Linear Relation Analysis [CH78] suffers from the cost of operations on convex polyhedra, which can be exponential with the number of involved variables. In order to reduce this cost, we propose to detect when a polyhedron is a Cartesian product of polyhedra of lower dimensions, i.e., when groups of variables are unrelated with each other. Classical operations are adapted to work on such factore...

In my doctoral dissertation (directed by W. P. Thurston) I studied the geometry of convex polyhedra in hyperbolic 3-space H3, and succeeded in producing a geometric characterization of dihedral angles of compact convex polyhedra by reducing the question to a convex isometric embedding problem in the De Sitter sphere, and resolving this problem. In particular, this produced a simple alternative ...

We present an abstraction of the effect of procedures through convex sets of transition matrices. Conditional branching is handled by postponing the conditional evaluation after the procedure call. In order to obtain an effective analysis convex sets are approximated by polyhedra. For an efficient implementation we approximate polyhedra by means of simplices. In [CH78], Cousot and Halbwachs pre...

This thesis introduces a new data structure, the Implicit Real Vector Automaton (IRVA), suited for representing symbolically polyhedra, i.e., regions of n-dimensional space defined by finite Boolean combinations of linear inequalities. IRVA can represent exactly arbitrary convex and non-convex polyhedra, including features such as open and closed boundaries, unconnected parts, and non-manifold ...

We propose techniques for the verification of hybrid systems using template polyhedra, i.e., polyhedra whose inequalities have fixed expressions but with varying constant terms. Given a hybrid system description and a set of template linear expressions as inputs, our technique constructs over-approximations of the reachable states using template polyhedra. Therefore, operations used in symbolic...

We address the problem of computation upon Z Z-polyhedra which are intersections of polyhedra and integral lattices. We introduce a canonic representation for Z Z-polyhedra which allow to perform comparisons and transformations of Z Z-polyhedra with the help of a computational kernel on polyhedra. This contribution is a step toward the manipulation of images of polyhedra by aane functions, and ...

Low-cost, large-scale production of the baculovirus Autographa californica multiple nucleopolyhedrovirus (AcMNPV) using continuous insect cell culture is seriously hindered by the accumulation of AcMNPV mutants. Specifically, few-polyhedra (FP) mutants, with a reduced yield of occluded virus (polyhedra) and decreased infectivity, usually accumulate upon passaging in cell culture. FP mutations r...

We study the uniqueness of minimal liftings of cut-generating functions obtained from maximal lattice-free polyhedra. We prove a basic invariance property of unique minimal liftings for general maximal lattice-free polyhedra. This generalizes a previous result by Basu, Cornuéjols and Köppe [BCK12] for simplicial maximal lattice-free polytopes, thus completely settling this fundamental question ...

The regular polyhedra have the highest order of 3D symmetries and are exceptionally attractive templates for (self)-assembly using minimal types of building blocks, from nano-cages and virus capsids to large scale constructions like glass domes. However, they only represent a small number of possible spherical layouts which can serve as templates for symmetric assembly. In this paper, we formal...

Convex polyhedra, commonly employed for the analysis and verification of both hardware and software, may be defined either by a finite set of linear inequality constraints or by finite sets of generating points and rays of the polyhedron. Although most implementations of the polyhedral operations assume that the polyhedra are topologically closed (i.e., all the constraints defining them are non...