Related papers: Symmetric cluster expansions with tensor networks
We study cluster synchronization in networks and show that the stability of all possible cluster synchronization patterns depends on a small set of Lyapunov exponents. Our approach can be applied to clusters corresponding to both orbital…
This is a short review on selected theory developments on Tensor Network (TN) states for strongly correlated systems. Specifically, we briefly review the effect of symmetries in TN states, fermionic TNs, the calculation of entanglement…
We introduce two-dimensional tensor network representations of finite groups carrying a 4-cocycle index. We characterize the associated gapped (2+1)D phases that emerge when these anomalous symmetries act on tensor network ground states. We…
Clustered solutions in oscillator networks provide an important insight into how a system might diversify from a synchronous solution into spatiotemporal complex solutions. They can therefore form a link between fully synchronized and…
The behaviour and functioning of a variety of complex physical and biological systems depend on the spatial organisation of their constituent units, and on the presence and formation of clusters of functionally similar or related…
In this paper we propose a new approach for Big Data mining and analysis. This new approach works well on distributed datasets and deals with data clustering task of the analysis. The approach consists of two main phases, the first phase…
The aim of this paper is to develop an approach to obtain self-adjoint extensions of symmetric operators acting on anti-dual pairs. The main advantage of such a result is that it can be applied for structures not carrying a Hilbert space…
Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different geometries. Matrix product states (MPS) in…
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 present a novel deep neural network architecture for unsupervised subspace clustering. This architecture is built upon deep auto-encoders, which non-linearly map the input data into a latent space. Our key idea is to introduce a novel…
There is a need to build intelligence in operating machinery and use data analysis on monitored signals in order to quantify the health of the operating system and self-diagnose any initiations of fault. Built-in control procedures can…
Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network…
Equivariant atomistic machine learning models have largely been built on spherical-tensor representations, where explicit angular-momentum coupling introduces substantial complexity and systematic extensions beyond energies and forces…
Twist fields are a powerful formal tool to compute R\'enyi entropies in quantum many-body systems, but their conventional formulation in tensor network states involves operations acting on virtual degrees of freedom, which are not directly…
This paper considers networks where relationships between nodes are represented by directed dissimilarities. The goal is to study methods that, based on the dissimilarity structure, output hierarchical clusters, i.e., a family of nested…
Recently, there has been increasing interest to leverage the competence of neural networks to analyze data. In particular, new clustering methods that employ deep embeddings have been presented. In this paper, we depart from centroid-based…
We show how to construct relevant families of matrix product operators in one and higher dimensions. Those form the building blocks for the numerical simulation methods based on matrix product states and projected entangled pair states. In…
This thesis is divided into two mainly independent parts: In the first part, we derive a criterion to determine when a translationally invariant Matrix Product State (MPS) has long range localizable entanglement, which indicates that the…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…
It has long been conjectured that hypotheses spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical networks than with shallow ones. Despite the vast…