Related papers: Sequential motion planning in connected sums of re…
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…
In this article, we study the effects of topological and smooth obstructions on the existence of rational homology complex projective planes that admit quotient singularities of small indices. In particular, we provide a classification of…
The maximum segment sum problem is to compute, given a list of integers, the largest of the sums of the contiguous segments of that list. This problem specification maps directly onto a cubic-time algorithm; however, there is a very elegant…
The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
Given two arbitrary closed sets in Euclidean space, a simple transversality condition guarantees that the method of alternating projections converges locally, at linear rate, to a point in the intersection. Exact projection onto nonconvex…
An isomorphism of symplectically tame smooth pseudocomplex structures on the complex projective plane which is a homeomorphism and differentiable of full rank at two points is smooth.
Sampling from distributions of implicitly defined shapes enables analysis of various energy functionals used for image segmentation. Recent work describes a computationally efficient Metropolis-Hastings method for accomplishing this task.…
We explicitly construct the twistor spaces of Joyce metrics with torus action that are not treated in Part I (math.DG/0603242). This finishes a construction of all the twistor spaces of Joyce metrics on the connected sum of four complex…
For real projective spaces, (a) the Euclidean immersion dimension, (b) the existence of axial maps, and (c) the topological complexity are known to be three facets of the same problem. But when it comes to embedding dimension, the classical…
Consider the projections of a finite set $A\subset R^n$ onto the coordinate hyperplanes. How small can the sum of the sizes of these projections be, given the size of $A$? In a different form, this problem has been studied earlier in the…
Let X be a subcomplex of the standard CW-decomposition of the n-dimensional torus. We exhibit an explicit optimal motion planning algorithm for X. This construction is used to calculate the topological complexity of complements of general…
We present in this paper a framework which leverages the underlying topology of a data set, in order to produce appropriate coordinate representations. In particular, we show how to construct maps to real and complex projective spaces,…
The topological complexity of a path-connected space $X,$ denoted $TC(X),$ can be thought of as the minimum number of continuous rules needed to describe how to move from one point in $X$ to another. The space $X$ is often interpreted as a…
Let A be a based subspace of Y. Under the assumptions that Y is path-connected and that the reduced diagonal map of A induces the zero map in all mod 2 reduced homology groups, we compute a formula for the mod 2 reduced Poincar\'{e} series…
In this paper, we focus attention on extending the topological conjugacy of adding machine maps and minimal systems to iterated function systems. We provide necessary and sufficient conditions for an iterated function system to be…
In this article we will apply complex projective metrics to sequences of complex transfer operators generated by Young towers, countable shifts and other types of distance expanding maps (possibly time dependent) with countable degrees. We…
A twisted sum in the category of topological abelian groups is a short exact sequence $0\to Y\to X \to Z\to 0$ where all maps are assumed to be continuous and open onto their images. The twisted sum splits if it is equivalent to $0\to Y\to…
We formalize and generalize the concept of a topological state-sum construction using the language of tensor networks. We give examples for constructions that are possibly more general than all state-sum constructions in the literature that…
In this paper, we describe geometrical constructions to obtain triangulations of connected sums of closed orientable triangulated 3-manifolds. Using these constructions, we show that it takes time polynomial in the number of tetrahedra to…