Density Matrix Renormalization Group Study of Random Dimerized Antiferromagnetic Heisenberg Chains

The effect of dimerization on the random antiferomagnetic Heisenberg chain with spin 1/2 is studied by the density matrix renormalization group method. The ground state energy, the energy gap distribution and the string order parameter are calculated. Using the finite size scaling analysis, the dimerization dependence of the these quantities are obtained. The ground state energy gain due to dimerization behaves as $u^a$ with $a > 2$ where $u$ denotes the degree of dimerization, suggesting the absence of spin-Peierls instability. It is explicitly shown that the string long range order survives even in the presence of randomness. The string order behaves as $u^{2\beta}$ with $\beta \sim 0.37$ in agreement with the recent prediction of real space renormalization group theory ($\beta =(3-\sqrt{5})/2 \simeq 0.382$). The physical picture of this behavior in this model is also discussed.Comment: 6 pages, 8 figures, to be published in Journal of the Physical Society of Japa

Connecting Seed Lists of Mammalian Proteins Using Steiner Trees

Multivariate experiments and genomics studies applied to mammalian cells often produce lists of genes or proteins altered under treatment/disease vs. control/normal conditions. Such lists can be identified in known protein-protein interaction networks to produce subnetworks that “connect” the genes or proteins from the lists. Such subnetworks are valuable for biologists since they can suggest regulatory mechanisms that are altered under different conditions. Often such subnetworks are overloaded with links and nodes resulting in connectivity diagrams that are illegible due to edge overlap. In this study, we attempt to address this problem by implementing an approximation to the Steiner Tree problem to connect seed lists of mammalian proteins/genes using literature-based protein-protein interaction networks. To avoid over-representation of hubs in the resultant Steiner Trees we assign a cost to Steiner Vertices based on their connectivity degree. We applied the algorithm to lists of genes commonly mutated in colorectal cancer to demonstrate the usefulness of this approach

Transcriptome Sequencing and Simple Sequence Repeat Marker Development for Three Macaronesian Endemic Plant Species

© 2016 White et al. Published by the Botanical Society of America. This work is licensed under a Creative Commons Attribution License (CC-BY-NC-SA). The attached file is the published version of the article

Morphology and reactivity of size-selected titanium oxide nanoclusters on Au(111).

The morphology and reactivity of mass-selected titania clusters, Ti3O6 and Ti3O5, deposited onto Au(111) were studied by scanning tunneling microscopy and temperature programmed desorption. Despite differing by only one oxygen atom, the stoichiometric Ti3O6 and the sub-stoichiometric ("reduced") Ti3O5 clusters exhibit very different structures and preferred binding sites. The Ti3O6 clusters bind at step edges and form small assemblies (2-4 clusters) on Au terraces, while the "reduced" Ti3O5 clusters form much larger fractal-like assemblies that can extend across step boundaries. Annealing the Ti3O5,6/Au(111) systems to higher temperatures causes changes in the size-distributions of cluster assemblies, but does not lead to the formation of TiOx nanoislands for temperatures ≤700 K. Reactivity studies show that the reduced Ti3O5 cluster has higher activity than Ti3O6 for 2-propanol dehydration, although both clusters exhibit substantial activity for dehydrogenation to acetone. Calculations using DFT+U suggest that the differences in aggregate morphology and reactivity are associated with the number of undercoordinated Ti3c sites in the supported clusters

Entanglement perturbation theory for the elementary excitation in one dimension

The entanglement perturbation theory is developed to calculate the excitation spectrum in one dimension. Applied to the spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model, it reproduces the des Cloiseaux-Pearson Bethe ansatz result. As for spin-1, the spin-triplet magnon spectrum has been determined for the first time for the entire Brillouin zone, including the Haldane gap at $k=\pi$

Determining SUSY model parameters and masses at the LHC using cross-sections, kinematic edges and other observables.

We address the problem of mass measurements of supersymmetric particles at the Large Hadron Collider, using the ATLAS detector as an example. By using Markov Chain sampling techniques to combine standard measurements of kinematic edges in the invariant mass distributions of decay products with a measurement of a missing $p_T$ cross-section, we show that the precision of mass measurements at the LHC can be dramatically improved, even when we do not assume that we have measured the kinematic endpoints precisely, or that we have identified exactly which particles are involved in the decay chain causing the endpoints. The generality of the technique is demonstrated in a preliminary investigation of a non-universal SUGRA model, in which we relax the requirements of mSUGRA by breaking the degeneracy of the GUT scale gaugino masses. The model studied is compatible with the WMAP limits on dark matter relic density

Application of Bayesian graphs to SN Ia data analysis and compression

Bayesian graphical models are an efficient tool for modelling complex data and derive self-consistent expressions of the posterior distribution of model parameters. We apply Bayesian graphs to perform statistical analyses of Type Ia supernova (SN Ia) luminosity distance measurements from the joint light-curve analysis (JLA) data set. In contrast to the $\chi^2$ approach used in previous studies, the Bayesian inference allows us to fully account for the standard-candle parameter dependence of the data covariance matrix. Comparing with $\chi^2$ analysis results, we find a systematic offset of the marginal model parameter bounds. We demonstrate that the bias is statistically significant in the case of the SN Ia standardization parameters with a maximal 6 $\sigma$ shift of the SN light-curve colour correction. In addition, we find that the evidence for a host galaxy correction is now only 2.4 $\sigma$. Systematic offsets on the cosmological parameters remain small, but may increase by combining constraints from complementary cosmological probes. The bias of the $\chi^2$ analysis is due to neglecting the parameter-dependent log-determinant of the data covariance, which gives more statistical weight to larger values of the standardization parameters. We find a similar effect on compressed distance modulus data. To this end, we implement a fully consistent compression method of the JLA data set that uses a Gaussian approximation of the posterior distribution for fast generation of compressed data. Overall, the results of our analysis emphasize the need for a fully consistent Bayesian statistical approach in the analysis of future large SN Ia data sets.Comment: 14 pages, 13 figures, 5 tables. Submitted to MNRAS. Compression utility available at https://gitlab.com/congma/libsncompress/ and example cosmology code with machine-readable version of Tables A1 & A2 at https://gitlab.com/congma/sn-bayesian-model-example/ v2: corrected typo in author's name. v3: 15 pages, incl. corrections, matches the accepted versio

gem-Dibromocyclopropanes and enzymatically derived cis-1,2-dihydrocatechols as building blocks in alkaloid synthesis

The application of the title building blocks, the 6,6-dibromobicyclo[3.1.0]hexanes and the cis-1,2-dihydrocatechols, to the total synthesis of crinine and lycorinine alkaloids is described.We thank the Australian Research Council and the Institute of Advanced Studies for generous financial support