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The false nearest neighbors (FNN) method estimates the variables of a system by sequentially embedding a time series into a higher-dimensional delay coordinate system and finding an embedding dimension in which the neighborhood of the delay coordinate vector in the lower dimension does not extend into the higher, that is, a dimension in which no false neighbors or neighborhoods exist. However, the FNN method requires an arbitrary threshold value to distinguish false neighborhoods, which must be considered each time for each time series to be analyzed. In this study, we propose a robust method to estimate the minimum embedding dimension, which eliminates the arbitrariness of threshold selection. We applied the proposed approach to the van der Pol and Lorenz equations as representative examples of chaotic time series. The results verified the accuracy of the proposed variable estimation method, which showed a lower error rate compared to the minimum dimension estimates for most of the thresholding intervals set by the FNN method.

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Background Arterial pressure (AP) and heart rate (HR) near or after the end of cold caloric test or the test of semicircular canal function were not changed, but those were not measured from the beginning of the test continuously. This study was aimed to evaluate the changes in AP and HR continuously during caloric test and 2) relationship between those changes and the semicircular canal function. Methods the Basic Principles of the Declaration of Helsinki and their expansion in the regulations governing research supported by the U.S. Government. This study was approved by the Institutional Review Boards, and written informed consent was obtained from all subjects. Airflow at 15°C was applied to the left ear (Ear15), and the left tragus (Tragus15); another airflow at 37°C was applied to the left ear (Ear37) for one minute each in healthy subjects. AP, HR were recorded and analyzed in time series. Furthermore, the cold airflow was applied to the right and left ear for one minute, and maximum changes in AP, HR and slow phase velocity (SPV) of nystagmus were measured in outpatients. Results AP remained constant or decreased during the Ear15, whereas their HR immediately decreased at the onset of the airflow uniformly. Thus, the decrease in HR was unlikely induced by the baroreflex. Neither AP nor HR changed during the Ear37 and Tragus15 stimulation. Thus, the decreases in HR were not induced by the mechanical stimulation and stimulation for the skin. Degree of nystagmus was significantly correlated with the changes in HR but in AP in outpatients. Conclusions Cold airflow for the ears immediately decreased HR, and the semicircular canals might be related the change.