43 citations · 238 across the 16 of their papers we have counts for
16 papers
A recursive theta body for hypergraphs
Davi Castro-Silva, Fernando Mário de Oliveira Filho, Lucas Slot +1
The theta body of a graph, introduced by Grötschel, Lovász, and Schrijver in 1986, is a tractable relaxation of the independent-set polytope derived from the Lovász theta number. I…
A recursive Lovász theta number for simplex-avoiding sets
Davi Castro-Silva, Fernando Mário de Oliveira Filho, Lucas Slot +1
We recursively extend the Lovász theta number to geometric hypergraphs on the unit sphere and on Euclidean space, obtaining an upper bound for the independence ratio of these hyper…
-point semidefinite programming bounds for equiangular lines
David de Laat, Fabrício Caluza Machado, Fernando Mário de Oliveira Filho +1
We give a hierarchy of -point bounds extending the Delsarte-Goethals-Seidel linear programming -point bound and the Bachoc-Vallentin semidefinite programming -point bound…
Complete positivity and distance-avoiding sets
Evan DeCorte, Fernando Mário de Oliveira Filho, Frank Vallentin
We introduce the cone of completely-positive functions, a subset of the cone of positive-type functions, and use it to fully characterize maximum-density distance-avoiding sets as…
Improving the semidefinite programming bound for the kissing number by exploiting polynomial symmetry
Fabrício Caluza Machado, Fernando Mário de Oliveira Filho
The kissing number of is the maximum number of pairwise-nonoverlapping unit spheres that can simultaneously touch a central unit sphere. Mittelmann and Vallentin (20…
New upper bounds for the density of translative packings of three-dimensional convex bodies with tetrahedral symmetry
Maria Dostert, Cristóbal Guzmán, Fernando Mário de Oliveira Filho +1
In this paper we determine new upper bounds for the maximal density of translative packings of superballs in three dimensions (unit balls for the -norm) and of Platonic and…
Better bounds for planar sets avoiding unit distances
Tamás Keleti, Máté Matolcsi, Fernando Mário de Oliveira Filho +1
A -avoiding set is a subset of that does not contain pairs of points at distance . Let denote the maximum fraction of that c…
Mathematical optimization for packing problems
Fernando Mário de Oliveira Filho, Frank Vallentin
During the last few years several new results on packing problems were obtained using a blend of tools from semidefinite optimization, polynomial optimization, and harmonic analysi…
Computing upper bounds for the packing density of congruent copies of a convex body
Fernando Mário de Oliveira Filho, Frank Vallentin
In this paper we prove a theorem that provides an upper bound for the density of packings of congruent copies of a given convex body in ; this theorem is a generaliza…
Spectral bounds for the independence ratio and the chromatic number of an operator
Christine Bachoc, Evan DeCorte, Fernando Mario de Oliveira Filho +1
We define the independence ratio and the chromatic number for bounded, self-adjoint operators on an L^2-space by extending the definitions for the adjacency matrix of finite graphs…
Upper bounds for packings of spheres of several radii
David de Laat, Fernando Mario de Oliveira Filho, Frank Vallentin
We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean…
Grothendieck inequalities for semidefinite programs with rank constraint
Jop Briet, Fernando Mario de Oliveira Filho, Frank Vallentin
Grothendieck inequalities are fundamental inequalities which are frequently used in many areas of mathematics and computer science. They can be interpreted as upper bounds for the…
A quantitative version of Steinhaus' theorem for compact, connected, rank-one symmetric spaces
Fernando Mário de Oliveira Filho, Frank Vallentin
Let , , ... be a sequence of positive numbers that converges to zero. A generalization of Steinhaus' theorem due to Weil implies that, if a subset of a homogeneous Rieman…
The positive semidefinite Grothendieck problem with rank constraint
Jop Briet, Fernando Mario de Oliveira Filho, Frank Vallentin
Given a positive integer n and a positive semidefinite matrix A = (A_{ij}) of size m x m, the positive semidefinite Grothendieck problem with rank-n-constraint (SDP_n) is maximize…
Fourier analysis, linear programming, and densities of distance avoiding sets in R^n
Fernando Mario de Oliveira Filho, Frank Vallentin
In this paper we derive new upper bounds for the densities of measurable sets in R^n which avoid a finite set of prescribed distances. The new bounds come from the solution of a li…
Lower bounds for measurable chromatic numbers
Christine Bachoc, Gabriele Nebe, Fernando Mario de Oliveira Filho +1
The Lovasz theta function provides a lower bound for the chromatic number of finite graphs based on the solution of a semidefinite program. In this paper we generalize it so that i…