that are missing at random. The application of classification and regression trees (CART) analysis using the MICE package in the R statistical programming language was compared with the predictive mean matching (PMM) method. The CART method performed better, with the pooled R-squared statistics of the imputed data ranging from 0.3 to 0.7, compared to a range of 0.02 to 0.25 for PMM. The MICE algorithm successfully resolved the incompleteness of the data. It was concluded that the CART method produced better reliable data than the PMM method. However, in this study, the pooled R2 values were accurate for NO2, but not so much for other pollutants.

Prediction of azeotropes position of refrigerant mixtures using the PHSC EoS

The work aims is predict the azeotropes' position in refrigerant mixtures using the Perturbed Hard Sphere Chain (PHSC) equation of state (EoS). The vapor-liquid equilibrium (VLE) of seventeen binary refrigerant mixtures has been correlated using two model-adjustable parameters. The results show that the proposed model can calculate the bubble and dew points of binary systems, accurately. The average ARD value of binary VLE calculations has been obtained 1.28 %. The azeotropes pressure and composition of binary mixtures have been predicted using the PHSC EoS with the average ARD values of 1.043 % and 2.23 %, respectively. The maximum relative deviation has been observed for R717+R125 systems with two azeotropes points; ARDx=12.2 %. The performance of the PHSC EoS has been evaluated by predicting the azeotropes position of ternary mixtures. The PHSC EoS results have been compared to three cubic-based EoSs containing the PR-vdW, PR-BM, and PR-MHV2-NRTL models. The results show that the PHSC EoS can predict the ternary VLE data and azeotropes position satisfactory. The relative absolute deviation does not exceed 1.7 % for the azeotropes pressure. The PHSC EoS can be used as a robust and efficient model for the prediction of the azeotropes' position in binary and ternary refrigerant mixtures. Prediction of azeotropic composition helps us to find promising refrigerant candidates in the pre-design stage of the desired apparatus.

Analytical approaches to the (2+1)-dimensional Heisenberg Ferromagnetic Spin Chain equation and their applications for optical devices

Analytical approaches to the (2+1)-dimensional Heisenberg Ferromagnetic Spin Chain equation and their applications for optical devices

Dubrovin method and the Toda chain

A hierarchy of Lax pairs with 2 × 2 2\times 2 matrix coefficients is presented. The compatibility conditions for these pairs include the Toda chain equation, and other differential-difference integrable systems. Various kinds of finite gap solutions for such systems are constructed. Examples of simplest one- and two-phase solutions are given, together with the corresponding spectral curves.

Exact solutions, symmetry groups and conservation laws for some (2+1)-dimensional nonlinear physical models

In this paper, the Bernoulli sub-equation function method is used to construct new exact travelling wave solutions for two important physical models: (2+1)-dimensional hyperbolic nonlinear Schrödinger (HNLS) equation and (2+1)-dimensional Heisenberg ferromagnetic spin chain (HFSC) equation. These solutions provide valuable insights into the behavior of these models, described in terms of exponential and hyperbolic tangent (tanh) functions. The study also involves an exploration of the infinitesimal generators and symmetry groups through the Lie symmetry method. In addition, by using multiplier approach, the conservation laws are established for these models. Graphical simulation of some solutions in the form of two-dimensional and three-dimensional are plotted to understanding of the underlying physical phenomena and mathematical properties of the (2+1)-dimensional HNLS and HFSC equations. The solutions and graphing are performed using Maple software.

FaceNet recognition algorithm subject to multiple constraints: Assessment of the performance

Literature has it that the performance of most face recognition algorithms still decline in multiple constrained environments (Occlusions and Expressions), despite the achieved successes of deep learning face recognition algorithms. Using expression variant test face images synthetically occluded at 30% and 40% rates, the study evaluated the performance of FaceNet deep learning model for face recognition under the aforementioned constraints and when three (3) statistical multiple imputation methods (Multivariable Imputation using Chain Equations (MICE), MissForest and Regularized Expectation Maximization (RegEM)) are adopted for occlusion recovery. Results of the study showed improved recognition rates of the study algorithm when the imputation-based recovered faces were used for recognition compared with using their multiple constrained counterparts. However, test faces reconstructed with the MissForest imputation method were more accurately recognized using the FaceNet deep learning algorithm. Furthermore, the study demonstrated that some simple augmentation schemes sufficed to further enhance the performance of the FaceNet model. Specifically, the FaceNet algorithms gave the highest average recognition rates (85.19% and 79.5% for 30% and 40% occlusion levels respectively) under augmentation scheme IV (slight rotations, horizontal flipping, shearing, brightness adjustments, and stretching) using MissForest as the de-occlusion mechanism. The study also found that, no disparity existed in its performance with the choice of either Support Vector Machines (SVM) or City Block (CB) for classification under augmentation scheme IV. The study recommends using the MissForest imputation method in dealing with moderately high occluded test faces with varying expressions to enhance the performance of the FaceNet face recognition model.

