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The advance of additive manufacturing makes it possible to design spatially varying lattice structures with complex geometric configurations. The homogenized elastic properties of these periodic lattice structures are known to deviate significantly from isotropic behavior where orthotropic material symmetry is often assumed. This paper addresses the need for a robust homogenization method for evaluating anisotropy of periodic lattice structures including an understanding of how the elastic properties transform under rotation. Here, periodic boundary conditions are applied on two-material representative volume element (RVE) finite element models to evaluate the complete homogenized stiffness tensor. A constrained multi-output regression approach is proposed to evaluate the elasticity tensor components under any assumed material symmetry model. This approach is applied to various lattice structures including scaffold and surface-based Triply Periodic Minimal Surface (TPMS). Our approach is used to assess the accuracy of rotation for assumed anisotropic and orthotropic homogenized material models over a range of lattice structures. 

Tracking studies for invasive lionfish ( Pterois volitans and P. miles ) in the Western Atlantic can provide key information on habitat use to inform population control, but to date have likely underestimated home range size and movement due to constrained spatial and temporal scales. We tracked 35 acoustically tagged lionfish for >1 yr (March 2018-May 2019) within a 35 km 2 acoustic array in Buck Island Reef National Monument, St. Croix, US Virgin Islands (an area 10× larger than previous studies). Tracking lionfish at this scale revealed that home range size is 3-20 times larger than previously estimated and varies more than 8-fold across individuals (~48000-379000 m 2 ; average: 101000 m 2 ), with estimates insensitive to assumptions about potential mortality for low-movement individuals. Lionfish move far greater distances than previously reported, with 37% of fish traveling >1 km from the initial tagging site toward deeper habitats, and 1 individual moving ~10 km during a 10 d period. Movement rates, home range size, and maximum distance traveled were not related to lionfish size (18-35 cm total length) or lunar phase. Lionfish movement was lowest at night and greatest during crepuscular periods, with fish acceleration (m s -2 ) increasing with water temperature during these times. Our results help reconcile observed patterns of rapid recolonization following lionfish removal, and suggest complex drivers likely result in highly variable patterns of movement for similarly sized fish occupying the same habitat. Culling areas ≥ the average lionfish home range size identified here (i.e. ~10 ha) or habitat patches isolated by ≥ ~180 m (radius of average home range) may minimize subsequent recolonization. If the shallow-deep long-distance movements observed here are unidirectional, mesophotic habitats may require culling at relatively greater frequencies to counteract ongoing migration.