Valence Bond Entanglement and Fluctuations in Random Singlet Phases

The ground state of the uniform antiferromagnetic spin-1/2 Heisenberg chain can be viewed as a strongly fluctuating liquid of valence bonds, while in disordered chains these bonds lock into random singlet states on long length scales. We show that this phenomenon can be studied numerically, even in the case of weak disorder, by calculating the mean value of the number of valence bonds leaving a block of $L$ contiguous spins (the valence-bond entanglement entropy) as well as the fluctuations in this number. These fluctuations show a clear crossover from a small $L$ regime, in which they behave similar to those of the uniform model, to a large $L$ regime in which they saturate in a way consistent with the formation of a random singlet state on long length scales. A scaling analysis of these fluctuations is used to study the dependence on disorder strength of the length scale characterizing the crossover between these two regimes. Results are obtained for a class of models which include, in addition to the spin-1/2 Heisenberg chain, the uniform and disordered critical 1D transverse-field Ising model and chains of interacting non-Abelian anyons.Comment: 8 pages, 6 figure

Infinite-Randomness Fixed Points for Chains of Non-Abelian Quasiparticles

One-dimensional chains of non-Abelian quasiparticles described by $SU(2)_k$ Chern-Simons-Witten theory can enter random singlet phases analogous to that of a random chain of ordinary spin-1/2 particles (corresponding to $k \to \infty$). For $k=2$ this phase provides a random singlet description of the infinite randomness fixed point of the critical transverse field Ising model. The entanglement entropy of a region of size $L$ in these phases scales as $S_L \simeq \frac{\ln d}{3} \log_2 L$ for large $L$, where $d$ is the quantum dimension of the particles.Comment: 4 pages, 4 figure

ArDM: a ton-scale liquid Argon experiment for direct detection of Dark Matter in the Universe

The ArDM project aims at developing and operating large noble liquid detectors to search for direct evidence of Weakly Interacting Massive Particle (WIMP) as Dark Matter in the Universe. The initial goal is to design, assemble and operate a $\approx$1 ton liquid Argon prototype to demonstrate the feasibility of a ton-scale experiment with the required performance to efficiently detect and sufficiently discriminate backgrounds for a successful WIMP detection. Our design addresses the possibility to detect independently ionization and scintillation signals. In this paper, we describe this goal and the conceptual design of the detector.Comment: 5 pages, 3 figures, Talk given at IXth international conference on Topics in Astroparticle and Underground Physics (TAUP05), Zaragoza, (Spain

Subsurface Volatile Deposition on Mars

We have modelled the transport of heat in the martian regolith, taking into account the change in thermal properties caused by an increase in water ice content. Under these conditions we have found that the addition of water ice allows for increased ice formation at depth, rather than under the assumption that thermal properties are unchanged. This is important because it will affect estimates of global subsurface volatile deposition

Subsurface Volatile Deposition on Mars

We have modelled the transport of heat in the martian regolith, taking into account the change in thermal properties caused by an increase in water ice content. Under these conditions we have found that the addition of water ice allows for increased ice formation at depth, rather than under the assumption that thermal properties are unchanged. This is important because it will affect estimates of global subsurface volatile deposition

On the Prior Sensitivity of Thompson Sampling

The empirically successful Thompson Sampling algorithm for stochastic bandits has drawn much interest in understanding its theoretical properties. One important benefit of the algorithm is that it allows domain knowledge to be conveniently encoded as a prior distribution to balance exploration and exploitation more effectively. While it is generally believed that the algorithm's regret is low (high) when the prior is good (bad), little is known about the exact dependence. In this paper, we fully characterize the algorithm's worst-case dependence of regret on the choice of prior, focusing on a special yet representative case. These results also provide insights into the general sensitivity of the algorithm to the choice of priors. In particular, with $p$ being the prior probability mass of the true reward-generating model, we prove $O(\sqrt{T/p})$ and $O(\sqrt{(1-p)T})$ regret upper bounds for the bad- and good-prior cases, respectively, as well as \emph{matching} lower bounds. Our proofs rely on the discovery of a fundamental property of Thompson Sampling and make heavy use of martingale theory, both of which appear novel in the literature, to the best of our knowledge.Comment: Appears in the 27th International Conference on Algorithmic Learning Theory (ALT), 201

Longitudinal Reproducibility of Neurite Orientation Dispersion and Density Imaging (NODDI) Derived Metrics in the White Matter

