A theoretical approach to the glucose–insulin regulatory system is presented. By means of integrated mathematical modeling and extensive numerical simulations, we probe the cell-level dynamics of the membrane potential, intracellular Ca²⁺ concentration, and insulin secretion in pancreatic β-cells, together with the whole-body level glucose–insulin dynamics in the liver, brain, muscle, and adipose tissues. In particular, the three oscillatory modes of insulin secretion are reproduced successfully. Such comprehensive mathematical modeling may provide a theoretical basis for the simultaneous assessment of the β-cell function and insulin resistance in clinical examination.

Infectious disease is no longer a local problem. Modern populations are more mobile than ever before, and with this mobility comes active global mixing of infectious disease. To understand the spread of diseases such as influenza, we use a multi-city epidemic model. We extend the SEIR (susceptible-exposed-infectious-recovered) model to incorporate population migration between cities, and use this model to analyze the geographic spread of influenza. We investigate the effectiveness of travel restrictions as a control against the spread of influenza.

First we obtain the basic reproduction number for the single city case, and observe two other control strategies suggested by this case: increasing the number of clinically ill individuals that are treated, and reducing the interval between infection and treatment of such individuals.

We evaluate the effectiveness of the three control strategies with numerical simulations. It is shown that travel restrictions are less effective than the other two strategies. In general, travel restriction tends to delay the spread of the disease into new cities. However, it can increase the peak height of infected populations in all cities. An understanding of the epidemiological structures of related cities is strongly recommended in order to effectively apply the travel restriction strategy.

The identification of modules in complex networks is important for the understanding of systems. Here, we propose an ensemble clustering method incorporating node groupings in various sizes and the sequential removal of weak ties between nodes which are rarely grouped together. This method successfully detects modules in various networks, such as hierarchical random networks and the American college football network, with known modular structures. Some of the results are compared with those obtained by modularity optimization and $K$ -means clustering.

Subterranean termites build extensive underground galleries consisting of elaborate tunnels and channels to forage food resources. Diverse soil conditions surrounding the tunnels, such as soil density, may cause irregularities in the size and shape of the tunnels, and termites are likely to encounter a number of tunnel irregularities while traveling. Considering the tunnel length, how termites respond to an irregularity is likely to affect their ment efficiency, and this in turn is directly correlated to their foraging efficiency. To understand the response of termites, we designed an artificial linear tunnel with rectangular irregularities in a 2-D arena. The tunnel widths, W, were 3 and 4 mm. The rectangular irregularities were 2 mm in width and of varying heights H (2, 1, 0, −1, and −2 mm). The positive and negative sign of H represents a convex and concave structure, respectively. We systematically observed the ment of termites, Coptotermes formosanus Shiraki, at the irregularity and quantified the time needed, τ, for a termite to pass the irregularity. The time τ was shorter for (W, H) = (3, 0) and (3, −1) than for (W, H) = (3, 1), (3, 2), and (3, −2). The time τ was longer for (W, H) = (4, −1), and (4, −2), than for (W, H) = (4, 0), (4, 1) and (4, 2). Four types of behaviors explained the response to the irregularity. The implications of these findings are briefly discussed in relation to termite foraging efficiency.

In our previous study, we defined the branch length similarity (BLS) entropy for a simple network consisting of a single node and numerous branches. As the first application of this entropy to characterize shapes, the BLS entropy profiles of 20 battle tank shapes were calculated from simple networks created by connecting pixels in the boundary of the shape. The profiles successfully characterized the tank shapes through a comparison of their BLS entropy profiles. Following the application, this entropy was used to characterize human’s emotional faces, such as happiness and sad, and to measure the degree of complexity for termite tunnel networks. These applications indirectly indicate that the BLS entropy profile can be a useful tool to characterize networks and shapes. However, the ability of the BLS entropy in the characterization depends on the image resolution because the entropy is determined by the number of nodes for the boundary of a shape. Higher resolution means more nodes. If the entropy is to be widely used in the scientific community, the effect of the resolution on the entropy profile should be understood. In the present study, we mathematically investigated the BLS entropy profile of a shape with infinite resolution and numerically investigated the variation in the pattern of the entropy profile caused by changes in the resolution change in the case of finite resolution.

