Unified microscopic approach to the interplay of pinned-Wigner-solid and liquid behavior of lowest-Landau-level states in the neighborhood of nu=1/3

Motivated by recent experiments, and using the rotating-and-vibrating electron-molecule (RVEM) theory [Yannouleas and Landman, Phys. Rev. B 66, 115315 (2002); Phys. Rev. A 81, 023609 (2010)], in conjunction with exact diagonalization, we develop a unified microscopic approach for the interplay between liquid fractional-quantum-Hall-effect (FQHE) states and Wigner-solid states in the lowest Landau level (LLL) in the neighborhood of nu=1/3. Liquid characteristics of the FQHE states are associated with the symmetry-conserving rotations and vibrations of the electron molecule. Although the electron densities of the symmetry-conserving LLL states do not exhibit crystalline patterns, the intrinsic crystalline correlations are reflected in the conditional probability distributions and the emergence of cusp yrast states in the LLL spectra. It is shown that away from the exact fractional fillings, weak pinning perturbations (due to weak disorder) may overcome the energy gaps between adjacent global states and generate pinned broken symmetry ground states as a superposition of symmetry-conserving LLL states with different total angular momenta. The electron densities of such mixed states (without good angular momentum quantum numbers) exhibit oscillating patterns that correspond to molecular crystallites. These pinned Wigner crystallites represent finite-size precursors of the bulk Wigner-solid state. It is further shown that the emergence of these molecular crystallites is a consequence of the presence of RVEM components in the symmetry-conserving LLL states. In addition, it is shown that the RVEM approach accounts for the Wigner-solid state in the neighborhood of nu=1, which was also found in the experiments. We utilize results for sizes in a wide range from N=6 to N=29 electrons, and we address the extrapolation to the thermodynamic limit.Comment: 19 pages, 17 figures, 4 tables. For related papers, see http://www.prism.gatech.edu/~ph274cy

Fiber Orientation Estimation Guided by a Deep Network

Diffusion magnetic resonance imaging (dMRI) is currently the only tool for noninvasively imaging the brain's white matter tracts. The fiber orientation (FO) is a key feature computed from dMRI for fiber tract reconstruction. Because the number of FOs in a voxel is usually small, dictionary-based sparse reconstruction has been used to estimate FOs with a relatively small number of diffusion gradients. However, accurate FO estimation in regions with complex FO configurations in the presence of noise can still be challenging. In this work we explore the use of a deep network for FO estimation in a dictionary-based framework and propose an algorithm named Fiber Orientation Reconstruction guided by a Deep Network (FORDN). FORDN consists of two steps. First, we use a smaller dictionary encoding coarse basis FOs to represent the diffusion signals. To estimate the mixture fractions of the dictionary atoms (and thus coarse FOs), a deep network is designed specifically for solving the sparse reconstruction problem. Here, the smaller dictionary is used to reduce the computational cost of training. Second, the coarse FOs inform the final FO estimation, where a larger dictionary encoding dense basis FOs is used and a weighted l1-norm regularized least squares problem is solved to encourage FOs that are consistent with the network output. FORDN was evaluated and compared with state-of-the-art algorithms that estimate FOs using sparse reconstruction on simulated and real dMRI data, and the results demonstrate the benefit of using a deep network for FO estimation.Comment: A shorter version is accepted by MICCAI 201

Edge and bulk components of lowest-Landau-level orbitals, correlated fractional quantum Hall effect incompressible states, and insulating behavior in finite graphene samples

Many-body calculations of the total energy of interacting Dirac electrons in finite graphene samples exhibit joint occurrence of cusps at angular momenta corresponding to fractional fillings characteristic of formation of incompressible (gapped) correlated states (nu=1/3 in particular) and opening of an insulating energy gap (that increases with the magnetic field) at the Dirac point, in correspondence with experiments. Single-particle basis functions obeying the zigzag boundary condition at the sample edge are employed in exact diagonalization of the interelectron Coulomb interaction, showing, at all sizes, mixed equal-weight bulk and edge components. The consequent depletion of the bulk electron density attenuates the fractional-quantum-Hall-effect excitation energies and the edge charge accumulation results in a gap in the many-body spectrum.Comment: 8 pages with 7 figures. REVTEX4. For related publications, see http://www.prism.gatech.edu/~ph274c

Celebration, preservation and promotion of struggle narratives with a focus on South African women of Indian heritage

