Tunnel volumes excavated by laboratory groups of the Formosan subterranean termite, Coptotermes formosanus Shiraki (Isoptera: Rhinotermitidae), and the eastern subterranean termite, Reticulitermes flavipes (Kollar) (Isoptera: Rhinotermitidae) were measured by using two-dimensional foraging arenas. Group sizes of 20, 40, 60, 80, 100, and 200 termites were used for the study. Analysis of the images of tunnels taken hourly showed tunnel volume increased and eventually reached equilibrium for both termite species, but Co. formosanus reached the equilibrium faster at lower volume than R. flavipes. Co. formosanus constructed fewer primary tunnels with less branching than R. flavipes and no additional tunneling activity was observed once the tunnel volume reached equilibrium. R. flavipes, however, continued tunnel excavation even after reaching equilibrium, but the equilibrated volume was maintained by filling unused tunnels with sand excavated from newly dug tunnels. For each termite species, the tunnel volume equilibrium was proportional to the group size. The mean individual tunnel volume (mm³ per termite ± SE) of all group sizes computed over the whole experiment was significantly higher for R. flavipes (198.58 ± 1.21) than for Co. formosanus (84.24 ± 0.59). The shape of the growth curves for tunnel volumes indicated the presence of a double feedback system for termite tunneling activity, and we suggest that the positive relationship between nest and population size previously reported for numerous termites species is the result of the self-organized nest-building activity.

The foraging territory of the Formosan subterranean termite, extit{ Coptotermes formosanus} Shiraki, was simulated by using a lattice model in order to understand how the fractal landscape structure affects the foraging territory and interacts with the territory size. Each lattice cell had a value ranging from 0.0 to 1.0, interpreted as a transition probability, extit{P} trans   , which represents the spatially-distributed property of the fractal landscape. The fractal landscape was characterized by a parameter, extit{H}, controlling aggregation of lattice cells with higher values of extit{P} trans   . At the beginning of the simulation, extit{N} (=30, 50, 80 and 100, depending on the condition) termite cells, each representing a founding pair, were randomly distributed within the lattice space. After fourteen simulation years, all territories had reached a steady state in which their shapes did not change over time. In this state, we investigated the size distribution of territories in size descending order. For large-sized territories (rank <  10 -- 20), the size increase with increasing extit{H}, which resulted from the fact that high extit{H }values indicated that fewer but larger, areas of contiguous cells with high values of extit{P} trans   were present. For small-sized territories (rank >  20), extit{H} had little affect on the territory size.

The process through which the Formosan subterranean termite, Coptotermes formosanus Shiraki, establishes territory was simulated using a lattice model in order to understand how such territories are formed from their seeds-founding pairs that fall to the ground every year. The model incorporated, summer–winter cycles, and fourteen years were simulated. Simulated pairs fell to random sites within the lattice space at the beginning of every summer, and their territories grew during the summer season, and shrunk during the winter season. Fourteen years were sufficient for territory size and shape to become stable over time. The simulation revealed that only pairs introduced at t = 0 had established large territories by the end of the simulation (t = 14). Pairs that were introduced later expanded their territory a little at first, but ultimately shrunk back into a single-cell-sized or small-sized territory. This means that stable-state territory size is mostly determined by when that territory was initially established.

Certificateless cryptography eliminates the need of certificates in the Public Key Infrastructure and solves the inherent key escrow problem in the identity-based cryptography. Recently, Huang et al. proposed two certificateless signature schemes from pairings. They claimed that their first short certificateless signature scheme is provably secure against a normal type I adversary and a super type II adversary. In this paper, we show that their short certificateless signature scheme is broken by a type I adversary who can replace users’ public keys and access to the signing oracle under the replaced public keys.

In this note we give a new proof of Witt's formula for Euler numbers, which are related to some known or new identities involving the Euler numbers. We also obtain a brief proof of a classical result on Euler numbers modulo of two due to M.A. Stern using the approach of p-adic integration, which was recently proved by G. Liu, and Z.-W. Sun. Finally some explicit formulas for Genocchi numbers are proved and applications are given.

For an infinite family of modular forms constructed from Klein forms we provide certain explicit formulas for their Fourier coefficients by using the theory of basic hypergeometric series (Theorem 2). By making use of these modular forms we investigate the bases of the vector spaces of modular forms of some levels (Theorem 5) and find its application.