Given a graph G, the m-step graph of G, denoted by S _m (G), has the same vertex set as G and an edge between two distinct vertices u and v if there is a walk of length m from u to v. The line graph of G, denoted by L(G), is a graph such that the vertex set of L(G) is the edge set of G and two vertices u and v of L(G) are adjacent if the edges corresponding to u and v share a common end vertex in G. We characterize connected graphs G such that S _m (G) and L(G) are isomorphic.

The optimal treatment strategies with an age-structured model of HIV infection are investigated. The age-structured model allows for variations in the virion production rate and the death rate of infected T cells as a function of age, which is the length of time since infection. The optimal therapy protocol is derived by formulating and analyzing an optimal control problem and the existence of solutions to the optimal control problem is established. The optimal treatment strategy is obtained by solving the corresponding optimality system numerically. It is demonstrated by numerical simulations that the dynamic treatment strategy delays the time to reach the peak viral load and reduces the viral load. Moreover, we propose that optimal therapy protocols should be changed according to different viral production rates and death rates of infected T cells.

The human body needs continuous and stable glucose supply for maintaining its biological functions. Stable glucose supply comes from the homeostatic regulation of the blood glucose level, which is controlled by various glucose consuming or producing organs. Therefore, it is important to understand the whole-body glucose regulation mechanism. In this article, we describe various mathematical models proposed for glucose regulation in the human body, and discuss the difficulty and limitation in reproducing real processes of glucose regulation.

Insulin secretion is one of the most characteristic features of β-cell physiology. As it plays a central role in glucose regulation, a number of experimental and theoretical studies have been performed since the discovery of the pancreatic β-cell. This review article aims to give an overview of the mathematical approaches to insulin secretion. Beginning with the bursting electrical activity in pancreatic β-cells, we describe effects of the gap-junction coupling between β-cells on the dynamics of insulin secretion. Then, implications of paracrine interactions among such islet cells as α-, β-, and δ-cells are discussed. Finally, we present mathematical models which incorporate effects of glycolysis and mitochondrial glucose metabolism on the control of insulin secretion.

A haplotype is a single nucleotide polymorphism (SNP) sequence and a representative genetic marker describing the diversity of biological organs. Haplotypes have a wide range of applications such as pharmacology and medical applications. In particular, as a highly social species, haplotypes of the Apis mellifera (honeybee) benefit human health and medicine in diverse areas, including venom toxicology, infectious disease, and allergic disease. For this reason, assembling a pair of haplotypes from individual SNP fragments drives research and generates various computational models for this problem. The minimum error correction (MEC) model is an important computational model for an individual haplotype assembly problem. However, the MEC model has been proved to be NP-hard; therefore, no efficient algorithm is available to address this problem. In this study, we propose an improved version of a branch and bound algorithm that can assemble a pair of haplotypes with an optimal solution from SNP fragments of a honeybee specimen in practical time bound. First, we designed a local search algorithm to calculate the good initial upper bound of feasible solutions for enhancing the efficiency of the branch and bound algorithm. Furthermore, to accelerate the speed of the algorithm, we made use of the recursive property of the bounding function together with a lookup table. After conducting extensive experiments over honeybee SNP data released by the Human Genome Sequencing Center, we showed that our method is highly accurate and efficient for assembling haplotypes.

Subterranean termites build complex tunnel networks below ground for foraging. During the foraging activity, termites may encounter a considerable number of tunnel intersections. When they encounter the intersections, they spend some time gathering information for making a decision regarding their moving direction by anntenation. The spent time is likely to be directly connected to the termites’ survival because depending on the time, the total traveling time taken by the termites for transferring food resources from the site of food to their nest can vary significantly because of many intersections. In the present study, we measured the time spent by a termite to pass an intersection with widths of W1 and W₂ (W₁ and W₂: 2, 3, or 4 mm); τL, τR, and τS are the passing time for turning left, turning right, and going straight, respectively. W₁ represents the width of the tunnel in which the termites advanced, and W₂ represents the width of the other tunnel encountered by the advancing termites. For the combinations of W₁ and W₂, (W₁, W₂) = (2, 2), (3, 3), (2, 3), (2, 4), (3, 4), and (4, 3), the values of τL, τR, and τS in each case were statistically equal. For (W₁, W₂) = (3, 2), (4, 2), and (4, 4), τS was shorter than τL and τR in each case. The experimental results are briefly discussed in relation to the termite foraging efficiency.

