MOTIVATION: Understanding cell differentiation and development dynamics is key for single-cell transcriptome analysis. Current cell differentiation trajectory inference algorithms face challenges such as high dimensionality, noise, and a need for users to possess certain biological information about the datasets to effectively utilize the algorithms. Here, we introduce Trajectory Inference with Cell-Cell Interaction (TICCI), a novel way to address these challenges by integrating intercellular communication information. In recognizing crucial intercellular communication during development, TICCI proposes Cell-Cell Interactions (CCI) at single-cell resolution. We posit that cells exhibiting higher gene expression similarity patterns are more likely to exchange information via biomolecular mediators. RESULTS: TICCI is initiated by constructing a cell-neighborhood matrix using edge weights composed of intercellular similarity and CCI information. Louvain partitioning identifies trajectory branches, attenuating noise, while single-cell entropy (scEntropy) is used to assess differentiation status. The Chu-Liu algorithm constructs a directed least-square model to identify trajectory branches, and an improved diffusion fitted time algorithm computes cell-fitted time in nonconnected topologies. TICCI validation on single-cell RNA sequencing (scRNA-seq) datasets confirms the accuracy of cell trajectories, aligning with genealogical branching and gene markers. Verification using extrinsic information labels demonstrates CCI information utility in enhancing accurate trajectory inference. A comparative analysis establishes TICCI proficiency in accurate temporal ordering. AVAILABILITY AND IMPLEMENTATION: Source code and binaries freely available for download at https://github.com/mine41/TICCI, implemented in R (version 4.32) and Python (version 3.7.16) and supported on MS Windows. Authors ensure that the software is available for a full two years following publication.

Order statistic Least Mean Square (OSLMS) algorithms are a class of adaptive algorithms which modify the ordinary Least Mean Square (LMS) algorithm by applying an order statistic (OS) filtering operation to the instantaneous gradient estimate. Adaptive filter performance may be improved by OSLMS since it effectively reduces effects of gradient noise at filter convergence. In this paper, the convergence analysis has been established for OSLMS. It is shown that OSLMS will converge on average, with noise corrupting both the filter input and the desired signal, and this result is confirmed via simulations. The optimal selection of the OS filter in the algorithm is also discussed. The OS filter is chosen to produce a minimum variance gradient estimate at the filter convergence point; a reduction of the mean squared coefficient error is shown to accrue from this choice of filter.>