Predicting micropapillary or solid pattern of lung adenocarcinoma with CT-based radiomics, conventional radiographic and clinical features

BackgroundTo build prediction models with radiomics features, clinical/conventional radiographic signs and combined scores for the discrimination of micropapillary or solid subtypes (high-risk subtypes) of lung adenocarcinoma.MethodsThis retrospective study enrolled 351 patients with and without high-risk subtypes. Least Absolute Shrinkage and Selection Operator (LASSO) regression with cross-validation was performed to determine the optimal features of radiomics model. Missing clinical data were imputed by Multiple Imputation with Chain Equations (MICE). Clinical model with radiographic signs was built and scores of both models were integrated to establish combined model. Receiver operating characteristics (ROC) curves, area under ROC curves and decision curve analysis (DCA) were plotted to evaluate the model performance and clinical application.ResultsStratified splitting allocated 246 patients into training set. MICE for missing values obtained complete and unbiased data for the following analysis. Ninety radiomic features and four clinical/conventional radiographic signs were used to predict the high-risk subtypes. The radiomic model, clinical model and combined model achieved AUCs of 0.863 (95%CI: 0.817–0.909), 0.771 (95%CI: 0.713–0.713) and 0.872 (95%CI: 0.829–0.916) in the training set, and 0.849 (95%CI: 0.774–0.924), 0.778 (95%CI: 0.687–0.868) and 0.853 (95%CI: 0.782–0.925) in the test set. Decision curve showed that the radiomic and combined models were more clinically useful when the threshold reached 37.5%.ConclusionsRadiomics features could facilitate the prediction of subtypes of lung adenocarcinoma. A simple combination of radiomics and clinical scores generated a robust model with high performance for the discrimination of micropapillary or solid subtype of lung adenocarcinoma.

A Predictive Score Based on Cytokines, CD4/CD8 Ratio and Age Predicts Hematological Neoplasm-Associated Hemophagocytic Lymphohistiocytosis (H-HLH)

Introduction Early diagnostic of Hematological neoplasm (H)-associated hemophagocytic lymphohistiocytosis (H-HLH) is a major goal in the management of adult (sporadic) HLH (HLHa) to allow appropriate and early intervention and reduce the risk of fatal outcome. At diagnosis, it is often difficult to distinguish H-HLH from other associated diseases autoimmune/inflammatory (MAS/AID), infectious like leishmaniosis or idiopathic forms. Here we have developed a predictive score for H-HLH that is based on clinical parameters and cytokines levels. Methods Serum levels of thirty cytokines were analysed by Elisa or by Luminex Technology, in 112 patients (age≥18 years old and “HScore”≥169) of the French HLH cohort data base (clinicaltrials.gov number NCT02113917). Multiple imputation chain equation was performed to account for the missingness in covariates. All following analyses were carried out based on the imputed datasets by combining estimates from each completed dataset using Rubin's rules. A logistic regression was used to develop and validate the risk score predicting H-HLH. Model calibration and discrimination were assessed using the Hosmer-Lemeshow and receiver operating characteristic (ROC) curves, respectively. A 10-fold cross-validation was carried out to consider overfitting bias. Risk scores were derived using the model parameters and individual covariates values. A threshold on the risk score was determined to maximize the Youden index (sensitivity+specificity-1). H-HLH high-risk and low-risk patients were then delineated according to this score threshold, respectively, defining an high and low risk H-HLH group (score ≥ or < threshold). Results The cohort (112 patients) included 45 H-HLH and 67 AID or idiopathic HLHa. Malignancies were distributed as Hodgkin Lymphoma (HL) (n=3), B cell-Non Hodgkin Lymphoma (NHL) (n=22, (EBV+, n=9)), and T cell-NHL (n=13 (EBV+, n=7)). The median [IQR] age of patients in the cohort was 48 years [36-61] old and 64 (57%) were men. From twenty-one potential predictors (including 9 HLH-related cytokines), eight were associated with H-HLH in univariate logistic regression: age > 48y (p<0.004), hemoglobin > 9g/l (p=0.03), platelets > 82G/l (p=0.03), Il-10 > 42 pg/mL (p=0.0003), TNF-α>43 pg/mL (p=0.0006), IL-18>574 pg/mL (p=0.0002), lymphocytes CD4/CD8 >1 (p=0.03), and five, independent in a multivariate analysis, were included in the risk score : age > 48y (OR [95%CI]: 3.0 [1.1 - 8.3], p=0.03), Il-10 > 42 pg/mL (OR [95%CI]: 4.5 [1.4-14.6], p=0.01), TNF-α>43 pg/mL (OR [95%CI]: 0.2 [0.07-0.57] ,p=0.003), IL-18>574 pg/mL (OR [95%CI]: 3.1[1.0-9.5], p=0.04) and lymphocytes CD4/CD8 >1 (OR [95%CI]: 0.3 [0.1-1.0], p=0.04). The score ranged from -28 and 37 with an attribution of points of 11 for age>48, 15 for Il-10 > 42, -16 for TNF-α > 43, 11 for Il-18 > 574 and -12 for CD4/CD8 > 1. The mean AUC in the cohort was 0.87 (95%CI, 0.79-0.92) and the AUC in the internal validation was 0.82 (95%CI, 0.61-1.00). The goodness-of-fit test showed a p-value of 0.30. The logistic model demonstrated that patients with a score ≥ 6 (sensitivity [95%CI]: 0.80 [0.65-0.90] and specificity [95%CI]: 0.75 [0.63-0.85] at the threshold of 6), the risk of having H-HLH increases by a factor of 12 compared to patients with a score < 6. (OR [95% CI] = 12 [4.7-29.7], p < 0.0001). Conclusion In this cohort, a risk score based on five parameters (age, IL10, TNF-a, IL-18, lymphocytes CD4/CD8) was developed that may help predict a patient's risk to have H-HLH.

