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.
Xiaojie QiuWhitehead Institute for Biomedical Research, Cambridge, MA, USAYan ZhangDepartment of Computational and System Biology, University of Pittsburgh, Pittsburgh, PA, USAJorge D. Martin-RufinoBroad Institute of MIT and Harvard, Cambridge, MA, USAChen WengWhitehead Institute for Biomedical Research, Cambridge, MA, USAShayan HosseinzadehDepartment of Molecular and Cell Biology, University of California, Berkeley, CA, USAJianhua XingDepartment of Computational and System Biology, University of Pittsburgh, Pittsburgh, PA, USAJonathan WeissmanWhitehead Institute for Biomedical Research, Cambridge, MA, USA
Data Analysis, Bio-Statistics, Bio-Mathematicsmathscidoc:2202.42001
Single-cell (sc)RNA-seq, together with RNA velocity and metabolic labeling, reveals cellular states and transitions at unprecedented resolution. Fully exploiting these data, however, requires kinetic models capable of unveiling governing regulatory functions. Here, we introduce an analytical framework dynamo (https://github.com/aristoteleo/dynamo-release), which infers absolute RNA velocity, reconstructs continuous vector fields that predict cell fates, employs differential geometry to extract underlying regulations, and ultimately predicts optimal reprogramming paths and perturbation outcomes. We highlight dynamo’s power to overcome fundamental limitations of conventional splicing-based RNA velocity analyses to enable accurate velocity estimations on a metabolically labeled human hematopoiesis scRNA-seq dataset. Furthermore, differential geometry analyses reveal mechanisms driving early megakaryocyte appearance and elucidate asymmetrical regulation within the PU.1-GATA1 circuit. Leveraging the least-action-path method, dynamo accurately predicts drivers of numerous hematopoietic transitions. Finally, in silico perturbations predict cell-fate diversions induced by gene perturbations. Dynamo, thus, represents an important step in advancing quantitative and predictive theories of cell-state transitions.
Forest above-ground biomass (AGB) can be estimated based on light detection and ranging (LiDAR) point clouds. This paper introduces an accurate and detailed quantitative structure model (AdQSM), which can estimate the AGB of large tropical trees. AdQSM is based on the reconstruction of 3D tree models from terrestrial laser scanning (TLS) point clouds. It represents a tree as a set of closed and complete convex polyhedra. We use AdQSM to model 29 trees of various species (total 18 species) scanned by TLS from three study sites (the dense tropical forests of Peru, Indonesia, and Guyana). The destructively sampled tree geometry measurement data is used as reference values to evaluate the accuracy of diameter at breast height (DBH), tree height, tree volume, branch volume, and AGB estimated from AdQSM. After AdQSM reconstructs the structure and volume of each tree, AGB is derived by combining the wood density of the specific tree species from destructive sampling. The AGB estimation from AdQSM and the post-harvest reference measurement data show a satisfying agreement. The coefficient of variation of root mean square error (CV-RMSE) and the concordance correlation coefficient (CCC) are 20.37% and 0.97, respectively. AdQSM provides accurate tree volume estimation, regardless of the characteristics of the tree structure, without major systematic deviations. We compared the accuracy of AdQSM and TreeQSM in modeling the volume of 29 trees. The tree volume from AdQSM is compared with the reference value, and the determination coefficient (R2), relative bias (rBias), and CV-RMSE of tree volume are 0.96, 6.98%, and 22.62%, respectively. The tree volume from TreeQSM is compared with the reference value, and the R2, relative Bias (rBias), and CV-RMSE of tree volume are 0.94, −9.69%, and 23.20%, respectively. The CCCs between the volume estimates based on AdQSM, TreeQSM, and the reference values are 0.97 and 0.96. AdQSM also models the branches in detail. The volume of branches from AdQSM is compared with the destructive measurement reference data. The R2, rBias, and CV-RMSE of the branches volume are 0.97, 12.38%, and 36.86%, respectively. The DBH and height of the harvested trees were used as reference values to test the accuracy of AdQSM’s estimation of DBH and tree height. The R2, rBias, and CV-RMSE of DBH are 0.94, −5.01%, and 9.06%, respectively. The R2, rBias, and CV-RMSE of the tree height were 0.95, 1.88%, and 5.79%, respectively. This paper provides not only a new QSM method for estimating AGB based on TLS point clouds but also the potential for further development and testing of allometric equations.
