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We present an efficient post-processing method for calculating the electronic structure of nanosystems based on the divide-and-conquer approach to density functional theory (DC-DFT), in which a system is divided into subsystems whose electronic structure is solved separately. In this post process, the Kohn-Sham Hamiltonian of the total system is easily derived from the orbitals and orbital energies of subsystems obtained by DC-DFT without time-consuming and redundant computation. The resultant orbitals spatially extended over the total system are described as linear combinations of the orbitals of the subsystems. The size of the Hamiltonian matrix can be much reduced from that for conventional calculation, so that our method is fast and applicable to general huge systems for investigating the nature of electronic states.
Compressed sensing (CS) theory assures us that we can accurately reconstruct magnetic resonance images using fewer k-space measurements than the Nyquist sampling rate requires. In traditional CS-MRI inversion methods, the fact that the energy within
Virtual memory (VM) is critical to the usability and programmability of hardware accelerators. Unfortunately, implementing accelerator VM efficiently is challenging because the area and power constraints make it difficult to employ the large multi-le
Spectral clustering is one of the most popular clustering methods. However, how to balance the efficiency and effectiveness of the large-scale spectral clustering with limited computing resources has not been properly solved for a long time. In this
Providing system-size independent lower bounds on the spectral gap of local Hamiltonian is in general a hard problem. For the case of finite-range, frustration free Hamiltonians on a spin lattice of arbitrary dimension, we show that a property of the
We consider the learning of algorithmic tasks by mere observation of input-output pairs. Rather than studying this as a black-box discrete regression problem with no assumption whatsoever on the input-output mapping, we concentrate on tasks that are