The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems

We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low spatial dimension at finite size, a physical scenario where tensor network methods, both Density Matrix Renormalization Group and beyond, have long proven to be winning strategies. Here we explore in detail the numerical frameworks and methods employed to deal with low-dimension physical setups, from a computational physics perspective. We focus on symmetries and closed-system simulations in arbitrary boundary conditions, while discussing the numerical data structures and linear algebra manipulation routines involved, which form the core libraries of any tensor network code. At a higher level, we put the spotlight on loop-free network geometries, discussing their advantages, and presenting in detail algorithms to simulate low-energy equilibrium states. Accompanied by discussions of data structures, numerical techniques and performance, this anthology serves as a programmer's companion, as well as a self-contained introduction and review of the basic and selected advanced concepts in tensor networks, including examples of their applications.Comment: 115 pages, 56 figure

Forward and inverse modelling of post-seismic deformation

We consider a new approach to both the forward and inverse problems in post-seismic deformation. We present a method for forward modelling post-seismic deformation in a self-gravitating, heterogeneous and compressible earth with a variety of linear and nonlinear rheologies. We further demonstrate how the adjoint method can be applied to the inverse problem both to invert for rheological structure and to calculate the sensitivity of a given surface measurement to changes in rheology or time-dependence of the source. Both the forward and inverse aspects are illustrated with several numerical examples implemented in a spherically symmetric earth model

Unsupervised learning of Arabic non-concatenative morphology

Unsupervised approaches to learning the morphology of a language play an important role in computer processing of language from a practical and theoretical perspective, due their minimal reliance on manually produced linguistic resources and human annotation. Such approaches have been widely researched for the problem of concatenative affixation, but less attention has been paid to the intercalated (non-concatenative) morphology exhibited by Arabic and other Semitic languages. The aim of this research is to learn the root and pattern morphology of Arabic, with accuracy comparable to manually built morphological analysis systems. The approach is kept free from human supervision or manual parameter settings, assuming only that roots and patterns intertwine to form a word. Promising results were obtained by applying a technique adapted from previous work in concatenative morphology learning, which uses machine learning to determine relatedness between words. The output, with probabilistic relatedness values between words, was then used to rank all possible roots and patterns to form a lexicon. Analysis using trilateral roots resulted in correct root identification accuracy of approximately 86% for inflected words. Although the machine learning-based approach is effective, it is conceptually complex. So an alternative, simpler and computationally efficient approach was then devised to obtain morpheme scores based on comparative counts of roots and patterns. In this approach, root and pattern scores are defined in terms of each other in a mutually recursive relationship, converging to an optimized morpheme ranking. This technique gives slightly better accuracy while being conceptually simpler and more efficient. The approach, after further enhancements, was evaluated on a version of the Quranic Arabic Corpus, attaining a final accuracy of approximately 93%. A comparative evaluation shows this to be superior to two existing, well used manually built Arabic stemmers, thus demonstrating the practical feasibility of unsupervised learning of non-concatenative morphology