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Abstract-A new method called Expanded Cholesky Method (ECM)is proposed in this paper. The method can be used to decompose sparse symmetric non-positive-definite finite element (FEM) matrices. There are some advantages of the ECM, such as low storage, simplicity and easy parallelization. Based on the method, multifrontal (MF) algorithm is applied in non-positive-definite FEM computation. Numerical results show that the hybrid ECM/MF algorithm is stable and effective. In comparison with Generalized Minimal Residual Method (GMRES) in FEM electromagnetic computation, hybrid ECM/MF technology has distinct advantages in precision. The proposed method can be used to calculate a class of non-positivedefinite electromagnetic problems.

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The relative roles of alpha beta or gamma delta T cells in protection against Actinobacillus actinomycetemcomitans were analysed by using mutant mice deficient in alpha beta or gamma delta T cell receptor (TCR). The dose of A. actinomycetemcomitans producing lethality for the TCR-alpha deficient mice was 25% of that for control C57BL/6 mice, while that of TCR-delta deficient mice was similar to that of C57BL/6 mice. Reverse transcription (RT)-PCR revealed that gamma delta T cells from the A. actinomycetemcomitans-infected alpha beta TCR deficient mice expressed significant levels of interferon (IFN)-gamma, interleukin (IL)-5 and IL-6 mRNA, whereas alpha beta T cells from A. actinomycetemcomitans-infected gamma delta TCR deficient mice exhibited significant levels of IFN-gamma and IL-2 mRNA. Delayed-type hypersensitivity (DTH) reactions against heat shock protein (HSP) 60 were prominently observed in A. actinomycetemcomitans-infected TCR-delta mutant and C57BL/6 mice, but were absent in TCR-alpha mutant mice, suggesting that the DTH response is exclusively dependent on HSP60-specific alpha beta T cells producing IFN-gamma and IL-2 mRNA. It was found that all the mice used exhibited similar levels of serum IgG and IgM responses against A. actinomycetemcomitans-specific antigens (whole cells and HSP60), suggesting that alpha beta as well as gamma delta T cells participate in the serum immune responses. In addition, the humoral antibody responses displayed in the TCR-alpha deficient mice implies resistance to A. actinomycetemcomitans infection. Thus, the resistance to A. actinomycetemcomitans infection may be ascribed mainly to alpha beta T cells, while gamma delta T cells can partially compensate for the alpha beta T cell defect.

The increasing control complexity of Noisy Intermediate-Scale Quantum (NISQ) systems underlines the necessity of integrating quantum hardware with quantum software. While mapping heterogeneous quantum-classical computing (HQCC) algorithms to NISQ hardware for execution, we observed a few dissatisfactions in quantum programming languages (QPLs), including difficult mapping to hardware, limited expressiveness, and counter-intuitive code. In addition, noisy qubits require repeatedly performed quantum experiments, which explicitly operate low-level configurations, such as pulses and timing of operations. This requirement is beyond the scope or capability of most existing QPLs. We summarize three execution models to depict the quantum-classical interaction of existing QPLs. Based on the refined HQCC model, we propose the Quingo framework to integrate and manage quantum-classical software and hardware to provide the programmability over HQCC applications and map them to NISQ hardware. We propose a six-phase quantum program life-cycle model matching the refined HQCC model, which is implemented by a runtime system. We also propose the Quingo programming language, an external domain-specific language highlighting timer-based timing control and opaque operation definition, which can be used to describe quantum experiments. We believe the Quingo framework could contribute to the clarification of key techniques in the design of future HQCC systems.