Related papers: Combining realization space models of polytopes

We describe a technique to obtain linear descriptions for polytopes from extended formulations. The simple idea is to first define a suitable lifting function and then to find linear constraints that are valid for the polytope and guarantee…

We complement our earlier position-space exploration of a recently proposed S-matrix for transplanckian scattering by a momentum-space analysis. As in the previous paper, we restrict ourselves to the case of axisymmetric collisions of…

In this paper we give gauged linear sigma model (GLSM) realizations of a number of geometries not previously presented in GLSMs. We begin by describing GLSM realizations of maps including Veronese and Segre embeddings, which can be applied…

In this paper, we present a unified approach using model category theory and an associative law to compare some classic variants of the geometric realization functor.

Some models providing shell-shaped static solutions with compact support (compactons) in 3+1 and 4+1 dimensions are introduced, and the corresponding exact solutions are calculated analytically. These solutions turn out to be topological…

There are many open problems and some mysteries connected to the realizations of the associahedra as convex polytopes. In this note, we describe three -- concerning special realizations with the vertices on a sphere, the space of all…

For an integer $n\geq 7$, we investigate the matroid realization space of a specific deformation of the regular $n$-gon along with its lines of symmetry. It turns out that this particular realization space is birational to the elliptic…

Let G be a connected complex simple Lie group with maximal compact subgroup U. Let g be the Lie algebra of G, and X = G/U be the associated Riemannian globally symmetric space of type IV. We have constructed three types of arithmetic…

Results of Koebe (1936), Schramm (1992), and Springborn (2005) yield realizations of $3$-polytopes with edges tangent to the unit sphere. Here we study the algebraic degrees of such realizations. This initiates the research on constrained…

Ellipsoids are a common representation for reachability analysis, because they can be transformed efficiently under affine maps, and allow conservative approximation of Minkowski sums, which let one incorporate uncertainty and linearization…

This paper approaches high-rank matrix completion (HRMC) by filling missing entries in a data matrix where columns lie near a union of subspaces, clustering these columns, and identifying the underlying subspaces. Current methods often lack…

Polymorphism offers rich and virtually unexplored space for discovering novel functional materials. To harness this potential approaches capable of both exploring the space of polymorphs and assessing their realizability are needed. One…

In areas such as kernel smoothing and non-parametric regression there is emphasis on smooth interpolation and smooth statistical models. Splines are known to have optimal smoothness properties in one and higher dimensions. It is shown, with…

We develop a bifurcation-theoretic description of Friedmann--Robertson--Walker cosmologies with a scalar field $\phi$, a barotropic fluid of index $\gamma$, and spatial curvature. For the strict exponential potential…

In this paper we try to find examples of integrable natural Hamiltonian systems on the sphere $S^2$ with the symmetries of each Platonic polyhedra. Although some of these systems are known, their expression is extremely complicated; we try…

The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higher-dimensional polyhedron has recently received increasing attention. In this paper (written for the…

We present a Mathematica package for performing algebraic and numerical computations in cosmological models based on supersymmetric theories. The programs allow for (I) evaluation and study of the properties of a scalar potential in a large…

Given two tuples of subspaces, can you tell whether the tuples are isomorphic? We develop theory and algorithms to address this fundamental question. We focus on isomorphisms in which the ambient vector space is acted on by either a unitary…

Any homogeneous polynomial $P(x, y, z)$ of degree $d$, being restricted to a unit sphere $S^2$, admits essentially a unique representation of the form $\lambda_0 + \sum_{k = 1}^d \lambda_k [\prod_{j = 1}^k L_{kj}]$, where $L_{kj}$'s are…

In the elastic shape analysis approach to shape matching and object classification, plane curves are represented as points in an infinite-dimensional Riemannian manifold, wherein shape dissimilarity is measured by geodesic distance. A…