The tree complex is a simplicial defined in recent work of Belk, Lanier, Margalit, and Winarski with applications to mapping class groups dynamics. This article introduces connection between this setting the convex polytopes known as associahedra cyclohedra. Specifically, we describe characterization these using planar embeddings trees show that barycentric subdivision polyhedral cell for which...

We have demonstrated a new strategy to synthesize Au mesocages using polyhedral Cu(2)O templates. The obtained polyhedral Au mesocages show a strong shape effect in highly sensitive single-particle surface-enhanced Raman spectroscopy (sp-SERS).

In this paper, we prove the existence of acute triangulations for general polyhedral surfaces. We also show how to obtain nonobtuse subtriangulations of triangulated polyhedral surfaces. © 2008 Elsevier Ltd. All rights reserved.

The polyhedral model is an algebraic framework for affine program representations and transformations for enhancing locality and parallelism. Compared with traditional AST-based transformation frameworks, the polyhedral model can easily handle imperfectly nested loops and complex data dependences within and across loop nests in a unified framework. On the other hand, AST-based transformation fr...

We prove a result relating the Euler characteristic of a polyhedral closed homology manifold to the finite space associated with a triangulation of the manifold. We then give a new proof that polyhedral closed homology manifolds have Euler characteristic 0.

Several recent papers have explored families of rational polyhedra whose integer points are in bijection with certain numerical semigroups. One such family, first introduced by Kunz, has semigroups fixed multiplicity, and another, Hellus Waldi, corresponding to oversemigroups two generators. In this paper, we provide a combinatorial framework from which study both polyhedra. We introduce new fa...

The goal of this thesis is to design algorithms that run with better complexity when compiling or parallelizing loop programs. The framework within which our algorithms operate is the polyhedral model of compilation which has been successful in the design and implementation of complex loop nest optimizers and parallelizing compilers. The algorithmic complexity and scalability limitations of the...

We present an algorithm for computing exact shortest paths, and consequently distances, from a generalized source (point, segment, polygonal chain or polygonal region) on a polyhedral terrain in which polygonal chain or polygon obstacles are allowed. We also present algorithms for computing discrete Voronoi diagrams of a set of generalized sites (points, segments, polygonal chains or polygons) ...

Let A' be a semisimple algebraic monoid with unit group G. Associated with E is its polyhedral root system (X, 0, C), where X = X(T) is the character group of the maximal torus T c G, $ c X(T) is the set of roots, and C = X(T) is the character monoid of T c E (Zariski closure). The correspondence £-»(A\ O, C) is a complete and discriminating invariant of the semisimple monoid £, extending the w...