Topological Data Analysis as a New Tool for EEG Processing

Transcriptome analysis reveals the genes involved in spermatogenesis in white feather broilers

Semen volume is an important economic trait of broilers and one of the important indices for continuous breeding. The objective of this study was to identify genes related to semen volume through transcriptome analysis of the testis tissue of white feather broilers. The testis samples with the highest semen volume (H group, n = 5) and lowest semen volume (L group, n = 5) were selected from 400-day-old roosters for transcriptome analysis by RNA sequencing. During the screening of differentially expressed genes (DEGs) between the H and L groups, a total of 386 DEGs were identified, among which 348 were upregulated and 38 were downregulated. Gene ontology (GO) enrichment analysis and Kyoto Encyclopedia of Genes and Genomes (KEGG) analysis revealed that the immune response, leukocyte differentiation, cell adhesion molecules and collagen binding played vital roles in spermatogenesis. The results showed that 4 genes related to spermatogenesis, namely, COL1A1, CD74, ARPC1B and APOA1, were significantly expressed in Group H, which was consistent with the phenotype results. Our findings may provide a basis for further research on the genetic mechanism of semen volume in white feather broilers.

Lean blowout detection using topological data analysis

Modern lean premixed combustors are operated in ultra-lean mode to conform to strict emission norms. However, this causes the combustors to become prone to lean blowout (LBO). Online monitoring of combustion dynamics may help to avoid LBO and help the combustor run more safely and reliably. Previous studies have suggested various techniques to early predict LBO in single-burner combustors. In contrast, early detection of LBO in multi-burner combustors has been little explored to date. Recent studies have discovered significantly different combustion dynamics between multi-burner combustors and single-burner combustors. In the present paper, we show that some well-established early LBO detection techniques suitable for single-burner combustor are less effective in early detecting LBO in multi-burner combustors. To resolve this, we propose a novel tool, topological data analysis (TDA), for real-time LBO prediction in a wide range of combustor configurations. We find that the TDA metrics are computationally cheap and follow monotonic trends during the transition to LBO. This indicates that the TDA metrics can be used to fine-tune the LBO safety margin, which is a desirable feature from practical implementation point of view. Furthermore, we show that the sublevel set TDA metrics show approximately monotonic changes during the transition to LBO even with low sampling-rate signals. Sublevel set TDA is computationally inexpensive and does not require phase-space embedding. Therefore, TDA can potentially be used for real-time monitoring of combustor dynamics with simple, low-cost, and low sampling-rate sensors.

Statistical inference for dependence networks in topological data analysis

Topological data analysis (TDA) provide tools that are becoming increasingly popular for analyzing multivariate time series data. One key aspect in analyzing multivariate time series is dependence between components. One application is on brain signal analysis. In particular, various dependence patterns in brain networks may be linked to specific tasks and cognitive processes. These dependence patterns may be altered by various neurological and cognitive impairments such as Alzheimer's and Parkinson's diseases, as well as attention deficit hyperactivity disorder (ADHD). Because there is no ground-truth with known dependence patterns in real brain signals, testing new TDA methods on multivariate time series is still a challenge. Our goal here is to develop novel statistical inference procedures via simulations. Simulations are useful for generating some null distributions of a test statistic (for hypothesis testing), forming confidence regions, and for evaluating the performance of proposed TDA methods. To the best of our knowledge, there are no methods that simulate multivariate time series data with potentially complex user-specified connectivity patterns. In this paper we present a novel approach to simulate multivariate time series with specific number of cycles/holes in its dependence network. Furthermore, we also provide a procedure for generating higher dimensional topological features.

Method for persistent topological features extraction of schizophrenia patients' electroencephalography signal based on persistent homology

With the development of network science and graph theory, brain network research has unique advantages in explaining those mental diseases, the neural mechanism of which is unclear. Additionally, it can provide a new perspective in revealing the pathophysiological mechanism of brain diseases from the system level. The selection of threshold plays an important role in brain networks construction. There are no generally accepted criteria for determining the proper threshold. Therefore, based on the topological data analysis of persistent homology theory, this study developed a multi-scale brain network modeling analysis method, which enables us to quantify various persistent topological features at different scales in a coherent manner. In this method, the Vietoris-Rips filtering algorithm is used to extract dynamic persistent topological features by gradually increasing the threshold in the range of full-scale distances. Subsequently, the persistent topological features are visualized using barcodes and persistence diagrams. Finally, the stability of persistent topological features is analyzed by calculating the Bottleneck distances and Wasserstein distances between the persistence diagrams. Experimental results show that compared with the existing methods, this method can extract the topological features of brain networks more accurately and improves the accuracy of diagnostic and classification. This work not only lays a foundation for exploring the higher-order topology of brain functional networks in schizophrenia patients, but also enhances the modeling ability of complex brain systems to better understand, analyze, and predict their dynamic behaviors.