相关论文: Tail bounds for detection times in mobile hyperbol…
Neural embeddings have been used with great success in Natural Language Processing (NLP). They provide compact representations that encapsulate word similarity and attain state-of-the-art performance in a range of linguistic tasks. The…
We significantly improve the generalization bounds for VC classes by using two main ideas. First, we consider the hypergeometric tail inversion to obtain a very tight non-uniform distribution-independent risk upper bound for VC classes.…
We prove the first eigenvalue repulsion bound for sparse random matrices. As a consequence, we show that these matrices have simple spectrum, improving the range of sparsity and error probability from the work of the second author and Vu.…
The VertexCover problem is proven to be computationally hard in different ways: It is NP-complete to find an optimal solution and even NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on…
We present an analytical method to estimate the continuous-time collision probability of motion plans for autonomous agents with linear controlled Ito dynamics. Motion plans generated by planning algorithms cannot be perfectly executed by…
We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodic points are obtained. A new method, based on the study of…
We study hidden boundary trace regularity for two-dimensional hyperbolic equations with boundary degeneracy governed by $\mcA\vp=-\Div(A\nabla \vp)$, where $A=\diag(1,r^\al)$ and $\al\in(0,1)$. We establish well-posedness in weighted…
In the last decades, the study of models for large real-world networks has been a very popular and active area of research. A reasonable model should not only replicate all the structural properties that are observed in real world networks…
We consider a single non-holonomic Dubins-like robot traveling with a constant longitudinal speed in an a priori unknown and unsteady planar environment. The robot should detect, locate, and track the boundary of a dynamic environmental…
Terrain-aware perception holds the potential to improve the robustness and accuracy of autonomous robot navigation in the wilds, thereby facilitating effective off-road traversals. However, the lack of multi-modal perception across various…
In this paper, we investigate the controllability of a linear time-invariant network following a Laplacian dynamics defined on a threshold graph. In this direction, an algorithm for deriving the modal matrix associated with the Laplacian…
Static wireless networks are by now quite well understood mathematically through the random geometric graph model. By contrast, there are relatively few rigorous results on the practically important case of mobile networks, in which the…
We revisit and refine known tail inequalities and confidence bounds for the hypergeometric distribution, i.e., for the setting where we sample without replacement from a fixed population with binary values or properties. The results are…
Given a directed graph and a source vertex, the fully dynamic single-source reachability problem is to maintain the set of vertices that are reachable from the given vertex, subject to edge deletions and insertions. It is one of the most…
In this paper, we derive the Cramer-Rao bound (CRB) for joint target position and velocity estimation using an active or passive distributed radar network under more general, and practically occurring, conditions than assumed in previous…
Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. The quality of the embeddings is usually determined by how well the geometry…
Representation learning over temporal networks has drawn considerable attention in recent years. Efforts are mainly focused on modeling structural dependencies and temporal evolving regularities in Euclidean space which, however,…
In this article, we investigate the transient behavior of a sequence of packets/bits traversing a multi-hop wireless network. Our work is motivated by novel applications from the domain of process automation, Machine-Type Communication…
Controllability is one of the central concepts of modern control theory that allows a good understanding of a system's behaviour. It consists in constraining a system to reach the desired state from an initial state within a given time…
The arrangement of network nodes in hyperbolic spaces has become a widely studied problem, motivated by numerous results suggesting the existence of hidden metric spaces behind the structure of complex networks. Although several methods…