Laser scanning is an effective tool for acquiring geometric attributes of trees and vegetation,
which lays a solid foundation for 3-dimensional tree modelling. Existing studies on tree modelling
from laser scanning data are vast. However, some works cannot guarantee sufficient modelling
accuracy, while some other works are mainly rule-based and therefore highly depend on user inputs.
In this paper, we propose a novel method to accurately and automatically reconstruct detailed 3D
tree models from laser scans. We first extract an initial tree skeleton from the input point cloud by
establishing a minimum spanning tree using the Dijkstra shortest-path algorithm. Then, the initial tree
skeleton is pruned by iteratively removing redundant components. After that, an optimization-based
approach is performed to fit a sequence of cylinders to approximate the geometry of the tree branches.
Experiments on various types of trees from different data sources demonstrate the effectiveness and
robustness of our method. The overall fitting error (i.e., the distance between the input points and the
output model) is less than 10 cm. The reconstructed tree models can be further applied in the precise
estimation of tree attributes, urban landscape visualization, etc. The source code of this work is freely
available at https://github.com/tudelft3d/adtree
The stochasticity of gene expression is manifested in the fluctuations of mRNA and protein copy numbers within a cell lineage over time. While data of this type can be obtained for many generations, most mathematical models are unsuitable to interpret such data since they assume non-growing cells. Here we develop a theoretical approach that quantitatively links the frequency content of lineage data to subcellular dynamics. We elucidate how the position, height, and width of the peaks in the power spectrum provide a distinctive fingerprint that encodes a wealth of information about mechanisms controlling transcription, translation, replication, degradation, bursting, promoter switching, cell cycle duration, cell division, gene dosage compensation, and cell size homeostasis. Predictions are confirmed by analysis of single-cell Escherichia coli data obtained using fluorescence microscopy. Furthermore, by matching the experimental and theoretical power spectra, we infer the temperature-dependent gene expression parameters, without the need of measurements relating fluorescence intensities to molecule numbers.
Hau-Tieng WuDepartment of Mathematics, Duke University, DurhamTze Leung LaiDepartment of Statistics, Stanford University, StanfordGabriel G. Haddad3Department of Pediatrics and Rady Children’s Hospital, University of CaliforniaAlysson MuotriDepartment of Cellular & Molecular Medicine and Department of Pediatrics
Data Analysis, Bio-Statistics, Bio-Mathematicsmathscidoc:2105.45001
Herein we describe new frontiers in mathematical modeling and statistical analysis of oscillatory biomedical signals, motivated by our recent studies of network formation in the human brain during the early stages of life and studies forty years ago on cardiorespiratory patterns during sleep in infants and animal models. The frontiers involve new nonlinear-type time-frequency analysis of signals with multiple oscillatory components, and efficient particle filters for joint state and parameter estimators together with uncertainty quantification in hidden Markov models and empirical Bayes inference.
Songting LiShanghai JIao Tong UniversityNan LiuBeijing Normal UniversityLi YaoBeijing Normal UniversityXiaohui ZhangBeijing Normal UniversityDongzhuo ZhouShanghai JIao Tong UniversityDavid CaiNew York University
Data Analysis, Bio-Statistics, Bio-Mathematicsmathscidoc:2104.42005
The interplay between excitatory and inhibitory neurons imparts rich functions of the brain. To understand the synaptic mechanisms underlying neuronal computations, a fundamental approach is to study the dynamics of excitatory and inhibitory synaptic inputs of each neuron. The traditional method of determining input conductance, which has been applied for decades, employs the synaptic current-voltage (I-V) relation obtained via voltage clamp. Due to the space clamp effect, the measured conductance is different from the local conductance on the dendrites. Therefore, the interpretation of the measured conductance remains to be clarified. Using theoretical analysis, electrophysiological experiments, and realistic neuron simulations, here we demonstrate that there does not exist a transform between the local conductance and the conductance measured by the traditional method, due to the neglect of a nonlinear interaction between the clamp current and the synaptic current in the
traditional method. Consequently, the conductance determined by the traditional method may not correlate with the local conductance on the dendrites, and its value could be unphysically negative as observed in experiment. To circumvent the challenge of the space clamp effect and elucidate synaptic impact on neuronal information processing, we propose the
concept of effective conductance which is proportional to the local conductance on the dendrite and reflects directly the functional influence of synaptic inputs on somatic membrane potential dynamics, and we further develop a framework to determine the effective conductance accurately. Our work suggests re-examination of previous studies involving conductance
measurement and provides a reliable approach to assess synaptic influence on neuronal computation.