Advanced stability analysis of a fractional delay differential system with stochastic phenomena using spectral collocation method.

In recent years, there has been a growing interest in incorporating fractional calculus into stochastic delay systems due to its ability to model complex phenomena with uncertainties and memory effects. The fractional stochastic delay differential equations are conventional in modeling such complex dynamical systems around various applied fields. The present study addresses a novel spectral approach to demonstrate the stability behavior and numerical solution of the systems characterized by stochasticity along with fractional derivatives and time delay. By bridging the gap between fractional calculus, stochastic processes, and spectral analysis, this work contributes to the field of fractional dynamics and enriches the toolbox of analytical tools available for investigating the stability of systems with delays and uncertainties. To illustrate the practical implications and validate the theoretical findings of our approach, some numerical simulations are presented.

A novel simulation-based analysis of a stochastic HIV model with the time delay using high order spectral collocation technique.

The economic impact of Human Immunodeficiency Virus (HIV) goes beyond individual levels and it has a significant influence on communities and nations worldwide. Studying the transmission patterns in HIV dynamics is crucial for understanding the tracking behavior and informing policymakers about the possible control of this viral infection. Various approaches have been adopted to explore how the virus interacts with the immune system. Models involving differential equations with delays have become prevalent across various scientific and technical domains over the past few decades. In this study, we present a novel mathematical model comprising a system of delay differential equations to describe the dynamics of intramural HIV infection. The model characterizes three distinct cell sub-populations and the HIV virus. By incorporating time delay between the viral entry into target cells and the subsequent production of new virions, our model provides a comprehensive understanding of the infection process. Our study focuses on investigating the stability of two crucial equilibrium states the infection-free and endemic equilibriums. To analyze the infection-free equilibrium, we utilize the LaSalle invariance principle. Further, we prove that if reproduction is less than unity, the disease free equilibrium is locally and globally asymptotically stable. To ensure numerical accuracy and preservation of essential properties from the continuous mathematical model, we use a spectral scheme having a higher-order accuracy. This scheme effectively captures the underlying dynamics and enables efficient numerical simulations.

Machine learning based detection of T-wave alternans in real ambulatory conditions.

BACKGROUND AND OBJECTIVE: T-wave alternans (TWA) is a fluctuation in the repolarization morphology of the ECG. It is associated with cardiac instability and sudden cardiac death risk. Diverse methods have been proposed for TWA analysis. However, TWA detection in ambulatory settings remains a challenge due to the absence of standardized evaluation metrics and detection thresholds. METHODS: In this work we use traditional TWA analysis signal processing-based methods for feature extraction, and two machine learning (ML) methods, namely, K-nearest-neighbor (KNN) and random forest (RF), for TWA detection, addressing hyper-parameter tuning and feature selection. The final goal is the detection in ambulatory recordings of short, non-sustained and sparse TWA events. RESULTS: We train ML methods to detect a wide variety of alternant voltage from 20 to 100 µV, i.e., ranging from non-visible micro-alternans to TWA of higher amplitudes, to recognize a wide range in concordance to risk stratification. In classification, RF outperforms significantly the recall in comparison with the signal processing methods, at the expense of a small lost in precision. Despite ambulatory detection stands for an imbalanced category context, the trained ML systems always outperform signal processing methods. CONCLUSIONS: We propose a comprehensive integration of multiple variables inspired by TWA signal processing methods to fed learning-based methods. ML models consistently outperform the best signal processing methods, yielding superior recall scores.

Cross-diffusive flow of MHD micropolar nanofluid past a slip stretching plate.

As a novel fluid of functional material, magnetohydrodynamic (MHD) micropolar fluid has the special properties of light, heat, magnetic and so on. It is of highly practical significance. The characteristics of flow, heat and mass transfer in MHD micropolar nanofluid boundary layer past a stretching plate are investigated based on the micropolar fluid theory in the present numerical work. In the presence of magnetic field, viscous dissipation and the cross-diffusion caused by Dufour effect and Soret effect are considered. First order slip velocity condition is employed. Mathematical models are built based on the assumptions. Collocation spectral method (CSM) via matrix multiplication is adopted to solve the two-dimensional dimensionless nonlinear partial governing equations. The program codes based on CSM is developed, validated and employed. The coupled effects of microrotation, Dufour effect, Soret effect, magnetic field as well as first order slip velocity boundary condition on the flow, heat and mass transfer are revealed. Besides, the variation trends of local Nusselt number and Sherwood number are analyzed in detail. The numerical results indicate that the fluid flow can be suppressed obviously in the consideration n of slip condition and magnetic field. As slip parameter δ and magnetic parameter M rise, the velocity in the boundary layer becomes lower gradually; further, both temperature and concentration increase. On the other hand, the opposite trend can be noticed with the effect of material parameter K. Moreover, Ec and Df augment the temperature; while, Sr leads to an upsurge in concentration. The temperature rises by about 79.73% with Dufour effect and Sh enlarges by a factor of about 38.15% with Soret effect. The concentration boundary layer decreases by about 37.50% is when K=5.0.

Numerical simulation of a fractional stochastic delay differential equations using spectral scheme: a comprehensive stability analysis.

The fractional stochastic delay differential equation (FSDDE) is a powerful mathematical tool for modeling complex systems that exhibit both fractional order dynamics and stochasticity with time delays. The purpose of this study is to explore the stability analysis of a system of FSDDEs. Our study emphasizes the interaction between fractional calculus, stochasticity, and time delays in understanding the stability of such systems. Analyzing the moments of the system's solutions, we investigate stochasticity's influence on FSDDS. The article provides practical insight into solving FSDDS efficiently using various numerical techniques. Additionally, this research focuses both on asymptotic as well as Lyapunov stability of FSDDS. The local stability conditions are clearly presented and also the effects of a fractional orders with delay on the stability properties are examine. Through a comprehensive test of a stability criteria, practical examples and numerical simulations we demonstrate the complexity and challenges concern with the analyzing FSDDEs.

