Related papers: Symmetric cluster expansions with tensor networks

Linked cluster expansions are generalized from an infinite to a finite volume. They are performed to 20th order in the expansion parameter to approach the critical region from the symmetric phase. A new criterion is proposed to distinguish…

After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…

In the context of clustering, we consider a generative model in a Euclidean ambient space with clusters of different shapes, dimensions, sizes and densities. In an asymptotic setting where the number of points becomes large, we obtain…

Cluster synchronization is a phenomenon in which a network self-organizes into a pattern of synchronized sets. It has been shown that diverse patterns of stable cluster synchronization can be captured by symmetries of the network. Here we…

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…

Multi-particle form factors of local operators in integrable models in two dimensions seem to have the property that they factorize when one subset of the particles in the external states are boosted by a large rapidity with respect to the…

We study cluster algebras with principal coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of perfect…

Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed…

We consider the problem of decentralized clustering and estimation over multi-task networks, where agents infer and track different models of interest. The agents do not know beforehand which model is generating their own data. They also do…

Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a…

The article presents a method of cluster expansions for groups of operators associated with the von Neumann equations for states and the Heisenberg equations for observables, aiming to construct generating operators for nonperturbative…

Network models provide a powerful and flexible framework for analyzing a wide range of structured data sources. In many situations of interest, however, multiple networks can be constructed to capture different aspects of an underlying…

Clustering high-dimensional datasets is hard because interpoint distances become less informative in high-dimensional spaces. We present a clustering algorithm that performs nonlinear dimensionality reduction and clustering jointly. The…

In this thesis I develop a formalism whereby a tensor network may be understood in terms of a unitary braided tensor category, and represented in a particularly efficient manner corresponding to the exploitation of this mathematical…

Several perspectives of the cluster Gutzwiller method are briefly discussed. I show that the cluster mean-field method can be used for large inhomogeneous lattices, for computing local excitations, and for the time evolution of correlated…

Distributed processing over networks relies on in-network processing and cooperation among neighboring agents. Cooperation is beneficial when agents share a common objective. However, in many applications agents may belong to different…

Constrained combinatorial optimization problems abound in industry, from portfolio optimization to logistics. One of the major roadblocks in solving these problems is the presence of non-trivial hard constraints which limit the valid search…

We introduce a novel statistical significance-based approach for clustering hierarchical data using semi-parametric linear mixed-effects models designed for responses with laws in the exponential family (e.g., Poisson and Bernoulli). Within…

We study the properties of 2D fibre clusters and networks formed by deposition processes. We first examine the growth and scaling properties of single clusters. We then consider a network of such clusters, whose spatial distribution obeys…

We generalize the technique of linked cluster expansions on hypercubic lattices to actions that couple fields at lattice sites which are not nearest neighbours. We show that in this case the graphical expansion can be arranged in such a way…