We define a polynomial generating pairing (PGP) and propose a method to construct a family of pairing friendly curves from PGP. We show that a bilinear map over the family is directly determined by the coefficients of the PGP and the map is non-degenerate under a minor condition which is satisfied with cryptographic parameters. Finally, we provide a criterion for PGP to obtain an optimal pairing.

The dynamics of an elastic rod in a viscous fluid at zero Reynolds number is investigated when the bottom end of the rod is tethered at a point in space and rotates at a prescribed angular frequency, while the other part of the rod freely s through the fluid. A rotating elastic rod, which is intrinsically straight, exhibits three dynamical motions: twirling, overwhirling, and whirling. The first two motions are stable, whereas the last motion is unstable. The stability of dynamical motions is determined by material and geometrical properties of the rod, fluid properties, and the angular frequency of the rod. We employ the regularized Stokes flow to describe the fluid motion and the Kirchhoff rod model to describe the elastic rod. Our simulation results display subcritical Hopf bifurcation diagrams indicating the bistability region. We also investigate the whirling motion generated by the rotation of an intrinsically bent rod. It is observed that the angular frequency determines the handedness of the whirling rod and thus the flow direction, and that there is a critical frequency which separates the positive (upward) flow at frequencies above it from the negative (downward) flow at frequencies below it.

The locomotion behavior of Caenorhabditis elegans has been extensively studied to understand the relationship between the changes in the organism’s neural activity and the biomechanics. However, so far, we have not yet achieved the understanding. This is because the worm complicatedly responds to the environmental factors, especially chemical stress. Constructing a mathematical model is helpful for the understanding the locomotion behavior in various surrounding conditions. In the present study, we built three hidden Markov models for the crawling behavior of C. elegans in a controlled environment with no chemical treatment and in a polluted environment by formaldehyde, toluene, and benzene (0.1 ppm and 0.5 ppm for each case). The organism’s crawling activity was recorded using a digital camcorder for 20 min at a rate of 24 frames per second. All shape patterns were quantified by branch length similarity entropy and classified into five groups by using the self-organizing map. To evaluate and establish the hidden Markov models, we compared correlation coefficients between the simulated behavior (i.e. temporal pattern sequence) generated by the models and the actual crawling behavior. The comparison showed that the hidden Markov models are successful to characterize the crawling behavior. In addition, we briefly discussed the possibility of using the models together with the entropy to develop bio-monitoring systems for determining water quality.

The foraging territories of two subterranean termites, Coptotermes formosanus Shiraki and Reticulitermes flavipes (Kollar), were simulated using a two-dimensional model to explore how territorial competition changes according to two variables characterizing territory formation: the total number of territories, and the blocking probability. Meanwhile, the blocking probability quantitatively describes the likelihood that a tunnel will be terminated when another tunnel is encountered. In our previous study, we introduced an interference coefficient c to characterize territorial competition, and obtained c as a function of the total number of territories and the blocking probability for a single termite species by model simulation. In the field, the territorial competition of more than two termite species is frequently observed. Here, we extended the c function to be able to explain the competition between the two species by applying statistical regression to the simulation data. Further, we statistically checked the extended c function by comparing the c function for a single species. We also discuss another approach to mathematically derive the extended c function, which can be easily generalized for use in cases of territorial competition involving more than two termite species.

Subterranean termites build extensive underground galleries that consist of elaborate tunnels and channels to forage for food resources. The changes in tunnel width along the length of the tunnel are related to both biotic (e.g., termite activity) and abiotic factors (e.g., soil density). Termites transport food through the tunnels from food sources to their nest. Thus, understanding the relationship between traveling behavior in the tunnels and changing width is important to comprehend the stability of the termite ecosystem. In the present study, we explored the traveling behavior of termites in terms of ment efficiency, where the ment efficiency was defined as the time (s) needed for a termite to pass through a tunnel. To do so, we designed artificial tunnels with linearly changing width in a two-dimensional arena. The tunnel widths, W1 (for the entrance) and W2 (for the exit), were 2, 3, 4, 5, and 6 mm. We systematically observed the traveling behavior of the termites Reticulitermes speratus kyushuensis Morimoto (Isoptera: Rhinotermitidae) in the artificial tunnels and measured s. The value of s increased with the increase of W2, regardless of W1. s was longer in the case of W1W2. The experimental results can be explained by behavioral differences observed in each case. The implications of the findings are briefly discussed in relation to termite foraging efficiency and the development of individual-based models for the construction of termite tunnels.

