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Consider an unlimited homogeneous medium disturbed by points generated via Poisson process. The neighborhood of a point plays an important role in spatial statistics problems. Here, we obtain analytically the distance statistics to $k$th…
We present a first numerical investigation of the accuracy of the recently proposed {\em non-classical transport equation}. This equation contains an extra independent variable (the path-length $s$), and models particle transport taking…
We survey theoretical, algorithmic, and computational results at the intersection of distance geometry problems and mathematical programming, both with and without adjacencies as part of the input. While mathematical programming methods can…
Random projection algorithm is an iterative gradient method with random projections. Such an algorithm is of interest for constrained optimization when the constraint set is not known in advance or the projection operation on the whole…
Many real objects are modeled as discrete sets of points, such as corners or other salient features. For our main applications in chemistry, points represent atomic centers in a molecule or a solid material. We study the problem of…
This paper aims at distributed multi-agent convex optimization where the communications network among the agents are presented by a random sequence of possibly state-dependent weighted graphs. This is the first work to consider both random…
We introduce a novel representation and optimization framework for discrete geodesics on triangle meshes that reduces artifacts of linear methods on uneven and coarse discretizations. Our method computes squared geodesic distances from…
Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…
Counting the number of triangles in a graph has many important applications in network analysis. Several frequently computed metrics like the clustering coefficient and the transitivity ratio need to count the number of triangles in the…
In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called…
Although many well-known algorithms can solve each bipartite matching problem instance efficiently, it remains an open question how one could estimate the expected optimal matching distance for arbitrary numbers of randomly distributed…
We address distributed learning problems over undirected networks. Specifically, we focus on designing a novel ADMM-based algorithm that is jointly computation- and communication-efficient. Our design guarantees computational efficiency by…
In this paper, we present a novel approach to reconstruct a unique image of an observed scene with widely distributed radar sensors. The problem is posed as a constrained optimization problem in which the global image which represents the…
In this work, arithmetic distribution matching (ADM) is presented. ADM invertibly transforms a discrete memoryless source (DMS) into a target DMS. ADM can be used for probabilistic shaping and for rate adaption. Opposed to existing…
This doctoral thesis concerns novel distributed algorithms for weight balancing over directed (communication) topologies. A directed topology (digraph) with nonnegative (or positive) weights assigned on each edge is weight-balanced if, for…
For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the…
The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which…
We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…
The dispersion problem on graphs asks $k\leq n$ robots placed initially arbitrarily on the nodes of an $n$-node anonymous graph to reposition autonomously to reach a configuration in which each robot is on a distinct node of the graph. This…
This study introduces an algorithm that generates undirected graphs with three main characteristics of real-world networks: scale-freeness, short distances between nodes (small-world phenomenon), and large clustering coefficients. The main…