In this article we focus on constructing an algorithm that automatizes the generation of LPN solving algorithms from the considered parameters. When searching for an algorithm to solve an LPN instance, we make use of the existing techniques and optimize their use. We formalize an LPN algorithm as a path in a graph G and our algorithm is searching for the optimal paths in this graph. The results...

Spaces with radially symmetric curvature at base point p are shown to be diffeomorphic to space forms. Furthermore, they are either isometric to Rn or Sn under a radially symmetric metric, to RPn with Riemannian universal covering of Sn equipped with a radially symmetric metric, or else have constant curvature outside a metric ball of radius equal to the injectivity

If g(t) is a three-dimensional Ricci flow solution, with sectional curvatures that are O(t) and diameter that is O(t 1 2 ), then the pullback Ricci flow solution on the universal cover approaches a homogeneous expanding soliton.

We address the problem of covering points with orthogonal polygons. Specifically, given a set of n grid-points in the plane each designated in advance with either a horizontal or vertical reading, we investigate the existence of an orthogonal polygon covering these n points in such a way that each edge of the polygon covers exactly one point and each point is covered by exactly one edge with th...

We study the fundamental group of one–dimensional spaces. Among the results we prove are that the fundamental group of a second countable, connected, locally path connected, one–dimensional metric space is free if and only if it is countable if and only if the space has a universal cover and that the fundamental group of a compact, one–dimensional, connected metric space embeds in an inverse li...

We prove several structural results on definably compact groups G in o-minimal expansions of real closed fields such as (i) G is definably an almost direct product of a semisimple group and a commutative group, (ii) (G, ·) is elementarily equivalent to (G/G, ·). We also prove results on the internality of finite covers of G in an o-minimal environment, as well as deducing the full compact domin...

In this paper we propose an algorithm for personalized learning based on a user’s query and a repository of lecture subparts —i.e., learning objects— both are described in a subset of OWL-DL. It works in two steps. First, it retrieves lecture subparts that cover as much as possible the user’s query. The solution is based on the concept covering problem for which we present a modified algorithm....

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We prove that the smallest covering code of length 8 and covering radius 2 has exactly 12 words. The proof is based on partial classi cation of even weight codewords, followed by a search for small sets of odd codewords covering the part of the space that has not been covered by the even subcode.

This work was partially supported by The Geometry Center of the University of Minnesota and the University of Massachusetts at Amherst. The soap film problem is to minimize area, and its dual is to maximize the flux of a divergenceless bounded vector field. This paper discretizes the continuous problem and solves it numerically. This gives upper and lower bounds on the area of the globally mini...