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A practical challenge which arises in the operation of sensor networks is the presence of sensor faults, biases, or adversarial attacks, which can lead to significant errors incurring in the localization of the agents, thereby undermining…
The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…
In the point set embeddability problem, we are given a plane graph $G$ with $n$ vertices and a point set $S$ with $n$ points. Now the goal is to answer the question whether there exists a straight-line drawing of $G$ such that each vertex…
In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast…
Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…
Geometric embedding of graphs in a point set in the plane is a well known problem. In this paper, the complexity of a variant of this problem, where the point set is bounded by a simple polygon, is considered. Given a point set in the plane…
We consider the problem of embedding unweighted, directed k-nearest neighbor graphs in low-dimensional Euclidean space. The k-nearest neighbors of each vertex provides ordinal information on the distances between points, but not the…
Iterated localization is considered where each node of a network needs to get localized (find its location on 2-D plane), when initially only a subset of nodes have their location information. The iterated localization process proceeds as…
When we represent a network of sensors in Euclidean space by a graph, there are two distances between any two nodes that we may consider. One of them is the Euclidean distance. The other is the distance between the two nodes in the graph,…
The design of fixed point algorithms is at the heart of monotone operator theory, convex analysis, and of many modern optimization problems arising in machine learning and control. This tutorial reviews recent advances in understanding the…
This paper presents methods to compare networks where relationships between pairs of nodes in a given network are defined. We define such network distance by searching for the optimal method to embed one network into another network, prove…
To reliably model real robot characteristics, interval linear systems of equations allow to describe families of problems that consider sets of values. This allows to easily account for typical complexities such as sets of joint states and…
We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…
We investigate the increasingly prominent task of jointly inferring multiple networks from nodal observations. While most joint inference methods assume that observations are available at all nodes, we consider the realistic and more…
The problem of covering random points in a plane with sets of a given shape has several practical applications in communications and operations research. One especially prominent application is the coverage of randomly-located points of…
Network alignment, the process of finding correspondences between nodes in different graphs, has many scientific and industrial applications. Existing unsupervised network alignment methods find suboptimal alignments that break up node…
In nearest-neighbor classification problems, a set of $d$-dimensional training points are given, each with a known classification, and are used to infer unknown classifications of other points by using the same classification as the nearest…
This paper studies the possibility of upper bounding the position error of an estimate for range based positioning algorithms in wireless sensor networks. In this study, we argue that in certain situations when the measured distances…
Accurate maps are a prerequisite for virtually all mobile robot tasks. Most state-of-the-art maps assume a static world; therefore, dynamic objects are filtered out of the measurements. However, this division ignores movable but non-moving…
Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…