Quantum Monte Carlo scheme for frustrated Heisenberg antiferromagnets

When one tries to simulate quantum spin systems by the Monte Carlo method, often the 'minus-sign problem' is encountered. In such a case, an application of probabilistic methods is not possible. In this paper the method has been proposed how to avoid the minus sign problem for certain class of frustrated Heisenberg models. The systems where this method is applicable are, for instance, the pyrochlore lattice and the $J_1-J_2$ Heisenberg model. The method works in singlet sector. It relies on expression of wave functions in dimer (pseudo)basis and writing down the Hamiltonian as a sum over plaquettes. In such a formulation, matrix elements of the exponent of Hamiltonian are positive.Comment: 19 LaTeX pages, 6 figures, 1 tabl

The effect of organelle discovery upon sub-cellular protein localisation.

Prediction of protein sub-cellular localisation by employing quantitative mass spectrometry experiments is an expanding field. Several methods have led to the assignment of proteins to specific subcellular localisations by partial separation of organelles across a fractionation scheme coupled with computational analysis. Methods developed to analyse organelle data have largely employed supervised machine learning algorithms to map unannotated abundance profiles to known protein–organelle associations. Such approaches are likely to make association errors if organelle-related groupings present in experimental output are not included in data used to create a protein–organelle classifier. Currently, there is no automated way to detect organelle-specific clusters within such datasets. In order to address the above issues we adapted a phenotype discovery algorithm, originally created to filter image-based output for RNAi screens, to identify putative subcellular groupings in organelle proteomics experiments. We were able to mine datasets to a deeper level and extract interesting phenotype clusters for more comprehensive evaluation in an unbiased fashion upon application of this approach. Organelle-related protein clusters were identified beyond those sufficiently annotated for use as training data. Furthermore, we propose avenues for the incorporation of observations made into general practice for the classification of protein–organelle membership from quantitative MS experiments. Biological significance Protein sub-cellular localisation plays an important role in molecular interactions, signalling and transport mechanisms. The prediction of protein localisation by quantitative mass-spectrometry (MS) proteomics is a growing field and an important endeavour in improving protein annotation. Several such approaches use gradient-based separation of cellular organelle content to measure relative protein abundance across distinct gradient fractions. The distribution profiles are commonly mapped in silico to known protein–organelle associations via supervised machine learning algorithms, to create classifiers that associate unannotated proteins to specific organelles. These strategies are prone to error, however, if organelle-related groupings present in experimental output are not represented, for example owing to the lack of existing annotation, when creating the protein–organelle mapping. Here, the application of a phenotype discovery approach to LOPIT gradient-based MS data identifies candidate organelle phenotypes for further evaluation in an unbiased fashion. Software implementation and usage guidelines are provided for application to wider protein–organelle association experiments. In the wider context, semi-supervised organelle discovery is discussed as a paradigm with which to generate new protein annotations from MS-based organelle proteomics experiments. This article is part of a Special Issue entitled: New Horizons and Applications for Proteomics [EuPA 2012]

Upon the existence of short-time approximations of any polynomial order for the computation of density matrices by path integral methods

In this article, I provide significant mathematical evidence in support of the existence of short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and bounded from below potentials. While for Theorem 2, which is ``experimental'', I only provide a ``physicist's'' proof, I believe the present development is mathematically sound. As a verification, I explicitly construct two short-time approximations to the density matrix having convergence orders 3 and 4, respectively. Furthermore, in the Appendix, I derive the convergence constant for the trapezoidal Trotter path integral technique. The convergence orders and constants are then verified by numerical simulations. While the two short-time approximations constructed are of sure interest to physicists and chemists involved in Monte Carlo path integral simulations, the present article is also aimed at the mathematical community, who might find the results interesting and worth exploring. I conclude the paper by discussing the implications of the present findings with respect to the solvability of the dynamical sign problem appearing in real-time Feynman path integral simulations.Comment: 19 pages, 4 figures; the discrete short-time approximations are now treated as independent from their continuous version; new examples of discrete short-time approximations of order three and four are given; a new appendix containing a short review on Brownian motion has been added; also, some additional explanations are provided here and there; this is the last version; to appear in Phys. Rev.

