A new technique for time series analysis, which is a combination of the maximum entropy method (MEM) for spectral analysis and the non-linear least squares method (LSM) for fitting analysis, is described. In this technique, the MEM power spectral density (MEMPSD) is calculated using a very large lag that could diminish the lag dependence of dominant periods estimated by the MEM analysis. The validity of this large lag is confirmed by the LSM, given that the ten dominant MEM periods are known quantities. To validate the MEM plus LSM technique, it is compared with autoregressive (AR) modelling, by analysing heart rate variability under pharmacological interventions (phenylephrine and trinitroglycerine), using 16 young males. The results indicate that the MEMPSD, when compared with the ARPSD, has numerous periods that could reproduce the original time series much more accurately, as revealed by the LSM analysis. However, both the low- and high-frequency powers with MEMPSD and ARPSDs shift in the expected directions in accordance with the pharmacological effects on the cardiovascular system. The implications of these results are discussed from the theoretical and practical standpoints of the MEM plus LSM technique, compared with AR modelling.

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A newly devised procedure of time series analysis, which is a linearized version of the nonlinear least squares method combined with the maximum entropy spectral analysis method, was proposed and applied to the annual sunspot number data from 1700 to 1991. Multiple periodicities of the temporal variation were elucidated in detail. The solar cycle of a 11.04-year period accompanied with the solar cycle multiplets, the periods of 50.41 years, the so-called “Yoshimura cycle”, and 107.11 years corresponding to the cycle of century-scale minima, for example, were clearly observed. The optimum least squares fitting curve for the data was extended over the past two millennia and the next millennium. The past grand minima such as the Maunder minimum were confirmed in the past extrapolation curve, and the next centennial minimum was predicted to occur between 2000 and 2030.

The structure factors Sm(Q) for aqueous solutions of LiCl and CsCl at room temperature, including those for heavy water, have been determined by means of the time-of-flight (TOF) neutron diffraction method using an electron linear accelerator (LINAC). Analysis of the diffraction data has been carried out for the aqueous ionic solutions as well as for pure heavy water. The following results were obtained with respect to the structure of the nearest hydration shell: (a) the coordination numbers are 4 for Li+ and 6 for Cl− in the LiCl solution, and 8 for Cs+ and 6 for Cl− in the CsCl solution, (b) the average ion-oxygen distances are 1.90±0.05 Å for Li+, 2.95±0.10 Å for Cs+ and 3.10±0.05 Å for Cl−, and (c) around cations water molecules take the configuration to orient the axis of one of two lone-pair hybrids on a straight line joining an oxygen atom and a cation.

BackgroundMuch effort has been expended on interpreting the mechanism of influenza epidemics, so as to better predict them. In addition to the obvious annual cycle of influenza epidemics, longer-term incidence patterns are present. These so-called interepidemic periods have long been a focus of epidemiology. However, there has been less investigation of the interepidemic period of influenza epidemics. In the present study, we used spectral analysis of influenza morbidity records to indentify the interepidemic period of influenza epidemics in Japan.MethodsWe used time series data of the monthly incidence of influenza in Japan from January 1948 through December 1998. To evaluate the incidence data, we conducted maximum entropy method (MEM) spectral analysis, which is useful in investigating the periodicities of shorter time series, such as that of the incidence data used in the present study. We also conducted a segment time series analysis and obtained a 3-dimensional spectral array.ResultsBased on the results of power spectral density (PSD) obtained from MEM spectral analysis, we identified 3 periodic modes as the interepidemic periods of the incidence data. Segment time series analysis revealed that the amount of amplitude of the interepidemic periods increased during the occurrence of influenza pandemics and decreased when vaccine programs were introduced.ConclusionsThe findings suggest that the temporal behavior of the interepidemic periods of influenza epidemics is correlated with the magnitude of cross-reactive immune responses.