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In this note, we discuss a supplementary explanation about works of Takahashi and Tanaka, which are a kind of replication study of Wilks & Meara (2002), where they discuss the structure of learners’ mental lexicon network from the viewpoint of psycholinguistics. Here we mainly discuss some mathematical structures which support their studies latently. Using some simple random graph techniques, we propose that the role of “densities” is important and useful under some suitable assumptions. Then, we exhibit the effectiveness of our method by applying it to the data of experiments in Takahashi and Tanaka, where some inequalities obtained mathematically help us to investigate some of the aspects of the L2 mental lexicon network. Mathematical proofs and detailed discussion are collected in the final section, in which we give also mathematical interpretation on some models which were shown by computer simulations in previous works.

High precision distant frequency transfer techniques are desired to compare the advanced atomic frequency standards (AFS), which are newly developed by metrological research institutes in the world. Fiber-link frequency transfer is the technique of current highest highest accuracy, although distance of comparison is limited by fiberlink. Two-way satellite time and frequency transfer (TWSTFT) is the technique used for high precision time and frequency transfer. Its drawbacks are dependency on geographical availability of satellite and running cost including transponder of satellite, radio signal transmission license. Space geodetic techniques such as Global Navigation Satellite Systems (GNSS) and Very Long Baseline Interferometry (VLBI) observations are passive method as the next choices for time and frequency transfer. VLBI observation determines the spatial coordinates of the station and clock difference simultaneously. The analysis is theoretically based on inertial reference frame using natural radio source fixed in celestial sphere. These features have advantages of VLBI in the aspect of long term stability of comparison than the other space techniques which uses artificial signal sources. We have developed a broadband VLBI system named GALA-V [1], which is designed for advanced delay precision with observing broad observation frequency range (3-14GHz).