We show that the conjectures by Matthews and Sumner (every 4-connected claw-free graph is hamiltonian), by Thomassen (every 4-connected line graph is hamiltonian) and by Fleischner (every cyclically 4-edge-connected cubic graph has either a 3-edgecoloring or a dominating cycle), which are known to be equivalent, are equivalent with the statement that every snark (i.e. a cyclically 4-edge-connec...

For odd primes p, we examine Ĥ(Aut(F2(p−1));Z(p)), the Farrell cohomology of the group of automorphisms of a free group F2(p−1) on 2(p − 1) generators, with coefficients in the integers localized at the prime (p) ⊂ Z. This extends results in [9] by Glover and Mislin, whose calculations yield Ĥ(Aut(Fn);Z(p)) for n ∈ {p− 1, p} and is concurrent with work by Chen in [6] where he calculates Ĥ(Aut(F...

Many correctness criteria have been proposed since linear logic was introduced and it is not clear how they relate to each other. In this paper, we study proof-nets and their correctness criteria from the perspective of dependency, as introduced by Mogbil and Jacobé de Naurois. We introduce a new correctness criterion, called DepGraph, and show that together with Danos' contractibility criterio...

Let C be a nontrivial cone and Y be a set in the «-dimensional Euclidean space. Denote by E( Y|C) the set of all efficient points of X with respect to C. It will be proven that under some adequate assumptions E(Y|C) is homeomorphic to a simplex while n = 2, and for n > 2 it is a contractible set. Furthermore, the set of all weak efficient points of X with respect to C is arcwise connected and i...

We present a pipeline that allows ordinary users to create deployable scissor linkages in arbitrary 3D shapes, whose mechanisms are inspired by Hoberman’s Sphere. From an arbitrary 3D model and a few user inputs, our method can generate a fabricable scissor linkage resembling that shape that aims to save as much space as possible in its most contracted state. Self-collisions are the primary obs...

How does imperfect contractibility of preferences in‡uence the governance of a contractual relationship? We analyze a two-party decision-making problem where the optimal decision is unknown at the time of contracting. In consequence, instead of contracting on the decision directly, the parties need to design a contract that will induce good decision-making in the future. We examine how environm...

Open forms of global constraints allow the addition of new variables to an argument during the execution of a constraint program. Such forms are needed for difficult constraint programming problems where problem construction and problem solving are interleaved. However, in general, filtering that is sound for a global constraint can be unsound when the constraint is open. This paper provides a ...

We associate a contractible “outer space” to any free product of groups G = G1 ∗ · · · ∗ Gq. It equals Culler-Vogtmann space when G is free, McCulloughMiller space when no Gi is Z. Our proof of contractibility (given when G is not free) is based on Skora’s idea of deforming morphisms between trees. Using the action of Out(G) on this space, we show that Out(G) has finite virtual cohomological di...

Given a Coxeter system (W,S) equipped with an involutive automorphism θ, the set of twisted identities is ι(θ) = {θ(w)w | w ∈ W}. We point out how ι(θ) shows up in several contexts and prove that if there is no s ∈ S such that sθ(s) is of odd order greater than 1, then the Bruhat order on ι(θ) is a graded poset with rank function ρ given by halving the Coxeter length. Under the same condition, ...

We consider the problem of estimating the locations of a set of points in a k-dimensional euclidean space given a subset of the pairwise distance measurements between the points. We focus on the case when some fraction of these measurements can be arbitrarily corrupted by large additive noise. Given that the problem is highly non-convex, we propose a simple semidefinite programming relaxation t...