A matrix is free, or generic, if its nonzero entries are algebraically independent. Necessary and sufficient combinatorial conditions are presented for a complex free matrix to have a free Moore-Penrose inverse. These conditions extend previously known results for square, nonsingular free matrices. The result used to prove this characterization relates the combinatorial structure of a free matr...

Lignin is a heteropolymer that is thought to form in the cell wall by combinatorial radical coupling of monolignols. Here, we present a simulation model of in vitro lignin polymerization, based on the combinatorial coupling theory, which allows us to predict the reaction conditions controlling the primary structure of lignin polymers. Our model predicts two controlling factors for the beta-O-4 ...

In perturbative QED, the approximation is improved by summing more Feynman graphs; in nonperturbative QCD, by refining the lattice. Here we observe that in quantum gravity the two procedures may well be the same. We outline the combinatorial structure of spinfoam quantum gravity, define the continuum limit, and show that under general conditions refining foams is the same as summing over them. ...

Abstract A new combinatorial-probabilistic diagnostic entropy has been introduced. It describes the pair-wise sum of probabilities of system conditions that have to be distinguished during the diagnosing process. The proposed measure describes the uncertainty of the system conditions, and at the same time complexity of the diagnosis problem. Treating the assumed combinatorialdiagnostic entropy ...

This paper reports the results of over 130 auctions conducted under controlled conditions to examine the robustness of several auction mechanisms to allocate multiple objects. The simultaneous discrete auction process used by the Federal Communications Commission to allocate Personal Communications licenses was contrasted with a sequential auction and a combinatorial auction over a variety of d...

Tightness of a triangulated manifold is a topological condition, roughly meaning that any simplexwise linear embedding of the triangulation into Euclidean space is “as convex as possible”. It can thus be understood as a generalization of the concept of convexity. In even dimensions, super-neighborliness is known to be a purely combinatorial condition which implies the tightness of a triangulati...

Recent advances in computational science enable the creation of massive datasets of ever increasing resolution and complexity. Dealing effectively with such data requires new analysis techniques that are provably robust and that generate reproducible results on any machine. In this context, combinatorial methods become particularly attractive, as they are not sensitive to numerical instabilitie...

In this paper, we study convex relaxations of combinatorial penalty functions. Specifically, we consider models penalized by the sum of an `p-norm and a set function defined over the support of the unknown parameter vector, which encodes prior knowledge on supports. We consider both homogeneous and non-homogeneous convex relaxations, and highlight the difference in the tightness of each relaxat...

We consider arrangements of axis-aligned rectangles in the plane. A geometric arrangement specifies the coordinates of all rectangles, while a combinatorial arrangement specifies only the respective intersection type in which each pair of rectangles intersects. First, we investigate combinatorial contact arrangements, i.e., arrangements of interior-disjoint rectangles, with a triangle-free inte...

A Gauss paragraph is a combinatorial formulation of a generic closed curve with multiple components on some surface. A virtual string is a collection of circles with arrows that represent the crossings of such a curve. Every closed curve has an underlying virtual string and every virtual string has an underlying Gauss paragraph. A word-wise partition is a partition of the alphabet set of a Gaus...