Recurrence plots bridge deterministic systems and stochastic systems topologically and measure-theoretically.

We connect a common conventional value to quantify a recurrence plot with its motifs, which have recently been termed "recurrence triangles." The common practical value we focus on is DET, which is the ratio of the points forming diagonal line segments of length 2 or longer within a recurrence plot. As a topological value, we use different recurrence triangles defined previously. As a measure-theoretic value, we define the typical recurrence triangle frequency dimension, which generally fluctuates around 1 when the underlying dynamics are governed by deterministic chaos. By contrast, the dimension becomes higher than 1 for a purely stochastic system. Additionally, the typical recurrence triangle frequency dimension correlates most precisely with DET among the above quantities. Our results show that (i) the common practice of using DET could be partly theoretically supported using recurrence triangles, and (ii) the variety of recurrence triangles behaves more consistently for identifying the strength of stochasticity for the underlying dynamics. The results in this study should be useful in checking basic properties for modeling a given time series.

Predictive analysis of multiple future scientific impacts by embedding a heterogeneous network.

Identifying promising research as early as possible is vital to determine which research deserves investment. Additionally, developing a technology for automatically predicting future research trends is necessary because of increasing digital publications and research fragmentation. In previous studies, many researchers have performed the prediction of scientific indices using specially designed features for each index. However, this does not capture real research trends. It is necessary to develop a more integrated method to capture actual research trends from various directions. Recent deep learning technology integrates different individual models and makes it easier to construct more general-purpose models. The purpose of this paper is to show the possibility of integrating multiple prediction models for scientific indices by network-based representation learning. This paper will conduct predictive analysis of multiple future scientific impacts by embedding a heterogeneous network and showing that a network embedding method is a promising tool for capturing and expressing scientific trends. Experimental results show that the multiple heterogeneous network embedding improved 1.6 points than a single citation network embedding. Experimental results show better results than baseline for the number of indices, including the author h-index, the journal impact factor (JIF), and the Nature Index after three years from publication. These results suggest that distributed representations of a heterogeneous network for scientific papers are the basis for the automatic prediction of scientific trends.

Imputation-free reconstructions of three-dimensional chromosome architectures in human diploid single-cells using allele-specified contacts.

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.

Improving time series prediction accuracy for the maxima of a flow by reconstructions using local cross sections.

Despite a long history of time series analysis/prediction, theoretically few is known on how to predict the maxima better. To predict the maxima of a flow more accurately, we propose to use its local cross sections or plates the flow passes through. First, we provide a theoretical underpinning for the observability using local cross sections. Second, we show that we can improve short-term prediction of local maxima by employing a generalized prediction error, which weighs more for the larger values. The proposed approach is demonstrated by rainfalls, where heavier rains may cause casualties.

Validity of Lognormal Distribution in Analyzing Laboratory Test Values.

We compared the distribution of laboratory test values with several parametric statistical distributions to show that a lognormal distribution can represent the distribution of laboratory test values. Then, we estimated the distributions of laboratory test values of four datasets including only three published values: two endpoints of reference interval (RI) and one median.

Detecting nonlinear stochastic systems using two independent hypothesis tests.

Various systems in the real world can be nonlinear and stochastic, but because nonlinear time series analysis has been developed to distinguish nonlinear deterministic systems from linear stochastic systems, there have been no appropriate methods developed so far for testing the nonlinear stochasticity for a given system. Thus, here we propose a set of two hypothesis tests, one for the nonlinearity and one for the stochasticity, independent of each other. The test for the linearity is based on Fourier-transform-based surrogate data with a nonlinear test statistic, while the test for determinism depends on the theory of ordinal patterns or permutations recently developed intensively. We demonstrate the proposed set of tests with time series generated from toy models. In addition, we show that both a foreign exchange market and a temperature series in Tokyo could be nonlinear and stochastic, as well as sometimes with determinism beyond pseudoperiodicity.

Surrogate Data Preserving All the Properties of Ordinal Patterns up to a Certain Length.

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.

Approximating high-dimensional dynamics by barycentric coordinates with linear programming.

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.