Related papers: A Study of End-Fed Arrays with Application to Sing…
The unit distance embeddability of a graph, like planarity, involves a mix of constraints that are combinatorial and geometric. We construct a unit distance embedding for $H-e$ in the hope that it will lead to an embedding for $H$. We then…
In a series of three papers we develop an end space theory for directed graphs. As for undirected graphs, the ends of a digraph are points at infinity to which its rays converge. Unlike for undirected graphs, some ends are joined by limit…
Maximum weight matching is one of the most fundamental combinatorial optimization problems with a wide range of applications in data mining and bioinformatics. Developing distributed weighted matching algorithms is challenging due to the…
One of the uses of sensor arrays is for spatial filtering or beamforming. Current digital signal processing methods facilitate complex-weighted beamforming, providing flexibility in array design. Previous studies proposed the use of…
Directed graphs can be studied by their associated directed flag complex. The homology of this complex has been successful in applications as a topological invariant for digraphs. Through comparison with path homology theory, we derive a…
A spanner graph on a set of points in $R^d$ contains a shortest path between any pair of points with length at most a constant factor of their Euclidean distance. In this paper we investigate new models and aim to interpret why good…
Grid maps are widely established for the representation of static objects in robotics and automotive applications. Though, incorporating velocity information is still widely examined because of the increased complexity of dynamic grids…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
Simple drawings of graphs are those in which each pair of edges share at most one point, either a common endpoint or a proper crossing. In this paper we study the problem of extending a simple drawing $D(G)$ of a graph $G$ by inserting a…
The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the…
Graphs drawn in the plane are ubiquitous, arising from data sets through a variety of methods ranging from GIS analysis to image classification to shape analysis. A fundamental problem in this type of data is comparison: given a set of such…
This article considers execution and analysis of laboratory experiments of pedestrians moving in a quasi-one-dimensional system with periodic boundary conditions. To analyze characteristics of jams in the system we aim to use the whole…
Designing a new class of rectangular two-dimensional sparse array to enhance the signal resolving capabilities with a limited number of sensors has always been a challenge. We explore the non-uniformity of the sparse arrays to enhance the…
Most of the existing path-following navigation algorithms cannot guarantee global convergence to desired paths or enable following self-intersected desired paths due to the existence of singular points where navigation algorithms return…
This paper shows the weighted matching problem on general graphs can be solved in time $O(n(m + n\log n))$ for $n$ and $m$ the number of vertices and edges, respectively. This was previously known only for bipartite graphs. The crux is a…
The $hp$-adaptive finite element method (FEM) - where one independently chooses the mesh size ($h$) and polynomial degree ($p$) to be used on each cell - has long been known to have better theoretical convergence properties than either $h$-…
Automated fiber placement (AFP) is an advanced manufacturing technology that increases the rate of production of composite materials. At the same time, the need for adaptable and fast inline control methods of such parts raises. Existing…
A little-known and highly economical characterization of the real interval [0, 1], essentially due to Freyd, states that the interval is homeomorphic to two copies of itself glued end to end, and, in a precise sense, is universal as such.…
In this paper, the optimal and precise array response control (OPARC) algorithm proposed in Part I of this two paper series is extended from single point to multi-points. Two computationally attractive parameter determination approaches are…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…