Understanding of an ecosystem’s resilience and stability requires an understanding of predatorprey dynamics because ecosystems consist of dynamical interacting subsystems that include predator-prey relationships. These relationships are closely related to the hunting-escaping strategies employed by the predator and prey. Therefore, understanding the effects of hunting and escaping strategies on ecosystems will lead to a better understanding of those systems. To this end, we constructed a spatially explicit lattice model to simulate integrative predator-prey-plant relationships. When an individual simultaneously encounters its predator and prey, either hunting or escaping should take priority. Hunting priority is referred to as a hunting preferred strategy (HPS), while escape priority is referred to as an escape preferred strategy (EPS). These strategies are associated with some degree of willingness to either hunt (H)orescape(E). In our model, the willingness of an individual to hunt or escape increased with increasing value ofH orE, respectively we investigated changes in the predicted population densities for predator, prey, and plant species with changes in the values of H andE. Simulation results indicated thatHPS positively contributed to ecosystem stability because those individuals that employedHPS had a greater chance of reproduction than those that employedEPS. In addition, we briefly discuss the development of our model as a tool for understanding behavioral strategies in specific predator-prey interactions.

Identification of butterfly species is essential because they are directly associated with crop plants used for human and animal consumption. However, the widely used reliable methods for butterfly identification are not efficient due to complicated butterfly shapes. We previously developed a novel shape recognition method that uses branch length similarity (BLS) entropy, which is a simple branching network consisting of a single node and branches. The method has been successfully applied to recognize battle tanks and characterize human faces with different emotions. In the present study, we used the BLS entropy profile (an assemble of BLS entropies) as an input feature in a feed-forward back-propagation artificial neural network to identify butterfly species according to their shapes when viewed from different angles (for vertically adjustable angle, θ = ±10°, ±20°, …, ±60° and for horizontally adjustable angle, φ = ±10°, ±20°, …, ±60°). In the field, butterfly images are generally captured obliquely by camera due to butterfly alignment and viewer positioning, which generates various shapes for a given specimen. To generate different shapes of a butterfly when viewed from different angles, we projected the shapes captured from top-view to a plane rotated through angles θ and φ. Projected shapes with differing θ and φ values were used as training data for the neural network and other shapes were used as test data. Experimental results showed that our method successfully identified various butterfly shapes. In addition, we briefly discuss extension of the method to identify more complicated images of different butterfly species.

To raise traditional medicine to a higher level of scientific research, a mathematical model has been proposed using symbolic notations and operators to describe several disease symptoms generally recognized in traditional medicine. Even though this model to a certain degree offers a mathematical approach to identify the relationships between yin-yang and the five viscera, it is not an efficient means of explaining the pathology in traditional medicine due to its use of superfluous notations and definitions. In this paper, we introduce two concise operators, a self-development operator and an action operator: the former describes the effect of a viscus in the unbalanced state on other viscera: the latter explains the engendering and restraining relationships between the two viscera. These tools are useful to elucidate the interactions among the states of the five viscera based on yin-yang and the five elements theory. Our mathematical model with these two operators facilitates deion for the scheme of deficiency-excess of yin-yang in the five viscera. Accordingly, we have mathematically refined the existing results and shown clinical applications as well.

Understanding the forest fire patterns is necessary to comprehend the stability of the forest ecosystems. Thus, researchers have suggested the simulation models to mimic the forest fire spread dynamics, which enables us to predict the forest damage in the scenarios that are difficult to be experimentally tested in laboratory scale. However, many of the models have the limitation that many of them did not consider the complicated environmental factors, such as fuel types, wind, and moisture. In this study, we suggested a simple model with the factors, especially, the geomorphological structure of the forest and two types of fuel. The two fuels correspond to susceptible tree and resistant tree with different probabilities of transferring fire. The trees were randomly distributed in simulation space at densities ranging from 0.5 (low) to 1.0 (high). The susceptible tree had higher value of the probability than the resistant tree. Based on the number of burnt trees, we then carried out the sensitivity analysis to quantify how the forest fire patterns are affected by the structure and tree density. We believe that our model can be a useful tool to explore forest fire spreading patterns.

최근 사회의 각 분야에서 언급되고 있는 빅데이터 열풍을 교육분야에서는 어떻게 수용 혹은 활용할 것인가? 본 연구는 수학교육에서의 빅데이터 활용 방안을 모색하기 위해 먼저 빅데이터의 개념과 활용 예시 등에 대해 살펴본 후, 두 가지로 향후 연구 방향을 모색하였다. 먼저, 기술과 환경의 변화에 따라 데이터 표현과 수용방식의 변화가 요구되고 있다. 다시 말해 수많은 정보들을 시각적으로 묘사하거나 필요한 정보를 '분석하고 추론'하여 효율적이고 명확하게 제공할 수 있도록 데이터를 다루는 학습 내용 및 방법의 변화가 요구되고 있고, 수학교육계는 21세기 학습자 역량강화와 연계하여 이를 수용하기 위한 교육과정 변화를 주도할 필요가 있다. 두 번째, 교수 학습 측면 뿐 아니라 교육분야에서 보다 적극적으로 필요한 데이터들을 수집하고 이러한 데이터 속에 기존에 알지 못했던 새로운 정보들을 파악함으로써, 이를 활용한 효율적인 수학교수학습 변화를 추구하고 수학 교육에 대한 정책적 결정 등에 활용할 수 있도록 많은 관심과 연구를 촉진할 필요가 있다.