Norio Ohtomo

Exponential Characteristics of Power Spectral Densities Caused by Chaotic Phenomena

Power spectral densities (PSDs) were calculated by the maximum entropy method (MEM) for three types of chaotic time series numerically generated from the Lorenz, Rossler and Duffing models. Every PSD indicated exponential decay until it levels off at a limit determined by the accuracy of the present computation. This exponential chracteristics were universally found in all chaotic time series irrespective of the data length as well as the time range of data. The values of the coefficient of exponent were 3.26, 5.72 and 7.36 for 6000-point data of the Lorenz, Rossler and Duffing models, respectively, and they slightly increased as the data length shortened. The exponential form was also recognized in the MEM-PSD for the Lorentzian-type time series as in theory.

Time Series Analysis of Incidence Data of Influenza in Japan

Background Much 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. Methods We 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. Results Based 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. Conclusions The findings suggest that the temporal behavior of the interepidemic periods of influenza epidemics is correlated with the magnitude of cross-reactive immune responses.

Relationship of cholera incidence to El Niño and solar activity elucidated by time-series analysis

Using time-series analysis, we investigated the monthly cholera incidence in Dhaka, Bangladesh during an 18-year period for its relationship to the sea surface temperature (SST) linked to El Niño, and to the sunspot number. Dominant periodic modes identified for cholera incidence were 11.0, 4.8, 3.5, 2.9, 1.6, 1.0 and 0.5 years. The majority of these modes, e.g. the 11.0-, 4.8-, 3.5-, 1.6- and 1.0-year modes, were essentially consistent with those obtained for the SST data (dominant modes: 5.1, 3.7, 2.5, 2.1, 1.5, 1.0 years) and the sunspot number data (dominant modes: 22.1, 11.1, 7.3, 4.8, 3.1 years). We confirmed that the variations of cholera incidence were synchronous with SSTs, and were inversely correlated to the sunspot numbers. These results suggest that the cholera incidence in Bangladesh may have been influenced by the occurrence of El Niño and also by the periodic change of solar activity.

Prediction Analysis for Measles Epidemics

A newly devised procedure of prediction analysis, which is a linearized version of the nonlinear least squares method combined with the maximum entropy spectral analysis method, was proposed. This method was applied to time series data of measles case notification in several communities in the UK, USA and Denmark. The dominant spectral lines observed in each power spectral density (PSD) can be safely assigned as fundamental periods. The optimum least squares fitting (LSF) curve calculated using these fundamental periods can essentially reproduce the underlying variation of the measles data. An extension of the LSF curve can be used to predict measles case notification quantitatively. Some discussions including a predictability of chaotic time series are presented.

Spectral Study of Measles Epidemics: The Dependence of Spectral Gradient on the Population Size of the Community.

We have carried out spectral analysis of measles notifications in several communities in Denmark, UK and USA. The results confirm that each power spectral density (PSD) shows exponential characteristics, which are universally observed in the PSD for time series generated from nonlinear dynamical system. The exponential gradient increases with the population size. For almost all communities, many spectral lines observed in each PSD can be fully assigned to linear combinations of several fundamental periods, suggesting that the measles data are substantially noise-free. The optimum least squares fitting curve calculated using these fundamental periods essentially reproduces an underlying variation of the measles data, and an extension of the curve can be used to predict measles epidemics. For the communities with large population sizes, some PSD patterns obtained from segment time series analysis show a close resemblance to the PSD patterns at the initial stages of a period-doubling bifurcation process for the so-called susceptible/exposed/infectious/recovered (SEIR) model with seasonal forcing. The meaning of the relationship between the exponential gradient and the population size is discussed.