Principled and interpretable alignability testing and integration of single-cell data.

Single-cell data integration can provide a comprehensive molecular view of cells, and many algorithms have been developed to remove unwanted technical or biological variations and integrate heterogeneous single-cell datasets. Despite their wide usage, existing methods suffer from several fundamental limitations. In particular, we lack a rigorous statistical test for whether two high-dimensional single-cell datasets are alignable (and therefore should even be aligned). Moreover, popular methods can substantially distort the data during alignment, making the aligned data and downstream analysis difficult to interpret. To overcome these limitations, we present a spectral manifold alignment and inference (SMAI) framework, which enables principled and interpretable alignability testing and structure-preserving integration of single-cell data with the same type of features. SMAI provides a statistical test to robustly assess the alignability between datasets to avoid misleading inference and is justified by high-dimensional statistical theory. On a diverse range of real and simulated benchmark datasets, it outperforms commonly used alignment methods. Moreover, we show that SMAI improves various downstream analyses such as identification of differentially expressed genes and imputation of single-cell spatial transcriptomics, providing further biological insights. SMAI's interpretability also enables quantification and a deeper understanding of the sources of technical confounders in single-cell data.

A Spectral Method for Identifiable Grade of Membership Analysis with Binary Responses.

Grade of membership (GoM) models are popular individual-level mixture models for multivariate categorical data. GoM allows each subject to have mixed memberships in multiple extreme latent profiles. Therefore, GoM models have a richer modeling capacity than latent class models that restrict each subject to belong to a single profile. The flexibility of GoM comes at the cost of more challenging identifiability and estimation problems. In this work, we propose a singular value decomposition (SVD)-based spectral approach to GoM analysis with multivariate binary responses. Our approach hinges on the observation that the expectation of the data matrix has a low-rank decomposition under a GoM model. For identifiability, we develop sufficient and almost necessary conditions for a notion of expectation identifiability. For estimation, we extract only a few leading singular vectors of the observed data matrix and exploit the simplex geometry of these vectors to estimate the mixed membership scores and other parameters. We also establish the consistency of our estimator in the double-asymptotic regime where both the number of subjects and the number of items grow to infinity. Our spectral method has a huge computational advantage over Bayesian or likelihood-based methods and is scalable to large-scale and high-dimensional data. Extensive simulation studies demonstrate the superior efficiency and accuracy of our method. We also illustrate our method by applying it to a personality test dataset.

Quantitative and stability study of the evolution of a thermoelastic body.

We prove the existence and uniqueness of a solution to a system of equations describing the evolution of a linear thermoelastic body by using a semi-group method. Moreover, the uniform exponential stability of the solution is shown in a particular case.•With respect to the existence and uniqueness of the solution, we have defined a linear operator which generates a contraction semi-group and show that it is monotone maximal.•With respect to the stability of the system, we have computed explicitly the expression of the solution of the system and show that the semi-group is uniformly exponentially stable in a particular case.

Machine Learning approach for TWA detection relying on ensemble data design.

Background and objective: T-wave alternans (TWA) is a fluctuation of the ST-T complex of the surface electrocardiogram (ECG) on an every-other-beat basis. It has been shown to be clinically helpful for sudden cardiac death stratification, though the lack of a gold standard to benchmark detection methods limits its application and impairs the development of alternative techniques. In this work, a novel approach based on machine learning for TWA detection is proposed. Additionally, a complete experimental setup is presented for TWA detection methods benchmarking. Methods: The proposed experimental setup is based on the use of open-source databases to enable experiment replication and the use of real ECG signals with added TWA episodes. Also, intra-patient overfitting and class imbalance have been carefully avoided. The Spectral Method (SM), the Modified Moving Average Method (MMA), and the Time Domain Method (TM) are used to obtain input features to the Machine Learning (ML) algorithms, namely, K Nearest Neighbor, Decision Trees, Random Forest, Support Vector Machine and Multi-Layer Perceptron. Results: There were not found large differences in the performance of the different ML algorithms. Decision Trees showed the best overall performance (accuracy 0.88 ± 0.04 , precision 0.89 ± 0.05 , Recall 0.90 ± 0.05 , F1 score 0.89 ± 0.03 ). Compared to the SM (accuracy 0.79, precision 0.93, Recall 0.64, F1 score 0.76) there was an improvement in every metric except for the precision. Conclusions: In this work, a realistic database to test the presence of TWA using ML algorithms was assembled. The ML algorithms overall outperformed the SM used as a gold standard. Learning from data to identify alternans elicits a substantial detection growth at the expense of a small increment of the false alarm.

Transient analysis and reliability modeling of fault-tolerant system operating under admission control policy with double retrial features and working vacation.

Maintaining a high-level reliability and efficiency without interruption are the key concerns for many real-time machining systems. Using the redundancy and repair facility features, we develop a double retrial orbit queueing model for the fault-tolerant machining system (FTMS) operating under the restriction of admission of repair jobs based on threshold policy and working vacation. The provision of primary and secondary orbits is made so that the failed units can wait there based on the facility available in case the repairman is occupied. From the orbits, the failed units retry to get the repairman free so that the repair job can be accomplished. Chapman-Kolmogorov equations for the system states of FTMS have been constructed to evaluate the transient reliability and queueing indices using the spectral technique. The sensitivity along with the relative sensitivity analysis of crucial system parameters, have facilitated. The impacts of parameter variability on the system metrics and total expected cost are examined for illustrative examples.