-dressing method for the complex modified KdV equation

The dressing method based on the 2 × 2 matrix -problem is generalized to study the complex modified KdV equation (cmKdV). Through two linear constraint equations, the spatial and time spectral problems related to the cmKdV equation are derived. The gauge equivalence between the cmKdV equation and the Heisenberg chain equation is obtained. Using a recursive operator, a hierarchy of cmKdV with source is proposed. On the basis of the -equation, the N-solition solutions of the cmKdV equation are obtained by selecting the appropriate spectral transformation matrix. Furthermore, we get explicit one-soliton and two-soliton solutions.

The solitary wave solutions of the stochastic Heisenberg ferromagnetic spin chain equation using two different analytical methods

Here, we consider the stochastic (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation which is forced by the multiplicative Brownian motion in the Stratonovich sense. We utilize the (G′/G)-expansion method and the mapping method to attain the analytical solutions of the stochastic (2 + 1)-dimensional Heisenberg ferromagnetic chain equation. Various types of analytical stochastic solutions, such as the hyperbolic, elliptic, and trigonometric functions, have been obtained. Physicists can utilize these solutions to understand a variety of important physical phenomena because the magnetic soliton has been categorized as one of the interesting groups of nonlinear excitations representing spin dynamics in the semiclassical continuum Heisenberg systems. Moreover, we employ MATLAB tools to plot 3D and 2D graphs for some obtained solutions to address the influence of Brownian motion on these solutions.

Exploring lump soliton solutions and wave interactions using new Inverse $$(G'/G)$$-expansion approach: applications to the (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation

Exploring lump soliton solutions and wave interactions using new Inverse $$(G'/G)$$-expansion approach: applications to the (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation

Fermi LAT AGN classification using supervised machine learning

ABSTRACT Classifying active galactic nuclei (AGNs) is a challenge, especially for BL Lacertae objects (BLLs), which are identified by their weak emission line spectra. To address the problem of classification, we use data from the fourth Fermi Catalog, Data Release 3. Missing data hinder the use of machine learning to classify AGNs. A previous paper found that Multivariate Imputation by Chain Equations (MICE) imputation is useful for estimating missing values. Since many AGNs have missing redshift and the highest energy, we use data imputation with MICE and k-nearest neighbours (kNN) algorithm to fill in these missing variables. Then, we classify AGNs into the BLLs or the flat spectrum radio quasars (FSRQs) using the SuperLearner, an ensemble method that includes several classification algorithms like logistic regression, support vector classifiers, Random Forest, Ranger Random Forest, multivariate adaptive regression spline (MARS), Bayesian regression, and extreme gradient boosting. We find that a SuperLearner model using MARS regression and Random Forest algorithms is 91.1 per cent accurate for kNN-imputed data and 91.2 per cent for MICE-imputed data. Furthermore, the kNN-imputed SuperLearner model predicts that 892 of the 1519 unclassified blazars are BLLs and 627 are FSRQs, while the MICE-imputed SuperLearner model predicts 890 BLLs and 629 FSRQs in the unclassified set. Thus, we can conclude that both imputation methods work efficiently and with high accuracy and that our methodology ushers the way for using SuperLearner as a novel classification method in the AGN community and, in general, in the astrophysics community.