Related papers: Euclidean distance matrix completion and point con…
The matching distance is a computationally tractable topological measure to compare multi-filtered simplicial complexes. We design efficient algorithms for approximating the matching distance of two bi-filtered complexes to any desired…
We examine a wide class of stochastic approximation algorithms for solving (stochastic) nonlinear problems on Riemannian manifolds. Such algorithms arise naturally in the study of Riemannian optimization, game theory and optimal transport,…
In this work we consider the hybrid Data-Driven Computational Mechanics (DDCM) approach, in which a smooth constitutive manifold is reconstructed to obtain a well-behaved nonlinear optimization problem (NLP) rather than the much harder…
Random geometric graphs are random graph models defined on metric measure spaces. A random geometric graph is generated by first sampling points from a metric space and then connecting each pair of sampled points independently with a…
We consider the problem of learning distance-based Graph Convolutional Networks (GCNs) for relational data. Specifically, we first embed the original graph into the Euclidean space $\mathbb{R}^m$ using a relational density estimation…
Despite the popularity of low-rank matrix completion, the majority of its theory has been developed under the assumption of random observation patterns, whereas very little is known about the practically relevant case of non-random…
The Restricted Shortest Path (RSP) problem, also known as the Delay-Constrained Least-Cost (DCLC) problem, is an NP-hard bicriteria optimization problem on graphs with $n$ vertices and $m$ edges. In a graph where each edge is assigned a…
A fundamental question in computational geometry is for a set of input points in the Euclidean space, that is subject to discrete changes (insertion/deletion of points at each time step), whether it is possible to maintain an approximate…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
In the Minimum Clique Routing Problem on Cycles \textsc{MCRPC} we are given a cycle together with a set of demands (weighted origin-destination pairs) and the goal is to route all the pairs minimizing the maximum weighted clique of the…
Low-rank approximation with zeros aims to find a matrix of fixed rank and with a fixed zero pattern that minimizes the Euclidean distance to a given data matrix. We study the critical points of this optimization problem using algebraic…
The Maximum Minimal Cut Problem (MMCP), a NP-hard combinatorial optimization (CO) problem, has not received much attention due to the demanding and challenging bi-connectivity constraint. Moreover, as a CO problem, it is also a daunting…
In this work, we focus on the Neumann-Neumann method (NNM), which is one of the most popular non-overlapping domain decomposition methods. Even though the NNM is widely used and proves itself very efficient when applied to discrete problems…
In this paper, we propose to study on sufficient control of complex networks which is to control a sufficiently large portion of the network, where only the quantity of controllable nodes matters. To the best of our knowledge, this is the…
An algorithm is proposed for constructing directed spanning forests of the minimum weight, in which the maximum possible degree of affinity between the minimum forests is preserved when the number of trees changes. The correctness of the…
A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an…
Minimal controllability problem plays an important role in the field of network control. A New concept-Minimum Perfect Critical Set (MPCS)is proposed. Four different MPCSs were found for k-distant tree graphs. Based on this concept of MPCS,…
Dimensionality reduction is a crucial first step for many unsupervised learning tasks including anomaly detection and clustering. Autoencoder is a popular mechanism to accomplish dimensionality reduction. In order to make dimensionality…
The calculation of Euclidean distance between points is generalized to one-dimensional objects such as strings or polymers. Necessary and sufficient conditions for the minimal transformation between two polymer configurations are derived.…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…