Pairs of Full-Rank Lattices With Parallelepiped-Shaped Common Fundamental Domains

We provide a complete characterization of pairs of full-rank lattices in $\mathbb{R}^{d}$ which admit common connected fundamental domains of the type $N\left[ 0,1\right) ^{d}$ where $N$ is an invertible matrix of order $d.$ Using our characterization, we construct several pairs of lattices of the type $\left( M\mathbb{Z}^{d},\mathbb{Z}^{d}\right)$ which admit a common fundamental domain of the type $N\left[ 0,1\right) ^{d}.$ Moreover, we show that for $d=2,$ there exists an uncountable family of pairs of lattices of the same volume which do not admit a common connected fundamental domain of the type $N\left[ 0,1\right) ^{2}.

Intended Consequences Statement in Conservation Science and Practice

As the biodiversity crisis accelerates, the stakes are higher for threatened plants and animals. Rebuilding the health of our planet will require addressing underlying threats at many scales, including habitat loss and climate change. Conservation interventions such as habitat protection, management, restoration, predator control, trans location, genetic rescue, and biological control have the potential to help threatened or endangered species avert extinction. These existing, well-tested methods can be complemented and augmented by more frequent and faster adoption of new technologies, such as powerful new genetic tools. In addition, synthetic biology might offer solutions to currently intractable conservation problems. We believe that conservation needs to be bold and clear-eyed in this moment of great urgency

Two Signed Associahedra

The associahedron is a convex polytope whose vertices correspond to triangulations of a convex polygon. We define two signed or hyperoctahedral analogues of the associahedron, one of which is shown to be a simple convex polytope, and the other a regular CW-sphere

LUMINES strategies

SCOPUS: cp.kProceedings of the 5th International Conference on Computers and Games (CG 2006)info:eu-repo/semantics/publishe