The subterranean termite, Reticulitermes speratus kyushuensis (Isoptera: Rhinotermitidae), excavate complex tunnel networks below the ground for foraging. The tunnels are either curved or meandering. In our previous study, results showed that termites passed smooth–rounded corners faster than they did around sharp corners. Smooth–rounded corners can be mathematically quantified by the curvature, representing the amount by which a geometric object deviates from a straight line. The present study explored how the time spent inside a tunnel changes in accordance with the degree of tunnel curvature. To do so, artificial tunnels with different curvatures were constructed in acryl substrates. Tunnels were 5 cm in length with widths of W = 2, 3, or 4 mm, and the distance between the two ends of the tunnel was D = 2, 3, 4, or 5 cm. A higher value of D signified a lower curvature. The time ( τ ) taken by a termite to pass through the tunnel was measured. In the case of W = 2 mm, the values of τ were statistically equal for D = 2, 3, or 4 cm, while τ for D = 5 cm was significantly lesser. In the case of W = 3, τ was statistically more for D = 2 and 3 cm than it was for D = 4 and 5 cm. For W = 4, τ was statistically equal for D = 2 and 3 cm, while τ for D = 4 cm was relatively shorter. Interestingly, the value of τ when D = 5 cm was statistically the same as D = 3 or 4 cm. These resulted from two types of termite behavior: biased walking and zigzag walking.

Environmental perturbations occur in ecosystems as the result of disturbance, which is closely related to ecosystem stability and resilience. To understand how perturbations can affect ecosystems, we constructed a spatially explicit lattice model to simulate the integrative predator–prey–grass relationships. In this model, a predator (or prey) gives birth to offspring, according to a specific birth probability, when it is able to feed on prey (or grass). When a predator or prey animal was initially introduced or newly born, its health state was set at a given high value. This state decreased by 1 with each time step. When the state of an animal decreased to zero, the animal was considered dead and was red from the system. In this model, the perturbation was defined as the sudden death of some portion of the population. The heterogeneous landscape was characterized by a parameter, H, which controlled the degree of heterogeneity. When H ≥ 0.6, the predator population size was positively influenced by the perturbation. However, the perturbation had little effect upon the population sizes of prey or grass, regardless of the value of H.

Subterranean termites excavate complex underground tunnels for foraging. Most tunnels comprise primary and secondary tunnels. Tunnels originating from the nest are called primary and those branching from the primary tunnels are named secondary tunnels; tertiary and quaternary tunnels are rarely observed. During foraging, termites may thus encounter a considerable number of tunnel-branching nodes. Directional selection at such a node is likely correlated to tunnel-growth activity because tunnels containing more termites have a higher probability of growth. In this study, we investigated how termites select the direction of ment at an artificially-designed branching node, by making chemical trails on filter paper, drawing lines using a ballpoint pen which contained the chemical substance that induces the termite to follow trails. The trails consisted of two lines: straight and branching. The branching line was drawn from the center of the straight line at an angle θ (10°, 20°,…, 90°). We then calculated the ratio of the directional selection as r = N_s/N_b, where N_s and N_b represent the number of straight and branching tunnels selected, respectively. The values of r were statistically classified into three groups based on the angle of the branching trail, as follows: 10° ≤ θ ≤ 20°, 30° ≤ θ ≤ 60°, and 70° ≤ θ ≤ 90°. Our paper briefly discusses the underlying mechanisms of the experimental results.

Growing interest in conservation and biodiversity increased the demand for accurate and consistent identification of biological objects, such as insects, at the level of individual or species. Among the identification issues, butterfly identification at the species level has been strongly addressed because it is directly connected to the crop plants for human food and animal feed products. However, so far, the widely-used reliable methods were not suggested due to the complicated butterfly shape. In the present study, we propose a novel approach based on a back-propagation neural network to identify butterfly species. The neural network system was designed as a multi-class pattern classifier to identify seven different species. We used branch length similarity (BLS) entropies calculated from the boundary pixels of a butterfly shape as the input feature to the neural network. We verified the accuracy and efficiency of our method by comparing its performance to that of another single neural network system in which the binary values (0 or 1) of all pixels on an image shape are used as a feature vector. Experimental results showed that our method outperforms the binary image network in both accuracy and efficiency.