Quantifying causality between variables from observed time series data is of great importance in various disciplines but also a challenging task, especially when the observed data are short. Unlike the conventional methods, we find it possible to detect causality only with very short time series data, based on embedding theory of an attractor for nonlinear dynamics. Specifically, we first show that measuring the smoothness of a cross map between two observed variables can be used to detect a causal relation. Then, we provide a very effective algorithm to computationally evaluate the smoothness of the cross map, or “Cross Map Smoothness” (CMS), and thus to infer the causality, which can achieve high accuracy even with very short time series data. Analysis of both mathematical models from various benchmarks and real data from biological systems validates our method.

Causality detection likely misidentifies indirect causations as direct ones, due to the effect of causation transitivity. Although several methods in traditional frameworks have been proposed to avoid such misinterpretations, there still is a lack of feasible methods for identifying direct causations from indirect ones in the challenging situation where the variables of the underlying dynamical system are non-separable and weakly or moderately interacting. Here, we solve this problem by developing a data-based, model-independent method of partial cross mapping based on an articulated integration of three tools from nonlinear dynamics and statistics: phase-space reconstruction, mutual cross mapping, and partial correlation. We demonstrate our method by using data from different representative models and real-world systems. As direct causations are keys to the fundamental underpinnings of a variety of complex dynamics, we anticipate our method to be indispensable in unlocking and deciphering the inner mechanisms of real systems in diverse disciplines from data.

SignificanceMaking accurate forecast or prediction is a challenging task in the big data era, in particular for those datasets involving high-dimensional variables but short-term time series points, and these datasets are omnipresent in many fields. In this work, a model-free framework, named as “randomly distributed embedding” (RDE), is proposed to accurately predict future dynamics based on such short-term but high-dimensional data. The RDE framework creates the distribution information from the interactions among high-dimensional variables to compensate for the lack of time points in real applications. Instead of roughly predicting a single trial of future values, this framework achieves the accurate prediction by using the distribution information.

2IgB7-H3 has recently been identified as a new member of the B7 family. Its expression at the protein level remains largely unknown due to the lack of the specific monoclonal antibody (mAb). To characterize the expression of 2IgB7-H3, we newly generated two mouse antihuman 2IgB7-H3 mAbs (4H7 and 21D4). We found the constitutive expression of 2IgB7-H3 on a series of tumor cell lines. Furthermore, the expression was examined on monocyte-derived dendritic cells (Mo-DCs) and DCs from CD34(+) hematopoietic progenitor cells (HPC) by means of mAb staining. The results showed that 2IgB7-H3 was expressed on Mo-DCs at a high and stable level during differentiation in vitro. With the maturation of DCs from CD34(+) HPCs, the expression of the molecule was upregulated. However, the 2IgB7-H3 was not expressed on fresh isolated T and B lymphocytes, monocytes, or CD34(+) HPCs. These results suggested that 2IgB7-H3 may be a valuable surface antigen for the detection of DCs.