We propose a weighted common subgraph (WCS) matching algorithm to find the most similar subgraphs in two labeled weighted graphs. WCS matching, as a natural generalization of the equal-sized graph matching or subgraph matching, finds wide application
s in many computer vision and machine learning tasks. In this paper, the WCS matching is first formulated as a combinatorial optimization problem over the set of partial permutation matrices. Then it is approximately solved by a recently proposed combinatorial optimization framework - Graduated NonConvexity and Concavity Procedure (GNCCP). Experimental comparisons on both synthetic graphs and real world images validate its robustness against noise level, problem size, outlier number, and edge density.
At present, fast waveform digitizing circuit is more and more employed in modern physics experiments for processing the signals from an array detector. A new fast waveform sampling digitizing circuit developed by us is presented in this paper. Differ
ent with the traditional waveform digitizing circuit constructed with analog to digital converter(ADC) or time to digital converter(TDC), it is developed based on domino ring sampler(DRS), a switched capacitor array(SCA) chip. A DRS4 chip is used as a core device in our circuit, which has a fast sampling rate up to five gigabit samples per second (GSPS). The circuit has advantages of high resolution, low cost, low power dissipation, high channel density and small size. The quite satisfactory results are acquired by the preliminary performance test of this circuit board. Eight channels can be provided by one board, which has a 1-volt input dynamic range for each channel. The circuit linearity is better than 0.1%, the noise is less than 0.5 mV (root mean square, RMS), and its time resolution is about 50ps. The several boards can be cascaded to construct a multi-board system. The good performances make the circuit board to be used not only for physics experiments, but also for other applications.
We investigate the mass spectrum and electromagnetic processes of charmonium system with the nonperturbative treatment for the spin-dependent potentials, comparing the pure scalar and scalar-vector mixing linear confining potentials. It is revealed t
hat the scalar-vector mixing confinement would be important for reproducing the mass spectrum and decay widths, and therein the vector component is predicted to be around 22%. With the state wave functions obtained via the full-potential Hamiltonian, the long-standing discrepancy in M1 radiative transitions of $J/psi$ and $psi^{prime}$ are alleviated spontaneously. This work also intends to provide an inspection and suggestion for the possible $cbar{c}$ among the copious higher charmonium-like states. Particularly, the newly observed X(4160) and X(4350) are found in the charmonium family mass spectrum as $M(2^1D_2)= 4164.9$ MeV and $M(3^3P_2)= 4352.4$ MeV, which strongly favor the $J^{PC}=2^{-+}, 2^{++}$ assignments respectively. The corresponding radiative transitions, leptonic and two-photon decay widths have been also predicted theoretically for the further experimental search.
