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The comparison of distant atomic clocks is foundational to international timekeeping, global positioning and tests of fundamental physics. Optical-fibre links allow the most precise optical clocks to be compared, without degradation, over intracontinental distances up to thousands of kilometres, but intercontinental comparisons remain limited by the performance of satellite transfer techniques. Here we show that very long baseline interferometry (VLBI), although originally developed for radio astronomy and geodesy, can overcome this limit and compare remote clocks through the observation of extragalactic radio sources. We developed dedicated transportable VLBI stations that use broadband detection and demonstrate the comparison of two optical clocks located in Italy and Japan separated by 9,000 km. This system demonstrates performance beyond satellite techniques and can pave the way for future long-term stable international clock comparisons. Very long baseline interferometry is used to compare two optical clocks located in Japan and Italy through the observation of extragalactic radio sources. This approach overcomes limitations of the performance of satellite transfer techniques.

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.

For the aim to enable precise frequency transfer over earth radius scale distance, NICT developed a broadband VLBI system observing 3-14 GHz radio frequency range, and that was implemented in a pair of transportable 2.4m diameter VLBI stations and Kashima 34m diameter VLBI station. The small diameter VLBI stations installed in Medicina observatory of INAF (Italy) and NICT headquarters in Koganei (Japan) were used compare the atomic frequency standards. The poor sensitivity of VLBI observation with the small antenna pair was compensated by participation of the large diameter antenna for boosting the signal to noise ratio (SNR) of the VLBI observation. Owing to the broad observing frequency range, a few pico seconds precision of group delay is achieved on intercontinental baseline even with small diameter antenna. Advanced digital data acquisition with highspeed 16 GHz sampling enabled stable group delay measurement. A series of frequency transfer experiments was conducted during Oct. 2018 – Feb. 2019 by using the broadband VLBI system between ytterbium (Yb) optical lattice clock of INRiM (Italy) and strontium (Sr) lattice clock of NICT(Japan) separated by 9000km. The deviation of fractional frequency ratio between Yb and Sr was obtained by VLBI observation as y(Yb/Sr)=2.5(2.8)x10-16. The uncertainty in this experiment is evaluated not to be limited by the VLBI link itself, and further improvement is expected. Prospect of VLBI frequency link and uncertainty budget in VLBI observation is discussed in this report.

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).