IDENTIFYING THE NUMBER OF COMPONENTS IN GAUSSIAN MIXTURE MODELS USING NUMERICAL ALGEBRAIC GEOMETRY

The development of an automated microscope image tracking and analysis system

Microscopy image analysis plays a crucial role in understanding cellular behavior and uncovering important insights in various biological and medical research domains. Tracking cells within the time-lapse microscopy images is a fundamental technique that enables the study of cell dynamics, interactions, and migration. While manual cell tracking is possible, it is time-consuming and prone to subjective biases that impact results. In order to solve this issue, we sought to create an automated software solution, named cell analyzer, which is able to track cells within microscopy images with minimal input required from the user. The program of cell analyzer was written in Python utilizing the open source computer vision (OpenCV) library and featured a graphical user interface that makes it easy for users to access. The functions of all codes were verified through closeness, area, centroid, contrast, variance, and cell tracking test. Cell analyzer primarily utilizes image preprocessing and edge detection techniques to isolate cell boundaries for detection and analysis. It uniquely recorded the area, displacement, speed, size, and direction of detected cell objects and visualized the data collected automatically for fast analysis. Our cell analyzer provides an easy-to-use tool through a graphical user interface for tracking cell motion and analyzing quantitative cell images.

Impact of components number selection in truncated Gaussian mixture model and interval partition on wind speed probability distribution estimation

Owing to global environmental concerns in recent years, wind power has garnered significant attention as a clean and renewable energy source. The probability distribution of the wind speed plays a pivotal role in assessing the wind energy potential and power system operation. As a single Gaussian may be powerless in capturing features of real wind speed distributions owing to the randomness of wind speed, this study aimed to use a truncated Gaussian mixture (TGM) distribution with determined optimal Gaussian components number and suitable interval partitions as a possible alternative model to estimate the wind speed probability distribution (WSPD). In particular, two expectation-maximization algorithms were employed to determine the parameters of the TGM models. Subsequently, the continuous ranked probability score loss theory related to TGM models with two arbitrary truncated points was developed and employed to detect the optimal number of Gaussian components in the TGM models, in addition to casually or empirically setting the number of Gaussian components. Subsequently, the WSPD is estimated using the detected optimal Gaussian component number and the corresponding parameter determination results. Considering that different interval partitions may result in diverse accuracy results, to enhance the flexibility of the above TGM models, another technique is designed using the False-Discovery-Rate-inspired algorithm. This algorithm performs well in the case of large-scale hypothesis tests and can determine the suitable interval partition number. The feasibility and effectiveness of the proposed model were validated using real wind speed data collected from two stations: Haikou and Wulumuqi stations. Comparison of the different goodness-of-fit evaluations demonstrates that the estimation accuracy of WSPD of the proposed approach is comparable to those of the truncated Gaussian mixture distribution with arbitrary Gaussian component numbers and some other comparison models.