Dictionary learning allows model-free pseudotime estimation of transcriptomic data

Background Pseudotime estimation from dynamic single-cell transcriptomic data enables characterisation and understanding of the underlying processes, for example developmental processes. Various pseudotime estimation methods have been proposed during the last years. Typically, these methods start with a dimension reduction step because the low-dimensional representation is usually easier to analyse. Approaches such as PCA, ICA or t-SNE belong to the most widely used methods for dimension reduction in pseudotime estimation methods. However, these methods usually make assumptions on the derived dimensions, which can result in important dataset properties being missed. In this paper, we suggest a new dictionary learning based approach, dynDLT, for dimension reduction and pseudotime estimation of dynamic transcriptomic data. Dictionary learning is a matrix factorisation approach that does not restrict the dependence of the derived dimensions. To evaluate the performance, we conduct a large simulation study and analyse 8 real-world datasets. Results The simulation studies reveal that firstly, dynDLT preserves the simulated patterns in low-dimension and the pseudotimes can be derived from the low-dimensional representation. Secondly, the results show that dynDLT is suitable for the detection of genes exhibiting the simulated dynamic patterns, thereby facilitating the interpretation of the compressed representation and thus the dynamic processes. For the real-world data analysis, we select datasets with samples that are taken at different time points throughout an experiment. The pseudotimes found by dynDLT have high correlations with the experimental times. We compare the results to other approaches used in pseudotime estimation, or those that are method-wise closely connected to dictionary learning: ICA, NMF, PCA, t-SNE, and UMAP. DynDLT has the best overall performance for the simulated and real-world datasets. Conclusions We introduce dynDLT, a method that is suitable for pseudotime estimation. Its main advantages are: (1) It presents a model-free approach, meaning that it does not restrict the dependence of the derived dimensions; (2) Genes that are relevant in the detected dynamic processes can be identified from the dictionary matrix; (3) By a restriction of the dictionary entries to positive values, the dictionary atoms are highly interpretable.

Neural Circuits for Dynamics-Based Segmentation of Time Series

The brain must extract behaviorally relevant latent variables from the signals streamed by the sensory organs. Such latent variables are often encoded in the dynamics that generated the signal rather than in the specific realization of the waveform. Therefore, one problem faced by the brain is to segment time series based on underlying dynamics. We present two algorithms for performing this segmentation task that are biologically plausible, which we define as acting in a streaming setting and all learning rules being local. One algorithm is model based and can be derived from an optimization problem involving a mixture of autoregressive processes. This algorithm relies on feedback in the form of a prediction error and can also be used for forecasting future samples. In some brain regions, such as the retina, the feedback connections necessary to use the prediction error for learning are absent. For this case, we propose a second, model-free algorithm that uses a running estimate of the autocorrelation structure of the signal to perform the segmentation. We show that both algorithms do well when tasked with segmenting signals drawn from autoregressive models with piecewise-constant parameters. In particular, the segmentation accuracy is similar to that obtained from oracle-like methods in which the ground-truth parameters of the autoregressive models are known. We also test our methods on data sets generated by alternating snippets of voice recordings. We provide implementations of our algorithms at https://github.com/ttesileanu/bio-time-series.

Data-driven model-free adaptive fractional-order sliding mode control for the SMA actuator with prescribed performance

In this paper, a novel data-driven model-free adaptive fractional-order sliding mode controller with prescribed performance is proposed for the shape memory alloy (SMA) actuator. Due to the strong asymmetric saturated hysteresis nonlinear characteristics of the SMA actuators, it is not easy to establish an accurate model and develop an effective controller. Therefore, we present a controller without using the model of the SMA actuators. In other words, the proposed controller depends merely on the input/output (I/O) data of the SMA actuators. To obtain the reasonable compensation for hysteresis, enhance the noise robustness of the controller, and reduce the chattering, a fractional-order sliding mode controller with memory characteristics is employed to improve the performance of the controller. In addition, the prescribed performance control (PPC) strategy is introduced in our work to guarantee the tracking errors converge to a sufficiently small boundary and the convergence rate is not less than a predetermined value which are significant and considerable in practical engineering applications of the SMA actuator. Finally, experiments are carried out, and results reveal the effectiveness and success of the proposed controller. Comparisons with the classical Proportional Integral Differential (PID), model-free adaptive control (MFAC), and model-free adaptive sliding mode control (MFAC-SMC) are also performed.