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We present a theory of the multi-threshold second-order phase transition, and experimentally demonstrate the multi-threshold secondorder phase transition phenomenon. With carefully selected parameters, in an external cavity diode laser system, we observe secondorder phase transition with multiple (three or four) thresholds in the measured power-current-temperature three dimensional phase diagram. Such controlled death and revival of second-order phase transition sheds new insight into the nature of ubiquitous secondorder phase transition. Our theory and experiment show that the single threshold second-order phase transition is only a special case of the more general multi-threshold second-order phase transition, which is an even richer phenomenon. [14][15][16][17][18][19][20]. However, all of these SOPTs observed in experiments or investigated in theories so far possess only a single critical point (or threshold). In other words, there is only one critical point for symmetry breaking [5]. second-order phase transition, external cavity diode laser, Ginzburg-Landau free energyIn this work, we present a theory of the multi-threshold SOPT, and demonstrate experimentally the multi-threshold SOPT phenomenon in an external cavity diode laser system with carefully selected parameters. Our results show that the single threshold SOPT is only a special case of the more general multi-threshold SOPT. Our theory and experiment imply that previous studied fascinating SOPTs, such as spontaneous magnetization [21], superfluidity [22,23] and superconductivity [24][25][26], which are solely limited to single critical-point *Corresponding author (email: jbchen@pku.edu.cn) behavior, may be extended to the multi-threshold SOPT.

The pulse waveform characteristic point detection is important for non-invasively detecting cardiovascular parameters. A novel designed algorithm based on wavelet transform (WT) is developed. For some pulse waveforms, characteristic points exactly correspond to the zero-crossing of a wavelet with one vanishing moment, while the others incompletely correspond to. And characteristic points also correspond to the local extrema of a wavelet with two vanishing moment. So an algorithm combining a wavelet with one vanishing moment and another one with two vanishing moment is used to improve the detection rate of characteristic points. The results show that automatic identification of characteristics points has a high rate of accuracy.

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Switching control of micro-grid operation modes belongs to short time scale control level, this paper proposes three-tier structure of micro-grid energy management system suitable for switching control of micro-grid operation modes on the basis of the analysis of micro-grid operation mode switching requirements for the control system, and builds micro-grid central control system based on multi-agent technology aiming at the coordinated control of micro-grid operation mode switching, which will effectively enhance the implementation effect of switching control strategy, and play important role in achieving the seamless switching control of micro-grid operation modes.