Entanglement renormalization for disordered systems

We propose a tensor network method for investigating strongly disordered systems that is based on an adaptation of entanglement renormalization [G. Vidal, Phys. Rev. Lett. 99, 220405 (2007)]. This method makes use of the strong disorder renormalization group to determine the order in which lattice sites are coarse-grained, which sets the overall structure of the corresponding tensor network ansatz, before optimization using variational energy minimization. Benchmark results from the disordered XXZ model demonstrates that this approach accurately captures ground state entanglement in disordered systems, even at long distances. This approach leads to a new class of efficiently contractible tensor network ansatz for 1D systems, which may be understood as a generalization of the multi-scale entanglement renormalization ansatz for disordered systems.Comment: 14 pages, 21 figure

Using entanglement to discern phases in the disordered one-dimensional Bose-Hubbard model

We perform a matrix product state based density matrix renormalisation group analysis of the phases for the disordered one-dimensional Bose-Hubbard model. For particle densities N/L = 1, 1/2 and 2 we show that it is possible to obtain a full phase diagram using only the entanglement properties, which come "for free" when performing an update. We confirm the presence of Mott insulating, superfluid and Bose glass phases when N/L = 1 and 1/2 (without the Mott insulator) as found in previous studies. For the N/L = 2 system we find a double lobed superfluid phase with possible reentrance.Comment: 6 pages, 4 figure

Leaf-to-leaf distances and their moments in finite and infinite m-ary tree graphs

We study the leaf-to-leaf distances on full and complete m-ary graphs using a recursive approach. In our formulation, leaves are ordered along a line. We find explicit analytical formulae for the sum of all paths for arbitrary leaf-to-leaf distance r as well as the average path lengths and the moments thereof. We show that the resulting explicit expressions can be recast in terms of Hurwitz-Lerch transcendants. Results for periodic trees are also given. For incomplete random binary trees, we provide first results by numerical techniques; we find a rapid drop of leaf-to-leaf distances for large r.Comment: 10 pages, 7 figure

Tensor networks and geometry for the modelling of disordered quantum many-body systems

Tensor networks provide a powerful and elegant approach to quantum manybody simulation. The simplest example is the density matrix renormalisation group (DMRG), which is based on the variational update of a matrix product state (MPS). It has proved to be the most accurate approach for the numerical study of strongly correlated one dimensional systems. We use DMRG to study the one dimensional disordered Bose-Hubbard model at fillings N=L = 1=2, 1 and 2 and show that the whole phase diagram for each can be successfully obtained by analysing entanglement properties alone. We �nd that the average entanglement is insufficient to accurately locate all of the phases, however using the standard error on the mean we are able to construct a phase diagram that is consistent with previous studies. It has recently been shown that there is a connection between the geometry of tensor networks and the entanglement and correlation properties that it can encode, which is a generalisation of the so called area law for entanglement entropy. This suggests that whilst gapped quantum systems can be accurately modeled using an MPS, a tensor network with a holographic geometry is natural to capture the logarithmic entanglement scaling and power law decaying correlation functions of critical systems. We create an algorithm for the disordered Heisenberg Hamiltonian that self assembles a tensor network based on the disorder in the couplings. The geometry created is that of a disordered tree tensor network (TTN) that when averaged has the holographic properties characteristic of critical systems. We continue the analysis of holographic tensor network geometry by considering the average length of leaf-to-leaf paths in various tree graphs, which is related to two-point correlation functions in tensor networks. For regular, complete trees we analytically calculate the average path length and all statistical moments, and generalise it for any splitting number. We then turn to the Catalan trees, which is the set of unique binary trees with n vertices, as it has a similar geometry to the disordered TTNs. We calculate the average depth of a leaf and show that it is equal to the average path length. We compare these analytic results with the structures found in the TTN and randomly constructed trees to show that the renormalisation involved in the TTN algorithm is crucial in the selection of the tree structure

Integration of datasets for individual prediction of DNA methylation-based biomarkers

BACKGROUND: Epigenetic scores (EpiScores) can provide biomarkers of lifestyle and disease risk. Projecting new datasets onto a reference panel is challenging due to separation of technical and biological variation with array data. Normalisation can standardise data distributions but may also remove population-level biological variation.RESULTS: We compare two birth cohorts (Lothian Birth Cohorts of 1921 and 1936 - nLBC1921 = 387 and nLBC1936 = 498) with blood-based DNA methylation assessed at the same chronological age (79 years) and processed in the same lab but in different years and experimental batches. We examine the effect of 16 normalisation methods on a novel BMI EpiScore (trained in an external cohort, n = 18,413), and Horvath's pan-tissue DNA methylation age, when the cohorts are normalised separately and together. The BMI EpiScore explains a maximum variance of R2=24.5% in BMI in LBC1936 (SWAN normalisation). Although there are cross-cohort R2 differences, the normalisation method makes a minimal difference to within-cohort estimates. Conversely, a range of absolute differences are seen for individual-level EpiScore estimates for BMI and age when cohorts are normalised separately versus together. While within-array methods result in identical EpiScores whether a cohort is normalised on its own or together with the second dataset, a range of differences is observed for between-array methods.CONCLUSIONS: Normalisation methods returning similar EpiScores, whether cohorts are analysed separately or together, will minimise technical variation when projecting new data onto a reference panel. These methods are important for cases where raw data is unavailable and joint normalisation of cohorts is computationally expensive.</p

Literatur für interdisziplinäre Wissenschaft – eine Anforderungsanalyse aus Anwendersicht [Literature for interdisciplinary scientists – a requirement engineering approach]

[english] Medical research is subject to continuous change, and scientific literature must be timely assessable for research, diagnosis, and teaching. However, biomedical sciences have become interdisciplinary, collective, and translational. Furthermore, novel technologies such as the Internet and smart phones have been established and are available almost everywhere. Medical libraries have to follow these trends offering novel integrated services to optimize the support of their customers. In this paper, we analyse the domain from the users’ perspective and give a categorization of future bibliographic services.<br>[german] Literatur ist die Kernkomponente der Wissenschaft, aber die medizinische Forschung ist im ständigen Wandel. Die Metapher des Elfenbeinturmes für den Arbeitsplatz des Wissenschaftlers ist längst nicht mehr gültig. Erfolgreiche Wissenschaft im biomedizinischen Bereich ist heute interdisziplinär, kollektiv und translational. Dieser Prozess wird begleitet von technologischen Innovationen wie dem Smart Phone und der Informationsressource Internet, die überall und immer verfügbar ist. Das medizinische Bibliothekswesen muss diesen Wandel mit vollziehen und mit innovativen, prozessintegrierten Diensten seine Kunden optimal unterstützen. Dieser Beitrag beleuchtet das Problemfeld aus Sicht des Anwenders und versucht, die Anforderungen an bibliothekarische Dienste zu kategorisieren und zu priorisieren

Data for Using entanglement to discern phases in the disordered one-dimensional Bose-Hubbard model

We perform a matrix-product-state–based density matrix renormalisation group analysis of the phases for the disordered one-dimensional Bose-Hubbard model. For particle densities N/L = 1, 1/2 and 2 we show that it is possible to obtain a full phase diagram using only the entanglement properties, which come for free when performing an update. We confirm the presence of Mott insulating, superfluid and Bose glass phases when N/L = 1 and 1/2 (without the Mott insulator) as found in previous studies. For the N/L = 2 system we find a double-lobed superfluid phase with possible re-entrance