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In recent years, free energy perturbation (FEP) calculations have garnered increasing attention as tools to support drug discovery. The lead optimization mapper (Lomap) was proposed as an algorithm to calculate the relative free energy…
Parameterized complexity seeks to use input structure to obtain faster algorithms for NP-hard problems. This has been most successful for graphs of low treewidth: Many problems admit fast algorithms relative to treewidth and many of them…
Network structure provides critical information for understanding the dynamic behavior of networks. However, the complete structure of real-world networks is often unavailable, thus it is crucially important to develop approaches to infer a…
Robust optimization is concerned with constructing solutions that remain feasible also when a limited number of resources is removed from the solution. Most studies of robust combinatorial optimization to date made the assumption that every…
It is difficult to relate the properties of liquids and glasses directly to their structure because of complexity in the structure which defies precise definition. The potential energy landscape (PEL) approach is a very insightful way to…
Knowledge graph embedding, which aims to learn the low-dimensional representations of entities and relationships, has attracted considerable research efforts recently. However, most knowledge graph embedding methods focus on the structural…
Graph Neural Networks struggle to capture long-range dependencies due to over-squashing, where information from exponentially growing neighborhoods must pass through a small number of structural bottlenecks. While recent rewiring methods…
The collection of all the strongly connected components in a directed graph, among each cluster of which any node has a path to another node, is a typical example of the intertwining structure and dynamics in complex networks, as its…
Enhanced sampling techniques have become an essential tool in computational chemistry and physics, where they are applied to sample activated processes that occur on a time scale that is inaccessible to conventional simulations. Despite…
We present a method to find globally optimal topology and trajectory jointly for planar linkages. Planar linkage structures can generate complex end-effector trajectories using only a single rotational actuator, which is very useful in…
Topology diagrams are widely seen in power system applications, but their automatic generation is often easier said than done. When facing power transmission systems with strongly-meshed structures, existing approaches can hardly produce…
Let $\Lambda(T)$ denote the set of leaves in a tree $T$. One natural problem is to look for a spanning tree $T$ of a given graph $G$ such that $\Lambda(T)$ is as large as possible. This problem is called maximum leaf number, and it is a…
Unsupervised graph alignment aims to find the node correspondence across different graphs without any anchor node pairs. Despite the recent efforts utilizing deep learning-based techniques, such as the embedding and optimal transport…
The reassembling of a simple connected graph G = (V,E) is an abstraction of a problem arising in earlier studies of network analysis. The reassembling process has a simple formulation (there are several equivalent formulations) relative to…
Growing graphs describe a multitude of developing processes from maturing brains to expanding vocabularies to burgeoning public transit systems. Each of these growing processes likely adheres to proliferation rules that establish an…
The global structure of the minimal spanning tree (MST) is expected to be universal for a large class of underlying random discrete structures. However, very little is known about the intrinsic geometry of MSTs of most standard models, and…
Revealing hidden geometry and topology in noisy data sets is a challenging task. Elastic principal graph is a computationally efficient and flexible data approximator based on embedding a graph into the data space and minimizing the energy…
This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…
Given a graph $G$, a cost function on the non-edges of $G$, and an integer $d$, the problem of finding a cheapest globally rigid supergraph of $G$ in $\mathbb{R}^d$ is NP-hard for $d\geq 1$. For this problem, which is a common…
We study numerically Anderson localization on lattices that are tree-like except for the presence of one loop of varying length $L$. The resulting expressions allow us to compute corrections to the Bethe lattice solution on i)…