Generic Construction of Efficient Matrix Product Operators

Matrix Product Operators (MPOs) are at the heart of the second-generation Density Matrix Renormalisation Group (DMRG) algorithm formulated in Matrix Product State language. We first summarise the widely known facts on MPO arithmetic and representations of single-site operators. Second, we introduce three compression methods (Rescaled SVD, Deparallelisation and Delinearisation) for MPOs and show that it is possible to construct efficient representations of arbitrary operators using MPO arithmetic and compression. As examples, we construct powers of a short-ranged spin-chain Hamiltonian, a complicated Hamiltonian of a two-dimensional system and, as proof of principle, the long-range four-body Hamiltonian from quantum chemistry.Comment: 13 pages, 10 figure

Hydroxyurea-induced synchronisation of bloodstream stage Trypanosoma brucei

Synchronisation of the <i>Trypanosoma brucei</i> cell cycle proved elusive for many years. A recent report demonstrated that synchronisation of procyclic form cells was possible following treatment with hydroxyurea. Here, that work is extended to the disease-relevant, mammalian-infective bloodstream stage trypanosome. Treatment of bloodstream stage Lister 427 <i>T. Brucei</i> cells growing <i>in vitro</i> with 10 μg ml<sup>−1</sup> hydroxyurea for 6 h led to an enrichment of cells in S phase. Following removal of the drug, cells proceeded uniformly through one round of the cell cycle, providing a much needed tool to enrich for specific cell cycle stages, in a manner similar to hydroxyurea treatment of procyclic form <i>T. brucei.</i&gt

Chebyshev matrix product state approach for time evolution

We present and test a new algorithm for time-evolving quantum many-body systems initially proposed by Holzner et al. [Phys. Rev. B 83, 195115 (2011)]. The approach is based on merging the matrix product state (MPS) formalism with the method of expanding the time-evolution operator in Chebyshev polynomials. We calculate time-dependent observables of a system of hardcore bosons quenched under the Bose-Hubbard Hamiltonian on a one-dimensional lattice. We compare the new algorithm to more standard methods using the MPS architecture. We find that the Chebyshev method gives numerically exact results for small times. However, the reachable times are smaller than the ones obtained with the other state-of-the-art methods. We further extend the new method using a spectral-decomposition-based projective scheme that utilizes an effective bandwidth significantly smaller than the full bandwidth, leading to longer evolution times than the non-projective method and more efficient information storage, data compression, and less computational effort.Comment: 14 pages, 8 figure

Pathways Out of Poverty During an Economic Crisis: An Empirical Assessment of Rural Indonesia

Most poor people in developing countries still live in rural areas and are primarily engaged in low productivity farming activities. Thus pathways out of poverty are likely to be strongly connected to productivity increases in the rural economy, whether they are realised in farming, rural non-farm enterprises or via rural-urban migration. We use cross-sectional data from the Central Statistical Board (BPS) for 1993 and 2002, as well as a panel data set from the Indonesia Family Life Survey (IFLS) for 1993 and 2000, to show which pathways out of poverty were most successful over this period. Our findings suggest that increased engagement of farmers in rural non-farm enterprises is an important route out of rural poverty, but that most of the rural agricultural poor that exit poverty still do so while remaining rural and agricultural. Thus changes in agricultural prices, wages and productivity still play a critical role in moving people out of poverty.Poverty dynamics, non-farm sector, micro-growth regression

Pathways out of poverty during an economic crisis : an empirical assessment of rural Indonesia

Most poor people in developing countries still live in rural areas and are primarily engaged in low productivity farming activities. Thus pathways out of poverty are likely to be strongly connected to productivity increases in the rural economy, whether they are realized in farming, in rural nonfarm enterprises, or by way of rural-urban migration. The authors use cross-sectional data from the Central Statistical Board for 1993 and 2002, as well as a panel data set from the Indonesia Family Life Survey for 1993 and 2000, to show which pathways out of poverty were most successful over this period. The findings suggest that increased engagement of farmers in rural nonfarm enterprises is an important route out of rural poverty, but that most of the rural agricultural poor that exit poverty still do so while remaining rural and agricultural. So changes in agricultural prices, wages, and productivity still play a critical role in moving people out of poverty.Rural Poverty Reduction,Population Policies,Achieving Shared Growth,Economic Theory&Research

Stochastic Hosting Capacity in LV Distribution Networks

Hosting capacity is defined as the level of penetration that a particular technology can connect to a distribution network without causing power quality problems. In this work, we study the impact of solar photovoltaics (PV) on voltage rise. In most cases, the locations and sizes of the PV are not known in advance, so hosting capacity must be considered as a random variable. Most hosting capacity methods study the problem considering a large number of scenarios, many of which provide little additional information. We overcome this problem by studying only cases where voltage constraints are active, with results illustrating a reduction in the number of scenarios required by an order of magnitude. A linear power flow model is utilised for this task, showing excellent performance. The hosting capacity is finally studied as a function of the number of generators connected, demonstrating that assumptions about the penetration level will have a large impact on the conclusions drawn for a given network

