Related papers: Sequential parametrized topological complexity of …

By a theorem of Edrei, an infinite, normalised totally nonnegative upper-triangular Toeplitz matrix is determined by a pair of nonnegative parameter sequences, the `Schoenberg parameters', where nonzero parameters correspond to the roots…

We study properties of the Weyl pseudometric associated with an action of a countable amenable group on a compact metric space. We prove that the topological entropy and the number of minimal subsets of the closure of an orbit are both…

We prove that many normal subgroups of the extended mapping class group of a surface with punctures are geometric, that is, that their automorphism groups and abstract commensurator groups are isomorphic to the extended mapping class group.…

In this paper we study symmetric motion planning algorithms, i.e. such that the motion from one state A to another B, prescribed by the algorithm, is the time reverse of the motion from B to A. We experiment with several different notions…

We find conditions which ensure that the topological complexity of a closed manifold $M$ with abelian fundamental group is nonmaximal, and see through examples that our conditions are sharp. This generalizes results of Costa and Farber on…

This paper presents a combinatorial analog of topological complexity for finite spaces. We demonstrate that this coincides with the genuine topological complexity of the original finite space, and constitutes an upper bound for the…

We prove new lower and upper bounds on the higher gonalities of finite graphs. These bounds are generalizations of known upper and lower bounds for first gonality to higher gonalities, including upper bounds on gonality involving…

In this note, we show that the epimorphic subgroups of an algebraic group are exactly the pull-backs of the epimorphic subgroups of its affinization. We also obtain epimorphicity criteria for subgroups of affine algebraic groups, which…

The synthesis of classical Computational Complexity Theory with Recursive Analysis provides a quantitative foundation to reliable numerics. Here the operators of maximization, integration, and solving ordinary differential equations are…

We provide isomorphism results for Hopf algebras that are obtained as graded twistings of function algebras on finite groups by cocentral actions of cyclic groups. More generally , we also consider the isomorphism problem for…

We couple projective limits of probability measures to direct limits of their symmetry groups. We show that the direct limit group is the group of symmetries of the projective limit probability measure. If projective systems of probability…

We establish a bound of $O(n^2k^{1+\eps})$, for any $\eps>0$, on the combinatorial complexity of the set $\T$ of line transversals of a collection $\P$ of $k$ convex polyhedra in $\reals^3$ with a total of $n$ facets, and present a…

We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…

We study the parameterized complexity of the graph isomorphism problem when parameterized by width parameters related to tree decompositions. We apply the following technique to obtain fixed-parameter tractability for such parameters. We…

This paper investigates the extension complexity of polytopes by exploiting the correspondence between non-negative factorizations of slack matrices and randomized communication protocols. We introduce a geometric characterization of…

In this paper we study some basic problems about Toeplitz subshifts of finite topological rank. We define the notion of a strong Toeplitz subshift of finite rank $K$ by combining the characterizations of Toeplitz-ness and of finite…

Introducing the notion of stabilized fundamental group for the complement of a branch curve in $CP^2$, we define effectively computable invariants of symplectic 4-manifolds that generalize those previously introduced by Moishezon and…

We give new lower bounds for the (higher) topological complexity of a space, in terms of the Lusternik-Schnirelmann category of a certain auxiliary space. We also give new lower bounds for the rational topological complexity of a space, and…

We revisit the isoperimetric inequalities for finitely generated groups introduced and studied by N. Varopoulos, T. Coulhon and L. Saloff-Coste. Namely we show that a lower bound on the isoperimetric quotient of finite subsets in a finitely…

We introduce a version of Farber's topological complexity suitable for investigating mechanical systems whose configuration spaces exhibit symmetries. Our invariant has vastly different properties to the previous approaches of Colman-Grant,…