Ultrafast fiber laser based on HfSe2 saturable absorber.

We demonstrate the HfSe2 saturable absorber (SA) for the generation of ultrafast pulse laser. The HfSe2 SA device is fabricated by integrating HfSe2 nanosheets (NSs) with a microfiber. The material and optical characteristics of HfSe2 NSs show their high quality. The nonlinear optical absorption of HfSe2 SA is measured with a modulation depth of 5.8%. Stable soliton mode-locked laser based on HfSe2 SA is realized at the central wavelength of 1561.43 nm with pulse duration of 297 fs and the maximum pulse energy of 2.68 nJ. Our soliton fiber laser has a maximum output power of 48.5 mW with a high slope efficiency of 12.8%, which indicate that HfSe2 is a good candidate of SA for high efficient ultrashort pulses generation.

A formal algorithm for verifying the validity of clustering results based on model checking.

The limitations in general methods to evaluate clustering will remain difficult to overcome if verifying the clustering validity continues to be based on clustering results and evaluation index values. This study focuses on a clustering process to analyze crisp clustering validity. First, we define the properties that must be satisfied by valid clustering processes and model clustering processes based on program graphs and transition systems. We then recast the analysis of clustering validity as the problem of verifying whether the model of clustering processes satisfies the specified properties with model checking. That is, we try to build a bridge between clustering and model checking. Experiments on several datasets indicate the effectiveness and suitability of our algorithms. Compared with traditional evaluation indices, our formal method can not only indicate whether the clustering results are valid but, in the case the results are invalid, can also detect the objects that have led to the invalidity.