To understand the effect of the probability of a predator catching prey, P_catch, on the stability of the predator–prey system, a spatially explicit lattice model consisting of predators, prey, and grass was constructed. The predators and prey randomly on the lattice space, and the grass grows according to its growth probability. When a predator encounters prey, the predator eats the prey in accordance with the probability P_catch. When a prey encounters grass, the prey eats the grass. The predator and prey give birth to offspring according to a birth probability after eating prey or grass, respectively. When a predator or prey is initially introduced or newly born, its health state is set at a high given value. This health state decreases by one with every time step. When the state of an animal decreases to less than zero, the individual dies and is red from the system. Population densities for predator and prey fluctuated significantly according to P_catch. System stability was characterized by the standard deviation ？ of the fluctuation. The simulation results showed that ？ for predators increased with an increase of P_catch; ？ for prey reached a maximum at P_catch = 0.4; and ？ for grass fluctuated little regardless of P_catch. These results were due to the tradeoff between P_catch and the predator–prey encounter rate, which represents the degree of interaction between predator and prey and the average population density, respectively.

The territory size distribution of Formosan subterranean termites in an urban landscape was studied by using a two-dimensional lattice model with minimized local rules on the basis of empirical data to determine the development of a territory. An urban landscape including components such as complex man-made structures, trees, and lakes was constructed on a lattice space. Each component was described by assigning values ranging from 0.0 to 1.0. These values were interpreted as transition probabilities, P_trans, which represented the spatially distributed properties of the components. The higher the P_trans values, better were the environmental conditions for territory growth. We applied this model to the termite colonies in Louis Armstrong Park in New Orleans, LA. A comparison of the model prediction and the observed territory size distribution showed very similar trends in maximum territory on a size-normalized scale. The trends emerged from two effects: first, when a founding pair was surrounded by lattice cells with low P_trans values, its growth was strongly inhibited, and second, when territories competed with each other at shared boundaries, their growth was restrained. In addition, we investigated the effect of the presence/absence of landscape components on the territory size distribution in the simulation.

In order to study how climate change affects the territory size of subterranean termites, a lattice model was used to simulate the foraging territory of the Formosan subterranean termite, Coptotermes formosanus Shiraki (Isoptera: Rhinotermitidae), and the minimized local rules that are based on empirical data from the development of termites’ foraging territory was applied. A landscape was generated by randomly assigning values ranging from 0.0 to 1.0 to each lattice site, which represented the spatially distributed property of the landscape. At the beginning of the simulation run, N territory seeds - one for each founding pair, were randomly distributed on the lattice space. The territories grew during the summer and shrank during the winter. In the model, the effects of climate change were demonstrated by changes in two variables: the period of the summer season, T, and the percentage of the remaining termite cells, σ, after the shrinkage. The territory size distribution was investigated in the size descending order for the values of T (= 10, 15, …, 50) and σ (= 10, 15, …, 50) at a steady state after a sufficiently long time period. The distribution was separated into two regions: the larger-sized territories and the smaller-sized territories. The slope, m, of the distribution of territory size on a semi-log scale for the larger-sized territories was maximal with T (45 ≤ T ≤ 50) in the maximal range and with σ in the optimal range (30 ≤ σ ≤ 40), regardless of the value of N. The results suggest that the climate change can influence the termite territory size distribution under the proper balance of T and σ in combination.

Branch length symmetry (BLS) entropy, defined on a simple network consisting of a single node and branches, was used to characterize facial expressions in both males and females. As a component of a larger network, this simple network is referred to as a unit branching network (UBN). We introduced a new variable, ¥ã, which represents the topological property of the network, as a function of entropy in order to topologically characterize a branching network composed of UBNs. We constructed UBNs for images of 70 male and 56 female faces displaying four different expressions (neutral, happy, angry, and screaming) by joining 17 facial landmark points such as the centers of the eyes, the corners of the mouth, and the underside tip of the nose. Based on these expressions, we computed the values of ¥ã for the facial networks and found a statistical difference between the ¥ã values of male and female faces. With the exception of a comparison between the neutral and the angry expressions, which had the same ¥ã values, there was a significant difference in the ¥ã values among different expressions within the same gender. Neutral and angry expressions had equal ¥ã values because the change in the distances between the facial landmark points for these two expressions was negligible. This study is valuable because it demonstrates that BLS entropy can be usefully applied to characterize facial expressions.

We investigate the possibility for two-mode probability density function (PDF) to have a non-zero flux steady state solution. We take the large volume limit so that the space of modes becomes continuous. It is shown that in this limit all the steady-state two- or higher-mode PDFs are the product of one-mode PDFs. The flux of this steady-state solution turns out to be zero for any finite mode PDF.

Two computational methods were applied to classification of ment patterns of zebrafish (Danio rerio) to elucidate Markov processes in behavioral changes before and after treatment of formaldehyde (0.1 mg/L) in semi-natural conditions. The complex data of the ment tracks were initially classified by the Self-organizing map (SOM) to present different behavioral states of test individuals. Transition probabilities between behavioral states were further evaluated to fit Markov processes by using the hidden Markov model (HMM). Emission transition probability was also obtained from the observed variables (i.e., speed) for training with the HMM. Experimental transition and emission probability matrices were successfully estimated with the HMM for recognizing sequences of behavioral states with accuracy rates in acceptable ranges at central and boundary zones before (77.3–81.2%) and after (70.1–76.5%) treatment. A heuristic algorithm and a Markov model were efficiently combined to analyze ment patterns and could be a means of in situ behavioral monitoring tool.

Recently, Xiong et al. and Selvi et al. proposed a certificateless signature scheme secure in the standard model and a certificateless multi-receiver signcryption scheme secure in the random oracle model, respectively. In this paper, we show that they are insecure against malicious-butpassive KGC attacks. More specifically, the former does not achieve unforgeability and the latter does not satisfy confidentiality against type II adversaries.

Vercauteren introduced the concept of optimal pairing, which by definition can be computed by using at most (log₂ r)/φ(k) + log₂ k basic Miller iterations, where r is the order of the groups involved and k is the embedding degree Vercauteren (IEEE Trans Inf Theory 56(1):455–461, 2010). Freeman et al. summarized and proposed all of the new constructions of pairing-friendly elliptic curves that currently exist Freeman et al. (J Cryptol 23(2):224–280, 2010). In this paper, we give an optimal pairing for each family of pairing-friendly curves in Freeman et al. (J Cryptol 23(2):224–280, 2010) by taking the Ate or R-ate pairing approach.