The QAP-polytope and the graph isomorphism problem
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Combinatorial Optimization"
DOI: 10.1007/s10878-018-0266-x
Abstract: In this paper we propose a geometric approach to solve the Graph Isomorphism (GI in short) problem. Given two graphs $$G_1, G_2$$G1,G2, the GI problem is to decide if the given graphs are isomorphic i.e.,… read more here.
Keywords: graph isomorphism; polytope; graphs isomorphic; problem ... See more keywords
On the Banach–Mazur distance to cross-polytope
Sign Up to like & getrecommendations! Published in 2019 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2019.01.013
Abstract: Let $n\geq 3$, and let $B_1^n$ be the standard $n$-dimensional cross-polytope (i.e. the convex hull of standard coordinate vectors and their negatives). We show that there exists a symmetric convex body $\mathcal G_m$ in ${\mathbb… read more here.
Keywords: cross polytope; polytope; banach mazur; mazur distance ... See more keywords
Designing a polytope for use in a broad-spectrum dengue virus vaccine
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Taibah University Medical Sciences"
DOI: 10.1016/j.jtumed.2017.11.002
Abstract: Objectives Dengue virus surface proteins are often used in the development of vaccines that protect against dengue virus infection. However, the surface proteins on the four serotypes of dengue virus display high variation, which increases… read more here.
Keywords: dengue virus; vaccine; use broad; polytope ... See more keywords
Frustration-induced complexity in order-disorder transitions of the J_{1}-J_{2}-J_{3} Ising model on the square lattice.
Sign Up to like & getrecommendations! Published in 2022 at "Physical review. E"
DOI: 10.1103/physreve.106.014105
Abstract: We revisit the field-free Ising model on a square lattice with up to third-neighbor (NNNN) interactions, also known as the J_{1}-J_{2}-J_{3} model, in the mean-field approximation. Using a systematic enumeration procedure, we show that the… read more here.
Keywords: order disorder; ising model; polytope; model ... See more keywords
Polytopic Matrix Factorization: Determinant Maximization Based Criterion and Identifiability
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Signal Processing"
DOI: 10.1109/tsp.2021.3112918
Abstract: We introduce Polytopic Matrix Factorization (PMF) as a novel data decomposition approach. In this new framework, we model input data as unknown linear transformations of some latent vectors drawn from a polytope. In this sense,… read more here.
Keywords: matrix; polytope; latent vectors; factorization ... See more keywords
COMBINATORIAL INSCRIBABILITY OBSTRUCTIONS FOR HIGHER DIMENSIONAL POLYTOPES
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DOI: 10.1112/mtk.12051
Abstract: For $3$-dimensional convex polytopes, inscribability is a classical property that is relatively well-understood due to its relation with Delaunay subdivisions of the plane and hyperbolic geometry. In particular, inscribability can be tested in polynomial time,… read more here.
Keywords: dimensional polytopes; higher dimensional; cyclic polytopes; combinatorial inscribability ... See more keywords
Convex cones spanned by regular polytopes
Sign Up to like & getrecommendations! Published in 2022 at "Advances in Geometry"
DOI: 10.1515/advgeom-2021-0041
Abstract: Abstract We study three families of polyhedral cones whose sections are regular simplices, cubes, and crosspolytopes. We compute solid angles and conic intrinsic volumes of these cones. We show that several quantities appearing in stochastic… read more here.
Keywords: regular polytopes; polytope; cones spanned; geometry ... See more keywords