Related papers: Saturating directed spaces
Randomized sampling based algorithms are widely used in robot motion planning due to the problem's intractability, and are experimentally effective on a wide range of problem instances. Most variants bias their sampling using various…
We show that choosing appropriate distributions of the randomness, the search for optimal paths links diverse problems of disordered media like directed percolation, invasion percolation, directed and non-directed spanning polymers. We also…
Notions of guardedness serve to delineate the admissibility of cycles, e.g. in recursion, corecursion, iteration, or tracing. We introduce an abstract notion of guardedness structure on a symmetric monoidal category, along with a…
Beyond-planarity focuses on combinatorial properties of classes of non-planar graphs that allow for representations satisfying certain local geometric or topological constraints on their edge crossings. Beside the study of a specific graph…
Transit functions were introduced as models of betweenness on undirected structures. Here we introduce directed transit function as the directed analogue on directed structures such as posets and directed graphs. We first show that…
The category of monotone determined spaces is an extended topological framework for dcpos in domain theory. We first show that monotone determined spaces are exactly the spaces generated by one-point convergence spaces, and then naturally…
The paper presents a topology optimization approach that designs an optimal structure, called a self-supporting structure, which is ready to be fabricated via additive manufacturing without the usage of additional support structures. Such…
We prove bounds on the saturation degrees of homogeneous ideals (and their powers) defining smooth complex projective varieties. For example, we show that a classical statement due to Macualay for zero-dimensional complete intersection…
In this thesis, we introduce the subject of D-spaces and some of its most important open problems which are related to well known covering properties. We then introduce a new approach for studying D-spaces and covering properties in…
In this thesis we propose and study a theory of ordered locales, a type of point-free space equipped with a preorder structure on its frame of opens. It is proved that the Stone-type duality between topological spaces and locales lifts to a…
A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…
As a practical foundation for a homotopy theory of abstract spacetime, we extend a category of certain compact partially ordered spaces to a convenient category of locally preordered spaces. In particular, we show that our new category is…
In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…
Induction in saturation-based first-order theorem proving is a new exciting direction in the automation of inductive reasoning. In this paper we survey our work on integrating induction directly into the saturation-based proof search…
In this paper, we study a generic direct-search algorithm in which the polling directions are defined using random subspaces. Complexity guarantees for such an approach are derived thanks to probabilistic properties related to both the…
A salient feature of topological phases are surface states and many of the widely studied physical properties are directly tied to their existence. Although less explored, a variety of topological phases can however similarly be…
We give a procedure that can be used to automatically satisfy invariants of a certain shape. These invariants may be written with the operations intersection, composition and converse over binary relations, and equality over these…
We define a class of subsets of a topological space that coincides with the class of compact saturated subsets when the space is sober, and with enough good properties when the space is not sober. This class is introduced especially in view…
This paper addresses planning and control of robot motion under uncertainty that is formulated as a continuous-time, continuous-space stochastic optimal control problem, by developing a topology-guided path integral control method. The path…
This is the second paper on the path integral approach of superintegrable systems on Darboux spaces, spaces of non-constant curvature. We analyze in the spaces $\DIII$ and $\DIV$ five respectively four superintegrable potentials, which were…