A novel coefficient for detecting and quantifying asymmetry of California electricity market based on asymmetric detrended cross-correlation analysis Chaos: An Interdisciplinary Journal of Nonlinear Science 26, 063109 (2016) The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data. Modeling and predicting a high-dimensional time series is still a challenge because common methods such as neural networks 1-5 and radial basis functions 6-11 have many parameters to be fitted compared with the length of the time series. This challenge is often called as the curse of dimensionality.12 Here, we propose to model a high-dimensional time series with barycentric coordinates 13 by using linear programming. 14 Mees 13 demonstrated that barycentric coordinates obtained by tessellations are effective to reproduce typical behavior of the two-dimensional H enon map and the threedimensional R€ ossler model, while the tessellations are difficult to be applied to high-dimensional phase space. We overcome this difficulty by formulating the problem for obtaining barycentric coordinates, employing linear programming and expressing the approximation error directly. Toy and real-world examples show the wide applicability of the proposed method.

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Single-cell Hi-C analysis of diploid human cells is difficult because of the lack of dense chromosome contact information and the presence of homologous chromosomes with very similar nucleotide sequences. Thus here, we propose a new algorithm to reconstruct the three-dimensional (3D) chromosomal architectures from the Hi-C dataset of single diploid human cells using allele-specific single-nucleotide variations (SNVs). We modified our recurrence plot-based algorithm, which is suitable for the estimation of the 3D chromosome structure from sparse Hi-C datasets, by newly incorporating a function of discriminating SNVs specific to each homologous chromosome. Here, we eventually regard a contact map as a recurrence plot. Importantly, the proposed method does not require any imputation for ambiguous segment information, but could efficiently reconstruct 3D chromosomal structures in single human diploid cells at a 1-Mb resolution. Datasets of segments without allele-specific SNVs, which were considered to be of little value, can also be used to validate the estimated chromosome structure. Introducing an additional mathematical measure called a refinement further improved the resolution to 40-kb or 100-kb. The reconstruction data supported the notion that human chromosomes form chromosomal territories and take fractal structures where the dimension for the underlying chromosome structure is a non-integer value.

We propose a method for generating surrogate data that preserves all the properties of ordinal patterns up to a certain length, such as the numbers of allowed/forbidden ordinal patterns and transition likelihoods from ordinal patterns into others. The null hypothesis is that the details of the underlying dynamics do not matter beyond the refinements of ordinal patterns finer than a predefined length. The proposed surrogate data help construct a test of determinism that is free from the common linearity assumption for a null-hypothesis.