The role of winding numbers in quantum Monte Carlo simulations

We discuss the effects of fixing the winding number in quantum Monte Carlo simulations. We present a simple geometrical argument as well as strong numerical evidence that one can obtain exact ground state results for periodic boundary conditions without changing the winding number. However, for very small systems the temperature has to be considerably lower than in simulations with fluctuating winding numbers. The relative deviation of a calculated observable from the exact ground state result typically scales as $T^{\gamma}$, where the exponent $\gamma$ is model and observable dependent and the prefactor decreases with increasing system size. Analytic results for a quantum rotor model further support our claim.Comment: 5 pages, 5 figure

Chaos, containment and change: responding to persistent offending by young people

This article reviews policy developments in Scotland concerning 'persistent young offenders' and then describes the design of a study intended to assist a local planning group in developing its response. The key findings of a review of casefiles of young people involved in persistent offending are reported. It emerges that youth crime and young people involved in offending are more complex and heterogeneous than is sometimes assumed. This, along with a review of some literature about desistance from offending, reaffirms the need for properly individualised interventions. Studies of 'desisters' suggest the centrality of effective and engaging working relationships in this process. However, these studies also re-assert the significance of the social contexts of workers’ efforts to bring 'change' out of 'chaos'. We conclude therefore that the 'new correctionalism' must be tempered with appreciation of the social exclusion of young people who offend

Brownian Dynamics Simulation of Polydisperse Hard Spheres

Standard algorithms for the numerical integration of the Langevin equation require that interactions are slowly varying during to the integration timestep. This in not the case for hard-body systems, where there is no clearcut between the correlation time of the noise and the timescale of the interactions. Starting from a short time approximation of the Smoluchowsky equation, we introduce an algorithm for the simulation of the overdamped Brownian dynamics of polydisperse hard-spheres in absence of hydrodynamics interactions and briefly discuss the extension to the case of external drifts

Quantum Monte Carlo in the Interaction Representation --- Application to a Spin-Peierls Model

A quantum Monte Carlo algorithm is constructed starting from the standard perturbation expansion in the interaction representation. The resulting configuration space is strongly related to that of the Stochastic Series Expansion (SSE) method, which is based on a direct power series expansion of exp(-beta*H). Sampling procedures previously developed for the SSE method can therefore be used also in the interaction representation formulation. The new method is first tested on the S=1/2 Heisenberg chain. Then, as an application to a model of great current interest, a Heisenberg chain including phonon degrees of freedom is studied. Einstein phonons are coupled to the spins via a linear modulation of the nearest-neighbor exchange. The simulation algorithm is implemented in the phonon occupation number basis, without Hilbert space truncations, and is exact. Results are presented for the magnetic properties of the system in a wide temperature regime, including the T-->0 limit where the chain undergoes a spin-Peierls transition. Some aspects of the phonon dynamics are also discussed. The results suggest that the effects of dynamic phonons in spin-Peierls compounds such as GeCuO3 and NaV2O5 must be included in order to obtain a correct quantitative description of their magnetic properties, both above and below the dimerization temperature.Comment: 23 pages, Revtex, 11 PostScript figure

Thermodynamic and diamagnetic properties of weakly doped antiferromagnets

Finite-temperature properties of weakly doped antiferromagnets as modeled by the two-dimensional t-J model and relevant to underdoped cuprates are investigated by numerical studies of small model systems at low doping. Two numerical methods are used: the worldline quantum Monte Carlo method with a loop cluster algorithm and the finite-temperature Lanczos method, yielding consistent results. Thermodynamic quantities: specific heat, entropy and spin susceptibility reveal a sizeable perturbation induced by holes introduced into a magnetic insulator, as well as a pronounced temperature dependence. The diamagnetic susceptibility introduced by coupling of the magnetic field to the orbital current reveals an anomalous temperature dependence, changing character from diamagnetic to paramagnetic at intermediate temperatures.Comment: LaTeX, 10 pages, 10 figures, submitted to Phys. Rev.

Quantum Monte Carlo Loop Algorithm for the t-J Model

We propose a generalization of the Quantum Monte Carlo loop algorithm to the t-J model by a mapping to three coupled six-vertex models. The autocorrelation times are reduced by orders of magnitude compared to the conventional local algorithms. The method is completely ergodic and can be formulated directly in continuous time. We introduce improved estimators for simulations with a local sign problem. Some first results of finite temperature simulations are presented for a t-J chain, a frustrated Heisenberg chain, and t-J ladder models.Comment: 22 pages, including 12 figures. RevTex v3.0, uses psf.te

Case management and Think First completion

“The final, definitive version of this article has been published in the Journal, Probation Journal, Vol 53 Issue 3, 2006, Copyright The Trade Union and Professional Association for Family Court and Probation Staff, by SAGE Publications Ltd at: http://prb.sagepub.com/ " DOI: 10.1177/0264550506066771This article considers the findings of a small-scale study of the practice of case managers supervising offenders required to attend the Think First Group. It explores the interface between one-to-one and group-based work within multi-modal programmes of supervision and seeks to identify those practices that support individuals in completing a group.Peer reviewe