Two groups of Chinese four-year-olds and their parents' interaction in joint activities were analyzed and compared. The children in Group 1 were high scorers in written number skills and the children in Group 2 were low scorers. Eighty-five dyads participated in four separate 15-minute joint activities such as book reading, mathematical worksheets, blank paper and blocks. A mini-questionnaire was also administered. The results indicated that a wide variety of mathematics and interactive strategies were involved in the activities, that there was no difference in the frequency of mathematical events occurring in the activities between the two groups, that more parents in Group 1 used several more positive strategies than the parents in Group 2, that more children in Group 2 had trouble remaining engaged in the activity, and that the frequency and the quality of parent-child joint activities at home, such as book reading and mathematical worksheets, were possible contributors to children's development of mathematics.

A free-space communication scheme is proposed based on orbital angular momentum (OAM) states and pulse position modulation (PPM). It can not only improve the channel capacity, but also be suitable for single-photon detection to realize the communication in the case of ultra-weak light. A parallel coding method is proposed to realize high-capacity and low bit error rate (BER) communication under high background. Theoretical simulation and experimental results show that the scheme can effectively suppress the background noise. The BER is as low as 1.27 × 10 −5 under the condition of 16 OAM states, 16 single-photon detectors (SPDs) coincidence, and the background noise of 10 7 counts per second. The BER performance is an order of magnitude better than the traditional PPM, and the channel capacity is increased by 12 times. This work provides an effective solution for deep space high-speed and low BER communication.

We demonstrate a portable system integrated with time comparison, absolute distance ranging, and optical communication (TRC) to meet the requirements of space gravitational wave detection. A 1 km free-space asynchronous two-way optical link is performed. The TRC realizes optical communication with 7.7 × 10 −5 bit error rate with a Si avalanche photodiode singlephoton detector, while the signal intensity is 1.4 photons per pulse with the background noise of 3 × 10 4 counts per second. The distance measurement uncertainty is 48.3 mm, and time comparison precision is 162.4 ps. In this TRC system, a verticalcavity surface-emitting laser diode with a power of 9.1 μW is used, and the equivalent receiving aperture is 0.5 mm. The TRC provides a miniaturization solution for ultra-long distance inter-satellite communication, time comparison, and ranging for space gravitational wave detectors.