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There is a graph reduction system so that every optimal 1-planar graph can be reduced to an irreducible extended wheel graph, provided the reductions are applied such that the given graph class is preserved. A graph is optimal 1-planar if…
Chaotic dynamical systems (DS) are ubiquitous in nature and society. Often we are interested in reconstructing such systems from observed time series for prediction or mechanistic insight, where by reconstruction we mean learning…
Graph reachability is the task of understanding whether two distinct points in a graph are interconnected by arcs to which in general a semantic is attached. Reachability has plenty of applications, ranging from motion planning to routing.…
In a random linear graph, vertices are points on a line, and pairs of vertices are connected, independently, with a link probability that decreases with distance. We study the problem of reconstructing the linear embedding from the graph,…
Learning directed acyclic graph (DAG) that describes the causality of observed data is a very challenging but important task. Due to the limited quantity and quality of observed data, and non-identifiability of causal graph, it is almost…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…
Layout is a fundamental component of any graphic design. Creating large varieties of plausible document layouts can be a tedious task, requiring numerous constraints to be satisfied, including local ones relating different semantic elements…
The decomposition of undirected graphs simplifies complex problems by breaking them into solvable subgraphs, following the philosophy of divide and conquer. This paper investigates the relationship between atom decomposition and the maximum…
We present a very fast algorithm for general matrix factorization of a data matrix for use in the statistical analysis of high-dimensional data via latent factors. Such data are prevalent across many application areas and generate an…
By incorporating physical consistency as inductive bias, deep neural networks display increased generalization capabilities and data efficiency in learning nonlinear dynamic models. However, the complexity of these models generally…
Learning to Rank has traditionally considered settings where given the relevance information of objects, the desired order in which to rank the objects is clear. However, with today's large variety of users and layouts this is not always…
Directed acyclic graphs (DAGs) are commonly used to model causal relationships among random variables. In general, learning the DAG structure is both computationally and statistically challenging. Moreover, without additional information,…
Learning rich and compact representations is an open topic in many fields such as object recognition or image retrieval. Deep neural networks have made a major breakthrough during the last few years for these tasks but their representations…
High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…
We introduce multiforce, a force-directed layout for multiplex networks, where the nodes of the network are organized into multiple layers and both in-layer and inter-layer relationships among nodes are used to compute node coordinates. The…
We present a novel approach to graph drawing based on reinforcement learning for minimizing the global and the local crossing number, that is, the total number of edge crossings and the maximum number of crossings on any edge, respectively.…
Front-door adjustment gives a simple closed-form identification formula under the classical front-door criterion, but its applicability is often viewed as narrow. By contrast, the general ID algorithm can identify many more causal effects…
Listing triangles is a fundamental graph problem with many applications, and large graphs require fast algorithms. Vertex ordering allows the orientation of edges from lower to higher vertex indices, and state-of-the-art triangle listing…
This paper studies the problem of designing networks that are strong structurally controllable, and robust simultaneously. For given network specifications, including the number of nodes $N$, the number of leaders $N_L$, and diameter $D$,…