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We discuss the salient features of Zolotarev optimal rational approximation for the inverse square root function, in particular, for its applications in lattice QCD with overlap Dirac quark. The theoretical error bound for the matrix-vector multiplication H w (H 2 w ) −1/2 Y is derived. We check that the error bound is always satisfied amply, for any QCD gauge configurations we have tested. An empirical formula for the error bound is determined, together with its numerical values ( by evaluating elliptic functions ) listed in Table 2 as well as plotted in Figure 3. Our results suggest that with Zolotarev approximation to (H 2 w ) −1/2 , one can practically preserve the exact chiral symmetry of the overlap Dirac operator to very high precision, for any gauge configurations on a finite lattice.

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Graphic design thinking is a key skill for landscape architects, but little is known about the links between the design process and brain activity. Based on Goel’s frontal lobe lateralization hypothesis (FLLH), we used functional magnetic resonance imaging (fMRI) to scan the brain activity of 24 designers engaging in four design processes—viewing, copy drawing, preliminary ideas, and refinement—during graphic design thinking. The captured scans produced evidence of dramatic differences between brain activity when copying an existing graphic and when engaging in graphic design thinking. The results confirm that designs involving more graphic design thinking exhibit significantly more activity in the left prefrontal cortex. These findings illuminate the design process and suggest the possibility of developing specific activities or exercises to promote graphic design thinking in landscape architecture.