Related papers: Complete and Sufficient Spatial Domination of Mult…
Dominating sets in graphs are often used to model some monitoring of the graph: guards are posted on the vertices of the dominating set, and they can thus react to attacks occurring on the unguarded vertices by moving there (yielding a new…
A general maximum principle (necessary and sufficient conditions) for an optimal control problem governed by a stochastic differential equation driven by an infinite dimensional martingale is established. The solution of this equation takes…
In previous work, we introduced a method for modeling a configuration of objects in 2D and 3D images using a mathematical "medial/skeletal linking structure." In this paper, we show how these structures allow us to capture positional…
A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the…
Spatial computing is a technological advancement that facilitates the seamless integration of devices into the physical environment, resulting in a more natural and intuitive digital world user experience. Spatial computing has the…
The concepts of domination and topological index hold great significance within the realm of graph theory. Therefore, it is pertinent to merge these concepts to derive the domination index of a graph. A novel concept of the domination index…
Modern extended reality XR systems provide rich analysis of image data and fusion of sensor input and demand AR/VR applications that can reason about 3D scenes in a semantic manner. We present a spatial reasoning framework that bridges…
The nearest neighbor problem is defined as follows: Given a set $P$ of $n$ points in some metric space $(X,D)$, build a data structure that, given any point $q$, returns a point in $P$ that is closest to $q$ (its "nearest neighbor" in $P$).…
Low-rank approximation of kernels is a fundamental mathematical problem with widespread algorithmic applications. Often the kernel is restricted to an algebraic variety, e.g., in problems involving sparse or low-rank data. We show that…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitrary totally bounded metric space where the rationals are…
Trying to be effective (no matter who exactly and in what field) a person face the problem which inevitably destroys all our attempts to easily get to a desired goal. The problem is the existence of some insuperable barriers for our mind,…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
Robots that can manipulate objects in unstructured environments and collaborate with humans can benefit immensely by understanding natural language. We propose a pipelined architecture of two stages to perform spatial reasoning on the text…
Probabilistic 3D map has been applied to object segmentation with multiple camera viewpoints, however, conventional methods lack of real-time efficiency and functionality of multilabel object mapping. In this paper, we propose a method to…
While general object recognition is still far from being solved, this paper proposes a way for a robot to recognize every object at an almost human-level accuracy. Our key observation is that many robots will stay in a relatively closed…
To autonomously navigate and plan interactions in real-world environments, robots require the ability to robustly perceive and map complex, unstructured surrounding scenes. Besides building an internal representation of the observed scene…
For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…
The secure domination numbers of the Cartesian products of two small graphs with paths or cycles is determined, as well as for Mobius ladder graphs. Prior to this work, in all cases where the secure domination number has been determined,…