Data-based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to science, engineering, and beyond. Inspired by the widely used methodology in recent years, the cross-map-based techniques, we develop a general framework to advance towards a comprehensive understanding of dynamical causal mechanisms, which is consistent with the natural interpretation of causality. In particular, instead of measuring the smoothness of the cross-map as conventionally implemented, we define causation through measuring the scaling law for the continuity of the investigated dynamical system directly. The uncovered scaling law enables accurate, reliable, and efficient detection of causation and assessment of its strength in general complex dynamical systems, outperforming those existing representative methods. The continuity scaling-based framework is rigorously established and demonstrated using datasets from model complex systems and the real world.
Rui DongYau Mathematical Sciences Center, Tsinghua University, Beijing, China; Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing, ChinaTaojun HuDepartment of Biostatistics, School of Public Health, Peking University, Beijing 100191, ChinaYunjun ZhangDepartment of Biostatistics, School of Public Health, Peking University, Beijing 100191, ChinaYang Li Chongqing School, University of Chinese Academy of Sciences, Chongqing 400020, ChinaXiao-Hua Zhou Department of Biostatistics, School of Public Health, Peking University, Beijing 100191, China; Beijing International Center for Mathematical Research, Peking University, Beijing 100191, China
Data Analysis, Bio-Statistics, Bio-Mathematicsmathscidoc:2204.42002
Omicron, the latest SARS-CoV-2 Variant of Concern (VOC), first appeared in Africa in November 2021. At present, the question of whether a new VOC will out-compete the currently predominant variant is important for governments seeking to determine if current surveillance strategies and responses are appropriate and reasonable. Based on both virus genomes and daily-confirmed cases, we compare the additive differences in growth rates and reproductive numbers (R_0) between VOCs and their predominant variants through a Bayesian framework and phylo-dynamics analysis. Faced with different variants, we evaluate the effects of current policies and vaccinations against VOCs and predominant variants. The model also predicts the date on which a VOC may become dominant based on simulation and real data in the early stage. The results suggest that the overall additive difference in growth rates of B.1.617.2 and predominant variants was 0.44 (95% confidence interval, 95% CI: −0.38, 1.25) in February 2021, and that the VOC had a relatively high R_0. The additive difference in the growth rate of BA.1 in the United Kingdom was 6.82 times the difference between Delta and Alpha, and the model successfully predicted the dominating process of Alpha, Delta and Omicron. Current vaccination strategies remain similarly effective against Delta compared to the previous variants. Our model proposes a reliable Bayesian framework to predict the spread trends of VOCs based on early-stage data, and evaluates the effects of public health policies, which may help us better prepare for the upcoming Omicron variant, which is now spreading at an unprecedented speed.
Rui DongYau Mathematical Sciences Center, Tsinghua University, Beijing, China; Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing, ChinaShaojun PeiDepartment of Mathematical Sciences, Tsinghua University, Beijing, ChinaMengcen GuanDepartment of Mathematical Sciences, Tsinghua University, Beijing, ChinaShek-Chung YauInformation Technology Services Center, The Hong Kong University of Science and Technology, Kowloon, Hong Kong, ChinaChangchuan YinDepartment of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, United StatesRong L. HeDepartment of Biological Sciences, Chicago State University, Chicago, IL, United StatesStephen S.-T. YauDepartment of Mathematical Sciences, Tsinghua University, Beijing, China; Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing, China
Data Analysis, Bio-Statistics, Bio-Mathematicsmathscidoc:2204.42001
A comprehensive description of human genomes is essential for understanding human evolution and relationships between modern populations. However, most published literature focuses on local alignment comparison of several genes rather than the complete evolutionary record of individual genomes. Combining with data from the 1,000 Genomes Project, we successfully reconstructed 2,504 individual genomes and propose Divided Natural Vector method to analyze the distribution of nucleotides in the genomes. Comparisons based on autosomes, sex chromosomes and mitochondrial genomes reveal the genetic relationships between populations, and different inheritance pattern leads to different phylogenetic results. Results based on mitochondrial genomes confirm the “out-of-Africa” hypothesis and assert that humans, at least females, most likely originated in eastern Africa. The reconstructed genomes are stored on our server and can be further used for any genome-scale analysis of humans (http://yaulab.math.tsinghua.edu.cn/2022_1000genomesprojectdata/). This project provides the complete genomes of thousands of individuals and lays the groundwork for genome-level analyses of the genetic relationships between populations and the origin of humans.