Diffusion-weighted magnetic resonance imaging (DWI) is undergoing constant evolution with the ambitious goal of developing in-vivo histology of the brain. A recent methodological advancement is Neurite Orientation Dispersion and Density Imaging (NODDI), a histologically validated multi-compartment model to yield microstructural features of brain tissue such as geometric complexity and neurite packing density, which are especially useful in imaging the white matter. Since NODDI is increasingly popular in clinical research and fields such as developmental neuroscience and neuroplasticity, it is of vast importance to characterize its reproducibility (or reliability). We acquired multi-shell DWI data in 29 healthy young subjects twice over a rescan interval of 4 weeks to assess the within-subject coefficient of variation (CVWS), between-subject coefficient of variation (CVBS) and the intraclass correlation coefficient (ICC), respectively. Using these metrics, we compared regional and voxel-by-voxel reproducibility of the most common image analysis approaches (tract-based spatial statistics [TBSS], voxel-based analysis with different extents of smoothing [“VBM-style”], ROI-based analysis). We observed high test–retest reproducibility for the orientation dispersion index (ODI) and slightly worse results for the neurite density index (NDI). Our findings also suggest that the choice of analysis approach might have significant consequences for the results of a study. Collectively, the voxel-based approach with Gaussian smoothing kernels of ≥4 mm FWHM and ROI-averaging yielded the highest reproducibility across NDI and ODI maps (CVWS mostly ≤3%, ICC mostly ≥0.8), respectively, whilst smaller kernels and TBSS performed consistently worse. Furthermore, we demonstrate that image quality (signal-to-noise ratio [SNR]) is an important determinant of NODDI metric reproducibility. We discuss the implications of these results for longitudinal and cross-sectional research designs commonly employed in the neuroimaging field

Vaccine-Induced Subcutaneous Granulomas in Goats Reflect Differences in Host–Mycobacterium Interactions between BCG- and Recombinant BCG-Derivative Vaccines

Tuberculous granulomas are highly dynamic structures reflecting the complex host–mycobacterium interactions. The objective of this study was to compare granuloma development at the site of vaccination with BCG and its recombinant derivatives in goats. To characterize the host response, epithelioid cells, multinucleated giant cells (MNGC), T cell subsets, B cells, plasma cells, dendritic cells and mycobacterial antigen were labelled by immunohistochemistry, and lipids and acid-fast bacteria (AFB) were labelled by specific staining. Granulomas with central caseous necrosis developed at the injection site of most goats though lesion size and extent of necrosis differed between vaccine strains. CD4(+) T and B cells were more scarce and CD8(+) cells were more numerous in granulomas induced by recombinant derivatives compared to their parental BCG strain. Further, the numbers of MNGCs and cells with lipid bodies were markedly lower in groups administered with recombinant BCG strains. Microscopic detection of AFB and mycobacterial antigen was rather frequent in the area of central necrosis, however, the isolation of bacteria in culture was rarely successful. In summary, BCG and its recombinant derivatives induced reproducibly subcutaneous caseous granulomas in goats that can be easily monitored and surgically removed for further studies. The granulomas reflected the genetic modifications of the recombinant BCG-derivatives and are therefore suitable models to compare reactions to different mycobacteria or TB vaccines

Finite size scaling for quantum criticality using the finite-element method

Finite size scaling for the Schr\"{o}dinger equation is a systematic approach to calculate the quantum critical parameters for a given Hamiltonian. This approach has been shown to give very accurate results for critical parameters by using a systematic expansion with global basis-type functions. Recently, the finite element method was shown to be a powerful numerical method for ab initio electronic structure calculations with a variable real-space resolution. In this work, we demonstrate how to obtain quantum critical parameters by combining the finite element method (FEM) with finite size scaling (FSS) using different ab initio approximations and exact formulations. The critical parameters could be atomic nuclear charges, internuclear distances, electron density, disorder, lattice structure, and external fields for stability of atomic, molecular systems and quantum phase transitions of extended systems. To illustrate the effectiveness of this approach we provide detailed calculations of applying FEM to approximate solutions for the two-electron atom with varying nuclear charge; these include Hartree-Fock, density functional theory under the local density approximation, and an "exact"' formulation using FEM. We then use the FSS approach to determine its critical nuclear charge for stability; here, the size of the system is related to the number of elements used in the calculations. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that it is possible to combine finite size scaling with the finite-element method by using ab initio calculations to obtain quantum critical parameters. The combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems.Comment: 15 pages, 19 figures, revision based on suggestions by referee, accepted in Phys. Rev.