A method for detecting the dimension of a dynamical system encompassing simultaneously two distinct discrete time series is presented. The time series are provided by the same observable taking distinct and independent initial conditions or they can be formed by realizations of different observables measured simultaneously in a symmetric attractor. The method is derived from an extension of the...

Dimension reduction is an important topic in data mining and machine learning. Especially dimension reduction combined with feature fusion is an effective preprocessing step when the data are described by multiple feature sets. Canonical Correlation Analysis (CCA) and Discriminative Canonical Correlation Analysis (DCCA) are feature fusion methods based on correlation. However, they are differen...

Chromatin is a major nuclear component, and it is an active matter of debate to understand its different levels of spatial organization, as well as its implication in gene regulation. Measurements of nuclear chromatin compaction were recently used to understand how DNA is folded inside the nucleus and to detect cellular dysfunctions such as cancer. Super-resolution imaging opens new possibiliti...

The transformation of rainfall into runoff is one of the most important processes in hydrology. In the past few decades, a wide variety of automated or computer-based approaches have been applied to model this process. However, many such approaches have an important limitation in that they treat the rainfall-runoff process as a realization of only a few parameters of linear relationships rather...

Careful attentions must be required for analyzing high dimensional Electroencephalographic (EEG) signals. There have many discrepancy or linearity when signals are recorded at different stimulations for a subject. When these signals are collected for different trails of a subject, there have similarity also. In this paper, we want to measure this correspondence on the basis of correlation aspec...

We present the essential dynmnic model of the •nesospheric photochemical system (PCS) •'md suggest a step-by-step procedure for elaborating such a model of an arbitrary atmospheric PCS. The model demonstrates the same possibilities ofnonlinear dynamic behavior and qualitatively the same dynamic haracteristics a the corresponding original model, but is much simpler than the latter. We show the a...

We compare two algorithms for the numerical estimation of the correlation dimension from a finite set of vectors: the "classical" algorithm of Grassberger and Procaccia (GPA) and the recently proposed algorithm of Judd (JA). Data set size requirements and their relations to systematic and statistical errors of the estimates are investigated. It is demonstrated that correlation dimensions of the...