Related papers: Partitioning the projective plane and the dunce ha…
We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite…
A novel generalization of photon surfaces to the case of massive charged particles is given for spacetimes with at least one isometry, including stationary ones. A related notion of glued massive particle surfaces is also defined. These…
We recently defined a property of Morse shellability (and tileability) of finite simplicial complexes which extends the classical one and its relations with discrete Morse theory. We now prove that the product of two Morse tileable or…
In this study, a geometric version of an NP-hard problem ("Almost $2-SAT$" problem) is introduced which has potential applications in clustering, separation axis, binary sensor networks, shape separation, image processing, etc. Furthermore,…
Partition of unity methods (PUMs) on graphs are simple and highly adaptive auxiliary tools for graph signal processing. Based on a greedy-type metric clustering and augmentation scheme, we show how a partition of unity can be generated in…
Whether it is object detection, model reconstruction, laser odometry, or point cloud registration: Plane extraction is a vital component of many robotic systems. In this paper, we propose a strictly probabilistic method to detect finite…
We prove that at least $\Omega(n^{0.51})$ hyperplanes are needed to slice all edges of the $n$-dimensional hypercube. We provide a couple of applications: lower bounds on the computational complexity of parity, and a lower bound on the…
We show how the separability problem is dual to that of decomposing any given matrix into a conic combination of rank-one partial isometries, thus offering a duality approach different to the positive maps characterization problem. Several…
A scalable graphical method is presented for selecting, and partitioning datasets for the training phase of a classification task. For the heuristic, a clustering algorithm is required to get its computation cost in a reasonable proportion…
A rectangular partition is the partition of an (axis-aligned) rectangle into interior-disjoint rectangles. We ask whether a rectangular partition permits a "nice" drawing of its dual, that is, a straight-line embedding of it such that each…
Let S be a closed orientable surface of genus at least two, and let C be an arbitrary (complex) projective structure on S. We show that there is a decomposition of S into pairs of pants and cylinders such that the restriction of C to each…
We define graftable curves on real projective surfaces. In particular, we construct graftable ones in Hitchin case and show that real projective structures with the same Hitchin holonomy, carrying the same weight type, are related to each…
We provide an alternative, simpler proof of the existence of thick triangulations for noncompact $\mathcal{C}^1$ manifolds. Moreover, this proof is simpler than the original one given in \cite{pe}, since it mainly uses tools of elementary…
We show how to construct a cubic partial cube from any simplicial arrangement of lines or pseudolines in the projective plane. As a consequence, we find nine new infinite families of cubic partial cubes as well as many sporadic examples.
We prove a gluing theorem which allows to construct an ample divisor on a rational surface from two given ample divisors on simpler surfaces. This theorem combined with the Cremona action on the ample cone gives rise to an algorithm for…
We investigate the set of partial partitions of a finite set, ordered by inclusion. With this ordering the set of partial partitions can be studied as an abstract simplicial complex. We use the theory of shellable nonpure complexes to find…
The goal of this paper is to discuss the possibility of finding an algorithm that can give all distinct knots up to a desired complexity. Two such algorithms are presented, one based on projections on a plane, the other on closed…
We develop a new semi-algebraic proof system called Stabbing Planes which formalizes modern branch-and-cut algorithms for integer programming and is in the style of DPLL-based modern SAT solvers. As with DPLL there is only a single rule:…
We show that the problem of covering a set of points in the plane with a minimum number of guillotine cuts is NP-complete. To that end, first we present a new NP-completeness proof for the problem of covering points with disjoint line…
We address two sets of long-standing open questions in probability theory, from a computational complexity perspective: divisibility of stochastic maps, and divisibility and decomposability of probability distributions. We prove that finite…