The relevance and value of oral history practices and principles and its impact on community history gives credence to its relationship with the liberation struggle. The liberation struggle heroines that formed the cohort of interviewees for this research were members of the South African Indian community. This interview- research process provides a platform that allows the veteran South African female of Indian Heritage to reflect almost 50 years later and be a part of the celebration, preservation and promotion of struggle narratives. The women who were interviewed for this research shed light on celebrating political achievements, whilst remembering and recalling the educational, material and economic assistance from international sources. Furthermore, these women referred to the preservation of South Africa’s unique heritage as, South Africa is united in its diversity. Promoting the values of the liberation struggle by sharing her anecdotes, honouring the cadres, relating experiences, retelling tales and sometimes possibly reliving military camp days completed the oral history interview process and eventually added to the body of knowledge that already exists and partially filled the gaps that exist. Contribution: From a multidisplinary religious perspective, this article contributes to the historical and social-cultural discourse on liberation theology within a paradigm in which the intersection of social sciences and humanities generates a transdisciplinary contested discourse

Edge states in graphene quantum dots: Fractional quantum Hall effect analogies and differences at zero magnetic field

We investigate the way that the degenerate manifold of midgap edge states in quasicircular graphene quantum dots with zig-zag boundaries supports, under free-magnetic-field conditions, strongly correlated many-body behavior analogous to the fractional quantum Hall effect (FQHE), familiar from the case of semiconductor heterostructures in high magnetic fields. Systematic exact-diagonalization (EXD) numerical studies are presented for the first time for 5 <= N <= 8 fully spin-polarized electrons and for total angular momenta in the range of N(N-1)/2 <= L <= 150. We present a derivation of a rotating-electron-molecule (REM) type wave function based on the methodology introduced earlier [C. Yannouleas and U. Landman, Phys. Rev. B 66, 115315 (2002)] in the context of the FQHE in two-dimensional semiconductor quantum dots. The EXD wave functions are compared with FQHE trial functions of the Laughlin and the derived REM types. It is found that a variational extension of the REM offers a better description for all fractional fillings compared with that of the Laughlin functions (including total energies and overlaps), a fact that reflects the strong azimuthal localization of the edge electrons. In contrast with the multiring arrangements of electrons in circular semiconductor quantum dots, the graphene REMs exhibit in all instances a single (0,N) polygonal-ring molecular (crystalline) structure, with all the electrons localized on the edge. Disruptions in the zig-zag boundary condition along the circular edge act effectively as impurities that pin the electron molecule, yielding single-particle densities with broken rotational symmetry that portray directly the azimuthal localization of the edge electrons.Comment: Revtex. 14 pages with 13 figures and 2 tables. Physical Review B, in press. For related papers, see http://www.prism.gatech.edu/~ph274cy

Quantifying evenly distributed states in exclusion and nonexclusion processes

Spatial-point data sets, generated from a wide range of physical systems and mathematical models, can be analyzed by counting the number of objects in equally sized bins. We find that the bin counts are related to the Pólya distribution. New measures are developed which indicate whether or not a spatial data set, generated from an exclusion process, is at its most evenly distributed state, the complete spatial randomness (CSR) state. To this end, we define an index in terms of the variance between the bin counts. Limiting values of the index are determined when objects have access to the entire domain and when there are subregions of the domain that are inaccessible to objects. Using three case studies (Lagrangian fluid particles in chaotic laminar flows, cellular automata agents in discrete models, and biological cells within colonies), we calculate the indexes and verify that our theoretical CSR limit accurately predicts the state of the system. These measures should prove useful in many biological applications.Benjamin J. Binder and Kerry A. Landma

Parasitic helminths induce fetal-like reversion in the intestinal stem cell niche.

Epithelial surfaces form critical barriers to the outside world and are continuously renewed by adult stem cells1. Whereas dynamics of epithelial stem cells during homeostasis are increasingly well understood, how stem cells are redirected from a tissue-maintenance program to initiate repair after injury remains unclear. Here we examined infection by Heligmosomoides polygyrus, a co-evolved pathosymbiont of mice, to assess the epithelial response to disruption of the mucosal barrier. H. polygyrus disrupts tissue integrity by penetrating the duodenal mucosa, where it develops while surrounded by a multicellular granulomatous infiltrate2. Crypts overlying larvae-associated granulomas did not express intestinal stem cell markers, including Lgr53, in spite of continued epithelial proliferation. Granuloma-associated Lgr5- crypt epithelium activated an interferon-gamma (IFN-γ)-dependent transcriptional program, highlighted by Sca-1 expression, and IFN-γ-producing immune cells were found in granulomas. A similar epithelial response accompanied systemic activation of immune cells, intestinal irradiation, or ablation of Lgr5+ intestinal stem cells. When cultured in vitro, granuloma-associated crypt cells formed spheroids similar to those formed by fetal epithelium, and a sub-population of H. polygyrus-induced cells activated a fetal-like transcriptional program, demonstrating that adult intestinal tissues can repurpose aspects of fetal development. Therefore, re-initiation of the developmental program represents a fundamental mechanism by which the intestinal crypt can remodel itself to sustain function after injury