Short- and long-distance circadian communication is essential for integration of temporal information. However, a major challenge in plant biology is to decipher how individual clocks are interconnected to sustain rhythms in the whole plant. Here we show that the shoot apex is composed of an ensemble of coupled clocks that influence rhythms in roots. Live-imaging of single cells, desynchronization of dispersed protoplasts, and mathematical analysis using barycentric coordinates for high-dimensional space show a gradation in the strength of circadian communication in different tissues, with shoot apex clocks displaying the highest coupling. The increased synchrony confers robustness of morning and evening oscillations and particular capabilities for phase readjustments. Rhythms in roots are altered by shoot apex ablation and micrografting, suggesting that signals from the shoot apex are able to synchronize distal organs. Similarly to the mammalian suprachiasmatic nucleus, shoot apexes play a dominant role within the plant hierarchical circadian structure.

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Forecasting the aftershock probability has been performed by the authorities to mitigate hazards in the disaster area after a main shock. However, despite the fact that most of large aftershocks occur within a day from the main shock, the operational forecasting has been very difficult during this time-period due to incomplete recording of early aftershocks. Here we propose a real-time method for efficiently forecasting the occurrence rates of potential aftershocks using systematically incomplete observations that are available in a few hours after the main shocks. We demonstrate the method's utility by retrospective early forecasting of the aftershock activity of the 2011 Tohoku-Oki Earthquake of M9.0 in Japan. Furthermore, we compare the results by the real-time data with the compiled preliminary data to examine robustness of the present method for the aftershocks of a recent inland earthquake in Japan.

Hormone therapy in the form of androgen deprivation is a major treatment for advanced prostate cancer. However, if such therapy is overly prolonged, tumour cells may become resistant to this treatment and result in recurrent fatal disease. Long-term hormone deprivation also is associated with side effects poorly tolerated by patients. In contrast, intermittent hormone therapy with alternating on-and off-treatment periods is a possible clinical strategy to delay progression to hormone-refractory disease with the advantage of reduced side effects during the off-treatment periods. In this paper, we first overview previous studies on mathematical modelling of prostate tumour growth under intermittent hormone therapy. The model is categorized into a hybrid dynamical system because switching between on-treatment and off-treatment intervals is treated in addition to continuous dynamics of tumour growth. Next, we present an extended model of stochastic differential equations and examine how well the model is able to capture the characteristics of authentic serum prostate-specific antigen (PSA) data. We also highlight recent advances in time-series analysis and prediction of changes in serum PSA concentrations. Finally, we discuss practical issues to be considered towards establishment of mathematical model-based tailor-made medicine, which defines how to realize personalized hormone therapy for individual patients based on monitored serum PSA levels.

We describe a method for investigating nonlinearity in irregular fluctuations ͑short-term variability͒ of time series even if the data exhibit long-term trends ͑periodicities͒. Such situations are theoretically incompatible with the assumption of previously proposed methods. The null hypothesis addressed by our algorithm is that irregular fluctuations are generated by a stationary linear system. The method is demonstrated for numerical data generated by known systems and applied to several actual time series.

Online social media are increasingly facilitating our social interactions, thereby making available a massive “digital fossil” of human behavior. Discovering and quantifying distinct patterns using these data is important for studying social behavior, although the rapid time-variant nature and large volumes of these data make this task difficult and challenging. In this study, we focused on the emergence of “collective attention” on Twitter, a popular social networking service. We propose a simple method for detecting and measuring the collective attention evoked by various types of events. This method exploits the fact that tweeting activity exhibits a burst-like increase and an irregular oscillation when a particular real-world event occurs; otherwise, it follows regular circadian rhythms. The difference between regular and irregular states in the tweet stream was measured using the Jensen-Shannon divergence, which corresponds to the intensity of collective attention. We then associated irregular incidents with their corresponding events that attracted the attention and elicited responses from large numbers of people, based on the popularity and the enhancement of key terms in posted messages or “tweets.” Next, we demonstrate the effectiveness of this method using a large dataset that contained approximately 490 million Japanese tweets by over 400,000 users, in which we identified 60 cases of collective attentions, including one related to the Tohoku-oki earthquake. “Retweet” networks were also investigated to understand collective attention in terms of social interactions. This simple method provides a retrospective summary of collective attention, thereby contributing to the fundamental understanding of social behavior in the digital era.

Because aftershock occurrences can cause significant seismic risks for a considerable time after the main shock, prospective forecasting of the intermediate-term aftershock activity as soon as possible is important. The epidemic-type aftershock sequence (ETAS) model with the maximum likelihood estimate effectively reproduces general aftershock activity including secondary or higher-order aftershocks and can be employed for the forecasting. However, because we cannot always expect the accurate parameter estimation from incomplete early aftershock data where many events are missing, such forecasting using only a single estimated parameter set (plug-in forecasting) can frequently perform poorly. Therefore, we here propose Bayesian forecasting that combines the forecasts by the ETAS model with various probable parameter sets given the data. By conducting forecasting tests of 1 month period aftershocks based on the first 1 day data after the main shock as an example of the early intermediate-term forecasting, we show that the Bayesian forecasting performs better than the plug-in forecasting on average in terms of the log-likelihood score. Furthermore, to improve forecasting of large aftershocks, we apply a nonparametric (NP) model using magnitude data during the learning period and compare its forecasting performance with that of the Gutenberg-Richter (G-R) formula. We show that the NP forecast performs better than the G-R formula in some cases but worse in other cases. Therefore, robust forecasting can be obtained by employing an ensemble forecast that combines the two complementary forecasts. Our proposed method is useful for a stable unbiased intermediate-term assessment of aftershock probabilities.

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