A Detailed Study of Power Spectral Density for Rossler System

Power spectral densities (PSDs) calculated by the maximum entropy method (MEM) for Rossler system indicated exponential decay with a large number of well-defined spectral lines. The spectral lines were confirmed to indicate a complete bifurcation up to the fifth-order period-doubling. An extremely anomalous behavior was recognized in the region of c =4.18–4.21 which is considered to be a transition region. The contribution of the power of the fundamental mode to the total power was overwhelmingly large: it becomes larger than 90%. A prediction of time series including chaotic ones was performed and the satisfactory results obtained. It will be discussed that the fluctuations due to amplitude instability of time series in the periodic solutions generate, resulting in the continuous component of PSD structured through the subharmonic cascade process, and this continuous region is restructured in the inverse cascade process (the socalled broad continuum in the chaotic mixing).

Proportion of Sporadic Gastroenteritis Cases Caused by Rotavirus, Norovirus, Adenovirus and Bacteria in Japan from January 2000 to December 2003

Many kinds of virus and bacterium have been identified as pathogens that cause sporadic gastroenteritis (SG). Among the pathogens, rotavirus (RV), norovirus (NV; previously known as Norwalk‐like virus), and adenovirus (AdV) types 40/41 have been considered as the prevalent viruses implicated in the aetiology of childhood gastroenteritis. In the present study, we attempted to estimate monthly proportions of SG cases caused by the viral agents (RV, NV, AdV and other viruses (OV)) and bacterial agents in the whole of Japan. The estimation was carried out by using time series data of the incidence of SG and the viral and bacterial agents of SG, which were collected by a nationwide surveillance system in Japan from January 2000 to December 2003. It was confirmed that, in the dominant period of RV and NV, the proportion of RV‐associated SG and that of NV‐associated SG indicate almost same level with each other: 46–69% during February–May for RV, and 41–75% during October–December for NV.

Development and Surface Evaluation of Large SiC X-Ray Mirrors for High-Brilliance Synchrotron Radiation.

Flat SiC mirrors coated with Pt, of which size are 800?50 mm2 and 1000?140 mm2 in area, are developed for high-brilliance synchrotron radiation. The large mirrors are well polished over the entire area from the viewpoint of surface roughness for application to the use for the synchrotron radiation beamline. The performance of the large mirror surface is evaluated by the measurements of not only reflectivity near the critical angle but also of the angle-resolved scattering (ARS) curve as a function of mirror surface position at several glancing angles with CuK? X-rays from a rotating target at the 30-m-long X-ray beamline facility of ISAS. By analyzing the ARS curves the power spectral density functions are derived as a function of the surface wave number. It is suggested that the large mirror may have a fractal surface finish like that of small mirrors. Evaluation of the longitudinal mirror curvature on the order of 10 km from the reflected beam profile width is also described. The results are compared with the measurements of the laser interferometers.

Study of the effect of vaccination on periodic structures of measles epidemics in Japan.

The purpose of this paper is to investigate the effect of vaccination on periodic structures of measles epidemics in Japan. We carried out spectral analysis for time series data of measles notifications collected in Japan. It was confirmed that the interepidemic period, which corresponds to the interval between major epidemics of measles, increases as the vaccination ratio increases. This result was supported by a theory based on a mathematical model for epidemics of infectious diseases. It was suggested that the interepidemic period is useful to estimate the effect of vaccination on measles incidences quantitatively.

New Method of Time Series Analysis and Its Application to Wolf's Sunspot Number Data. II: Periodicities of The Daily Sunspot Numbers

The daily sunspot numbers data from 1979 October 1 to 1993 December 31 were analyzed using a new method of time series analysis proposed by the authors, and the long- and short-term periodicities were investigated. A three-dimensional (3D) spectral array of the normalized power spectral densities (PSDs) obtained by the segment time series analysis revealed the temporal behavior of the 27- and 155-d periodicities in the solar activity minimum. In the normalized 3D spectral array, the solar rotation cycle of 27-d accompanied by its multiplets was confirmed to migrate gradually from the low frequency region toward the high frequency region in the solar activity minimum as the solar activity increases, while the 155-d periodicity exists in the solar activity maximum only. Moreover, the behavior of the daily sunspot numbers variation was conjectured to be deterministic chaos, based on the exponential characteristics of the PSDs and the subharmonic relations of the spectral lines.