A terminal-state tracking optimal control problem for linear hyperbolic equations with distributed control is studied in this paper. An analytic solution formula for the optimal control problem is derived in the form of eigenseries. We show that the optimal solution satisfies the approximate controllability property. An explicit solution formula for the exact controllability problem is also expressed by the eigenseries formula when the target state and the controlled state have matching boundary conditions. We demonstrate by numerical simulations that the optimal solutions expressed by the series formula approach the target functions.

1. Objectives: The objectives of this paper are to report Traditional Chinese Medicine (TCM) Constitution Theory and the present state of Chinese Health Administration Center. 2. Methods: We visited China for "China Technology Survey" in 2009. Our purposes were to research for the study of constitutional medicine in China and to search for the Development Plan of Constitutional Medicine Through the Research of Chinese Constitutional Medicine. This paper is the report of the "China Technology Survey". 3. Results & Conclusions: In China, the concept and diagnosis of TCM constitutions is nine(Balanced Constitution, Qi-deficient Constitution, Yang-deficient Constitution, Yin-deficient Constitution, Phlegm-dampness Constitution, Damp-heat Constitution, Stagnant blood Constitution, Stagnant qi Constitution, Inherited specific Constitution). And Chinese government established the Classification and Diagnosis Standards for the Constitutions of TCM in 2009. TCM Constitution Theory is being widely applied at Health Administration Center that treats 'predisease' patients. Theses Chinese clinical implications of constitutional medicine are a good example for "Sasang Constituional Medicine" Care Service.

The Iterated Prisoner's Dilemma is a simultaneous two-player game. The actual values of payoffs take on different values in different research projects. In this study we perform an affine normalization of the payoff matrix and compare the agents that evolve when each of five different payoff matrices is used. Four of the matrices are chosen to lie near extremes of the normalized space, while the other lies in its center. The probability of cooperative behavior evolving is strongly influenced by the choice of payoff matrix. Fingerprinting of the evolved agents demonstrates a significant shift in the distribution of strategies that arise. A significant difference in pairwise competitive ability is also found between agents evolved with different payoff matrices. Placed into tournaments with agents evolved using all five payoff matrices, the players evolved with the central payoff matrix were found to have significantly better average tournament ranking. We conclude that the choice of payoff values is not a neutral choice and must be controlled for in any design of experiments.

In this paper, we present a study of a discrete version of a reaction–diffusion system which corresponds to the Turing model of morphogenesis. We present a review on spatio-temporal chaos in lattice systems, and then show that the discrete version possesses a hyperbolic property displaying spatio-temporal chaos. Finally, some numerical computation will be performed to observe the hyperbolic properties of the system.

This paper introduces the concept of a virtual ecosystem and reports the following three mathematical approaches that could be widely used to construct such an ecosystem, along with examples: (1) a molecular dynamics simulation approach for animal flocking behavior, (2) a stochastic lattice model approach for termite colony behavior, and (3) a rule-based cellular automata approach for biofilm growth. The ecosystem considered in this study consists of artificial organisms and their environment. Each organism in the ecosystem is an agent that interacts autonomously with the dynamic environment, including the other organisms within it. The three types of model were successful to account for each corresponding ecosystem. In order to accurately mimic a natural ecosystem, a virtual ecosystem needs to take many ecological variables into account. However, doing so is likely to introduce excess complexity and nonlinearity in the analysis of the virtual ecosystem's dynamics. Nonetheless, the development of a virtual ecosystem is important, because it can provide possible explanations for various phenomena such as environmental disturbances and disasters, and can also give insights into ecological functions from an individual to a community level from a synthetic viewpoint. As an example of how lower and higher levels in an ecosystem can be connected, this paper also briefly discusses the application of the second model to the simulation of a termite ecosystem and the influence of climate change on the termite ecosystem.

In field, one can observe without difficulties that two flocks are intersected or combined with each other. For
example, a fish flock in a stream separates into two part by obstacles (e.g. stone) and rejoins behind the obstacles.
The dynamics of two flocks guided by their leader were studied in the situation where the flocks cross each other
with a crossing angle, ？？, between their moving directions. Each leader is unaffected by its flock members whereas
each member is influenced by its leader and other members. To understand the dynamics, I investigated the order
parameter,？？, defined by the absolute value of the average unit velocity of the flocks’ members. When the two flocks
were encountered, the first peak in？？ was appeared due to the breaking of the flocks’ momentum balance. When
the flocks began to separate, the second peak in？？ was observed. Subsequently, erratic peaks were emerged by some
individuals that were delayed to rejoin their flock. The amplitude of the two peaks, d1 (first) and d2 (second), were
measured. Interestingly, they exhibited a synchronized behavior for different ？？. This simulation model can be a
useful tool to explore animal behavior and to develop multi-agent robot systems.

We defined a novel “branch length similarity” (BLS) entropy, S, on a simple network consisting of a single node and branches. This simple network is referred to as “unit branching network” (UBN) because UBNs are components of larger networks. As an application of BLS entropy, we considered the characterization of termite tunnel patterns because termite tunnel patterns can be broken down into a collection of simple units consisting of a single node and branches. These simple units correspond to UBNs. To this end, in additional to the entropy, we introduced the standard deviation (σ) of the difference in S between UBNs connected by a single tunnel branch. Forty simulated tunnel patterns were created for each of two termite species, Reticulitermes flavipes (Kollar) and Coptotermes formosanus Shiraki. These patterns were projected into <S>–σ phase space in order to assess their topological properties. This approach showed that for R. flavipes, their coordinates were relatively more clustered than those of C. formosanus. This result reflected that these two species were differently constrained by emergent property resulting from simple worker's tunneling behavior. We believe that the approach proposed in this study can be a useful tool to explore termite tunnel systems, but not limited to termite system.

We study the nature of the phase transition in the fully frustrated simple cubic lattice with the $XY$ spin model. This system is the Villain’s model generalized in three dimensions. The ground state is very particular with a 12-fold degeneracy. Previous studies have shown unusual critical properties. With the powerful Wang-Landau flat-histogram Monte Carlo method, we carry out in this work intensive simulations with very large lattice sizes. We show that the phase transition is clearly of first order, putting an end to the uncertainty which has lasted for more than 20 years.

Most subterranean termites forage for food by creating tunnel galleries underground. These tunnel networks reflect a compromise between foraging efficiency and other environmental constraints, such as soil hardness and moisture content. Thus, understanding tunnel networks is important for understanding foraging behavior. Due to the difficulties in direct observation of tunneling patterns in the field, we used a theoretical approach for this analysis. We first constructed a lattice model to simulate the tunnel networks of Coptotermes formosanus Shiraki and Reticulitermes flavipes (Kollar) on the basis of the experimental data provided by Su et al. (Su, N.-Y., Stith, B.M., Puche, H., Bardunias, P., 2004. Characterization of tunneling geometry of subterranean termites (Isoptera: Rhinotermitidae) by computer simulation. Sociobiology 44 (3), 471–483.). Using this model and two of its modified versions, we explored the relationship between the food encounter rate and food distributions and analyzed how this relationship is influenced by changes in the tunnel characteristic constituents, such as the branching tunnel length and frequency. Additionally, we investigated the effects of landscape heterogeneity on the foraging efficiency. In the discussion, we briefly introduced our novel individual-based model comprising individual termites and their surroundings, and we addressed the necessity of this model in the functioning of the network and the formation of the network in relation to foraging behavior.