Numerical Analysis of Split-Step Backward Euler Method with Truncated Wiener Process for a Stochastic Susceptible-Infected-Susceptible Model.

This article deals with the numerical positivity, boundedness, convergence, and dynamical behaviors for stochastic susceptible-infected-susceptible (SIS) model. To guarantee the biological significance of the split-step backward Euler method applied to the stochastic SIS model, the numerical positivity and boundedness are investigated by the truncated Wiener process. Motivated by the almost sure boundedness of exact and numerical solutions, the convergence is discussed by the fundamental convergence theorem with a local Lipschitz condition. Moreover, the numerical extinction and persistence are initially obtained by an exponential presentation of the stochastic stability function and strong law of the large number for martingales, which reproduces the existing theoretical results. Finally, numerical examples are given to validate our numerical results for the stochastic SIS model.

A Method Based on Differential Entropy-Like Function for Detecting Differentially Expressed Genes Across Multiple Conditions in RNA-Seq Studies.

The advancement of high-throughput RNA sequencing has uncovered the profound truth in biology, ranging from the study of differential expressed genes to the identification of different genomic phenotype across multiple conditions. However, lack of biological replicates and low expressed data are still obstacles to measuring differentially expressed genes effectively. We present an algorithm based on differential entropy-like function (DEF) to test for the differential expression across time-course data or multi-sample data with few biological replicates. Compared with limma, edgeR, DESeq2, and baySeq, DEF maintains equivalent or better performance on the real data of two conditions. Moreover, DEF is well suited for predicting the genes that show the greatest differences across multiple conditions such as time-course data and identifies various biologically relevant genes.

DTWscore: differential expression and cell clustering analysis for time-series single-cell RNA-seq data.

BACKGROUND: The development of single-cell RNA sequencing has enabled profound discoveries in biology, ranging from the dissection of the composition of complex tissues to the identification of novel cell types and dynamics in some specialized cellular environments. However, the large-scale generation of single-cell RNA-seq (scRNA-seq) data collected at multiple time points remains a challenge to effective measurement gene expression patterns in transcriptome analysis. RESULTS: We present an algorithm based on the Dynamic Time Warping score (DTWscore) combined with time-series data, that enables the detection of gene expression changes across scRNA-seq samples and recovery of potential cell types from complex mixtures of multiple cell types. CONCLUSIONS: The DTWscore successfully classify cells of different types with the most highly variable genes from time-series scRNA-seq data. The study was confined to methods that are implemented and available within the R framework. Sample datasets and R packages are available at https://github.com/xiaoxiaoxier/DTWscore .

Micro-object motion tracking based on the probability hypothesis density particle tracker.

Tracking micro-objects in the noisy microscopy image sequences is important for the analysis of dynamic processes in biological objects. In this paper, an automated tracking framework is proposed to extract the trajectories of micro-objects. This framework uses a probability hypothesis density particle filtering (PF-PHD) tracker to implement a recursive state estimation and trajectories association. In order to increase the efficiency of this approach, an elliptical target model is presented to describe the micro-objects using shape parameters instead of point-like targets which may cause inaccurate tracking. A novel likelihood function, not only covering the spatiotemporal distance but also dealing with geometric shape function based on the Mahalanobis norm, is proposed to improve the accuracy of particle weight in the update process of the PF-PHD tracker. Using this framework, a larger number of tracks are obtained. The experiments are performed on simulated data of microtubule movements and real mouse stem cells. We compare the PF-PHD tracker with the nearest neighbor method and the multiple hypothesis tracking method. Our PF-PHD tracker can simultaneously track hundreds of micro-objects in the microscopy image sequence.