State Differentiation by Transient Truncation in Coupled Threshold Dynamics

Dynamics with a threshold input--output relation commonly exist in gene, signal-transduction, and neural networks. Coupled dynamical systems of such threshold elements are investigated, in an effort to find differentiation of elements induced by the interaction. Through global diffusive coupling, novel states are found to be generated that are not the original attractor of single-element threshold dynamics, but are sustained through the interaction with the elements located at the original attractor. This stabilization of the novel state(s) is not related to symmetry breaking, but is explained as the truncation of transient trajectories to the original attractor due to the coupling. Single-element dynamics with winding transient trajectories located at a low-dimensional manifold and having turning points are shown to be essential to the generation of such novel state(s) in a coupled system. Universality of this mechanism for the novel state generation and its relevance to biological cell differentiation are briefly discussed.Comment: 8 pages. Phys. Rev. E. in pres

Integral representations of q-analogues of the Hurwitz zeta function

Two integral representations of q-analogues of the Hurwitz zeta function are established. Each integral representation allows us to obtain an analytic continuation including also a full description of poles and special values at non-positive integers of the q-analogue of the Hurwitz zeta function, and to study the classical limit of this q-analogue. All the discussion developed here is entirely different from the previous work in [4]Comment: 14 page

Demonstration of 2.65 / 3.3 Gbit per sec X Band Radiowave Down Link Communications from LEO Small Satellite

This paper reports our new communication system and downlink demonstrations with a small satellite of 2.65 Gbps data rate with 64 APSK modulation and 3.3Gbps data rate with 256 APSK modulation by utilizing two circular polarization channels of X band. We have developed an on-board X-band transmitter, an on-board dual circularly polarized-wave antenna with 17dBi gain and \u3e37dB Cross Polarization Discrimination (XPD) and a 10m ground station with 39dB/K of G/T and \u3e37dB XPD for low-crosstalk polarization multiplexing. Since there are not real- time demodulator systems in such high communication speed, the downlinked signals are stored in a data recorder at an antenna site. Afterwards, we decode downlinked signals by using our non-real-time software demodulator. The system was demonstrated in orbit the RAPid Innovative payload demonstration Satellite (RAPIS-1) of JAXA in 2019. We have achieved 2.65 Gbps and 3.3Gbps communication speed in the X-band for LEO satellite at 300 M symbols per second (Msps) and polarization multiplexing of 64APSK (coding rate 4/5) and 256APSK (coding rate 3/4) following DVB-S2X protocol with roll-off factor α=0.05. The communication speeds correspond to of frequency efficiency 8.4 bit/s/Hz and 10.8 bit/s/Hz of frequency utilization efficiency. As far as authors know, these direct downlink communication speeds and frequency utilization efficiencies are the highest ones at present in LEO satellites, excluding bent-pipe communication systems