Related papers: Introducing the Correlation Concentration Ratio (C…

Correlation matrices are a major type of multivariate data. To examine properties of a given correlation matrix, a common practice is to compare the same quantity between the original correlation matrix and reference correlation matrices,…

Wave-particle duality is an essential character of quantum systems. In the last few years, much progress has being made towards formally quantifying these quantum features. The properties of the quantum density matrix were shown to lead to…

Apart from the role the clustering coefficient plays in the definition of the small-world phenomena, it also has great relevance for practical problems involving networked dynamical systems. To study the impact of the clustering coefficient…

We discuss a cluster-like 1D system with triplet interaction. We study the topological properties of this system. We find that the degeneracy depends on the topology of the system, and well protected against external local perturbations.…

Large-scale continuous variable (CV) cluster state is necessary in quantum information processing based on measurement-based quantum computing (MBQC). Specially, generating large-scale CV cluster state multiplexed in time domain is easier…

Density functional theory (DFT)-based simulations of materials have first-principles accuracy, but are very computationally expensive. For simulating various properties of multi-component alloys, the cluster expansion (CE) technique has…

Identifying clusters of similar elements in a set is a common task in data analysis. With the immense growth of data and physical limitations on single processor speed, it is necessary to find efficient parallel algorithms for clustering…

We propose clustering algorithms based on a recently developed geometric digraph family called cluster catch digraphs (CCDs). These digraphs are used to devise clustering methods that are hybrids of density-based and graph-based clustering…

The clustering coefficient quantifies the abundance of connected triangles in a network and is a major descriptive statistics of networks. For example, it finds an application in the assessment of small-worldness of brain networks, which is…

Bipartite Correlation clustering is the problem of generating a set of disjoint bi-cliques on a set of nodes while minimizing the symmetric difference to a bipartite input graph. The number or size of the output clusters is not constrained…

Quantum networks are natural scenarios for the communication of information among distributed parties, and the arena of promising schemes for distributed quantum computation. Measurement-based quantum computing is a prominent example of how…

Several clustering frameworks with interactive (semi-supervised) queries have been studied in the past. Recently, clustering with same-cluster queries has become popular. An algorithm in this setting has access to an oracle with full…

Continuous-variable Gaussian cluster states are a potential resource for universal quantum computation. They can be efficiently and unconditionally built from sources of squeezed light using beam splitters. Here we report on the generation…

Graph clustering problems typically aim to partition the graph nodes such that two nodes belong to the same partition set if and only if they are similar. Correlation Clustering is a graph clustering formulation which: (1) takes as input a…

Correlation Clustering is an elegant model that captures fundamental graph cut problems such as Min $s-t$ Cut, Multiway Cut, and Multicut, extensively studied in combinatorial optimization. Here, we are given a graph with edges labeled $+$…

Measurement-based quantum computation (MBQC) represents a powerful and flexible framework for quantum information processing, based on the notion of entangled quantum states as computational resources. The most prominent application is the…

Graph clustering has many important applications in computing, but due to the increasing sizes of graphs, even traditionally fast clustering methods can be computationally expensive for real-world graphs of interest. Scalability problems…

Measuring graph clustering quality remains an open problem. To address it, we introduce quality measures based on comparisons of intra- and inter-cluster densities, an accompanying statistical test of the significance of their differences…

Graphs are commonly used to represent and visualize causal relations. For a small number of variables, this approach provides a succinct and clear view of the scenario at hand. As the number of variables under study increases, the graphical…

Entangled graph states can be used for quantum sensing and computing applications. Error correction in measurement-based quantum computing schemes will require the construction of cluster states in at least 3 dimensions. Here we generate…