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The ground-state kinetic energy of the t-J model is studied within the mean field approximation by using the fermion-spin transformation, the results show that the mean field ground-state kinetic energy is close to the numerical result at under dopings, and roughly consistent with the numerical result at optimal dopings. It is also shown that the frustration term J′ is favourable to diminish the range of the phase seperation in the t-J model.

In this paper, the slice-within-Gibbs sampler has been introduced as a method for estimating cognitive diagnosis models (CDMs). Compared with other Bayesian methods, the slice-within-Gibbs sampler can employ a wide-range of prior specifications; moreover, it can also be applied to complex CDMs with the aid of auxiliary variables, especially when applying different identifiability constraints. To evaluate its performances, two simulation studies were conducted. The first study confirmed the viability of the slice-within-Gibbs sampler in estimating CDMs, mainly including G-DINA and DINA models. The second study compared the slice-within-Gibbs sampler with other commonly used Markov Chain Monte Carlo algorithms, and the results showed that the slice-within-Gibbs sampler converged much faster than the Metropolis-Hastings algorithm and more flexible than the Gibbs sampling in choosing the distributions of priors. Finally, a fraction subtraction dataset was analyzed to illustrate the use of the slice-within-Gibbs sampler in the context of CDMs.

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The diversified top-k weight clique (DTKWC) search problem is an important generalization of the diversified top-k clique (DTKC) search problem with extensive applications, which extends the DTKC search problem by taking into account the weight of vertices. In this paper, we formulate DTKWC search problem using mixed integer linear program constraints and propose an efficient hybrid evolutionary algorithm (HEA-D) that combines a clique-based crossover operator and an effective simulated annealing-based local optimization procedure to find high-quality local optima. The experimental results show that HEA-D performs much better than the existing methods on two representative real-world benchmarks.