The locomotion behavior of Caenorhabditis elegans has been studied extensively to understand the respective roles of neural control and biomechanics as well as the interaction between them. In the present study, we suggest a new approach to characterize the temporal patterns in the swimming behavior of the organism. The approach is based on the branching length similarity (BLS) entropy defined on a simple branching network consisting of a single node and branches. The organism’s swimming activity is recorded using a charge-coupled device (CCD) camera for 3 h at a rate of 4 frames per second. In each frame, we place 13 points as nodes, those points being distributed at equal intervals along the organism’s length. Thus, the organism is represented by 13 nodes and 12 edges between nodes. By using the nodes and edges, we construct two simple networks. One is formed by connecting the center point to all other points, and the other is generated from the angles between edges. The BLS entropy values are calculated as S _L for the former network and S _θ for the latter. We investigate the distributions of the S _L and the S _θ values in the phase space of S _L — S _θ and compare those with the values obtained from a simulated C. elegans generated by using randomly-moving chained particles along a certain angle. The comparison revealed distinctive features of the ment patterns of C. elegans during swimming activity. In addition, we briefly discuss the application of our method to bio-monitoring systems to capture behavioral changes of test organisms before and after chemical treatment at low concentrations.

In recent decades, the behavior of Caenorhabditis elegans (C. elegans) has been extensively studied to understand the respective roles of neural control and biomechanics. Thus far, however, only a few studies on the simulation modeling of C. elegans swimming behavior have been conducted because it is mathematically difficult to describe its complicated behavior. In this study, we built two hidden Markov models (HMMs), corresponding to the ments of C. elegans in a controlled environment with no chemical treatment and in a formaldehyde-treated environment (0.1 ppm), respectively. The ment was characterized by a series of shape patterns of the organism, taken every 0.25 s for 40 min. All shape patterns were quantified by branch length similarity (BLS) entropy and classified into seven patterns by using the self-organizing map (SOM) and the k-means clustering algorithm. The HMM coupled with the SOM was successful in accurately explaining the organism’s behavior. In addition, we briefly discussed the possibility of using the HMM together with BLS entropy to develop bio-monitoring systems for real-time applications to determine water quality.

We present results from a search for gravitational-wave bursts in the data collected by the LIGO and Virgo detectors between July 7, 2009 and October 20, 2010: data are analyzed when at least two of the three LIGO-Virgo detectors are in coincident operation, with a total observation time of 207 days. The analysis searches for transients of duration $\lesssim 1\text{ s}$ over the frequency band 64-5000 Hz, without other assumptions on the signal waveform, polarization, direction or occurrence time. All identified events are consistent with the expected accidental background. We set frequentist upper limits on the rate of gravitational-wave bursts by combining this search with the previous LIGO-Virgo search on the data collected between November 2005 and October 2007. The upper limit on the rate of strong gravitational-wave bursts at the Earth is 1.3 events per year at 90% confidence. We also present upper limits on source rate density per year and $\text{Mpc}^3$ for sample populations of standard-candle sources. As in the previous joint run, typical sensitivities of the search in terms of the root-sum-squared strain amplitude for these waveforms lie in the range $\sim 5\times 10^{-22} \text{ Hz}^{-1/2}$ to $\sim 1 \times 10^{-20} \text{ Hz}^{-1/2}$. The combination of the two joint runs entails the most sensitive all-sky search for generic gravitational-wave bursts and synthesizes the results achieved by the initial generation of interferometric detectors.

We present the results of a weakly modeled burst search for gravitational waves from mergers of non-spinning intermediate mass black holes (IMBH) in the total mass range $100-450$ solar masses and with the component mass ratios between $1:1$ and $4:1$. The search was conducted on data collected by the LIGO and Virgo detectors between November of 2005 and October of 2007. No plausible signals were observed by the search which constrains the astrophysical rates of the IMBH mergers as a function of the component masses. In the most efficiently detected bin centered on $88+88$ solar masses, for non-spinning sources, the rate density upper limit is 0.13 per $\text{Mpc}^3$ per Myr at the 90% confidence level.