The stress radionuclide assessment of diastolic function

Background Many patients are referred from primary care with suspected heart failure and are found to have preserved systolic function. These patients may be labelled as having normal ejection fraction or diastolic heart failure, the diagnosis of which is both controversial and difficult. Previous work has identified a large proportion of these patients to have an alternative, pre- existing diagnosis. This thesis prospectively assesses the prevalence of undiagnosed ischaemic heart disease and respiratory disease in this patient group and assess diastolic function using multiple methods. The central hypothesis being tested was that first third fractional filling, a radionuclide ventriculogram (RNVG) parameter previously used to assess diastolic function at rest, would identify diastolic dysfunction more accurately under stress conditions. Methods Patients were recruited from an open access echocardiography service. Echocardiography, including tissue Doppler assessment, was carried out independently by 2 experienced observers. Confounding diagnoses including coronary artery disease and respiratory disease were actively sought by myocardial perfusion imaging and spirometry. N-terminal proBNP was measured. List mode radionuclide ventriculography was performed at rest supine and during upright bicycle exercise with simultaneous measurement of VO2 max. Validation of the reliability and reproducibility of first third fractional filling, peak filling rate, time to peak filling and other radionuclide parameters of systolic and diastolic function was undertaken. This demonstrated that it was possible to measure both first third fractional filling and peak filling rate with the short acquisition times necessary for assessment during stress. Time to peak filling was poorly reproducible under these conditions. A normal range for first third fractional filling at rest and during exercise was established. Due to a strong inverse relationship between heart rate and first third fractional filling, a continuous reference range was constructed using an exponential model. This unique approach enables the calculation of the lower limit of normal at any heart rate. A more conventional mean ± 2 standard deviations was used for the other RNVG parameters. Results Eighty three patients were recruited and completed an extensive multi-modality assessment of systolic and diastolic function. As with previous work in this field, the patients were predominantly female (82%) and elderly (mean age 66.7). Mild left ventricular systolic dysfunction as determined by RNVG was missed by echocardiography in one third of patients. Systolic dysfunction more significant than this was not observed. N-terminal proBNP was elevated in 21 of 82 patients where it was available with no significant difference in left ventricular ejection fraction between those with normal and elevated levels. Myocardial perfusion scanning was normal in 46 of 83 patients and showed significant ischaemia in 20 of 83. Spirometry was normal in 58 of 82 patients, with mild airflow obstruction in 20 patients and moderate obstruction in 4. In only one patient were no alternative diagnoses present. There was poor correlation between indices of diastolic function at rest including first third fractional filling, echocardiographic parameters and NT-proBNP. The assessment of diastolic function using stress radionuclide ventriculography did not improve the correlation between measured indices. On stress, however, low first third fractional filling predicted exercise intolerance as an inability to reach anaerobic threshold. Conclusions Alternative diagnoses to diastolic dysfunction are present almost universally in patients with suspected normal ejection fraction heart failure. This is true even where these diagnoses are not previously established. This thesis underlines the need to fully assess this patient group to allow appropriate targeting of therapy. It is also clear that echocardiography alone is potentially misleading and it is suggested that it is better placed within a tiered assessment process. The assessment of diastolic function using stress radionuclide ventriculography, although an appealing concept, does not improve diagnostic accuracy within this patient group. The marked heterogeneity of this patient group is likely to have played a role in this and it may be of interest to reassess stress radionuclide ventriculography in a more acute heart failure population

Applying matrix product operators to model systems with long-range interactions

An algorithm is presented which computes a translationally invariant matrix product state approximation of the ground state of an infinite 1D system; it does this by embedding sites into an approximation of the infinite ``environment'' of the chain, allowing the sites to relax, and then merging them with the environment in order to refine the approximation. By making use of matrix product operators, our approach is able to directly model any long-range interaction that can be systematically approximated by a series of decaying exponentials. We apply our techniques to compute the ground state of the Haldane-Shastry model and present results.Comment: 7 pages, 3 figures; manuscript has been expanded and restructured in order to improve presentation of the algorith

Domain-wall melting in ultracold boson systems with holes and spin-flip defects

Quantum magnetism is a fundamental phenomenon of nature. As of late, it has garnered a lot of interest because experiments with ultracold atomic gases in optical lattices could be used as a simulator for phenomena of magnetic systems. A paradigmatic example is the time evolution of a domain-wall state of a spin-1/2 Heisenberg chain, the so-called domain-wall melting. The model can be implemented by having two species of bosonic atoms with unity filling and strong on-site repulsion U in an optical lattice. In this paper, we study the domain-wall melting in such a setup on the basis of the time-dependent density matrix renormalization group (tDMRG). We are particularly interested in the effects of defects that originate from an imperfect preparation of the initial state. Typical defects are holes (empty sites) and flipped spins. We show that the dominating effects of holes on observables like the spatially resolved magnetization can be taken account of by a linear combination of spatially shifted observables from the clean case. For sufficiently large U, further effects due to holes become negligible. In contrast, the effects of spin flips are more severe as their dynamics occur on the same time scale as that of the domain-wall melting itself. It is hence advisable to avoid preparation schemes that are based on spin-flips.Comment: 15 pages, 12 figures. Supplemental Material: 2 animations (avi) comparing the domain-wall melting with and without defects, corresponding to figures 3, 4 and the discussion in section V.B; minor improvements; published versio