Related papers: Optimizing linked cluster expansions by white grap…
In many real-world contexts, such as social or transport networks, data exhibit both structural connectivity and node-level attributes. For example, roads in a transport network can be characterized not only by their connectivity but also…
A natural approach to analyze interaction data of form "what-connects-to-what-when" is to create a time-series (or rather a sequence) of graphs through temporal discretization (bandwidth selection) and spatial discretization (vertex…
Graph-based clustering methods have demonstrated the effectiveness in various applications. Generally, existing graph-based clustering methods first construct a graph to represent the input data and then partition it to generate the…
A general precedure is outlined for an algorithmic implementation of the strong coupling expansion of lattice chiral models on arbitrary lattices. A symbolic character expansion in terms of connected values of group integrals on skeleton…
This paper initiates the study of the classic balanced graph partitioning problem from an online perspective: Given an arbitrary sequence of pairwise communication requests between $n$ nodes, with patterns that may change over time, the…
Linked cluster expansions are generalized from an infinite to a finite volume on a $d$-dimensional hypercubic lattice. They are performed to 20th order in the expansion parameter to investigate the phase structure of scalar $O(N)$ models…
We develop a systematic cluster expansion for dilute systems in the highly dilute phase. We first apply it to the calculation of the entropy of the K-satisfiability problem in the satisfiable phase. We derive a series expansion in the…
The main issue of this work consists in extracting one or several finite values for the sum of series involved in perturbation theories. It is supposed to work for all cases in which two physical parameters are involved, and makes thorough…
We propose schemes to extract arbitrary graph states from two-dimensional cluster states by locally manipulating the qubits solely via single-qubit measurements. We introduce graph state manipulation tools that allow one to increase the…
We develop strong-coupling series expansion methods to study two-particle spectra of quantum lattice models. At the heart of the method lies the calculation of an effective Hamiltonian in the two-particle subspace. We explicitly consider an…
The unitary coupled cluster (UCC) approximation is one of the more promising wave-function ans\"atze for electronic structure calculations on quantum computers via the variational quantum eigensolver algorithm. However, for large systems…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
We revisit the classical approach to cluster expansions, based on tree graphs, and establish a new convergence condition that improves those by Kotecky-Preiss and Dobrushin, as we show in some examples. The two ingredients of our approach…
We propose an efficient linear-time graph-based divisive cluster analysis approach called Reductive Clustering. The approach tries to reveal the hierarchical structural information through reducing the graph into a more concise one…
An Eulerian orientation is an orientation of the edges of a graph such that every vertex is balanced: its in-degree equals its out-degree. Counting Eulerian orientations corresponds to the crucial partition function in so-called ``ice-type…
Capacitated spatial clustering, a type of unsupervised machine learning method, is often used to tackle problems in compressing, classifying, logistic optimization and infrastructure optimization. Depending on the application at hand, a…
We propose a novel perspective on varied-density clustering for high-dimensional data by framing it as a label propagation process in neighborhood graphs that adapt to local density variations. Our method formally connects density-based…
Link prediction aims to reveal missing edges in a graph. We address this task with a Gaussian process that is transformed using simplified graph convolutions to better leverage the inductive bias of the domain. To scale the Gaussian process…
Expander decompositions of graphs have significantly advanced the understanding of many classical graph problems and led to numerous fundamental theoretical results. However, their adoption in practice has been hindered due to their…
Higher-order connectivity patterns such as small induced sub-graphs called graphlets (network motifs) are vital to understand the important components (modules/functional units) governing the configuration and behavior of complex networks.…