Spectral Weights, d-wave Pairing Amplitudes, and Particle-hole Tunneling Asymmetry of a Strongly Correlated Superconductor

The spectral weights (SW's) for adding and removing an electron of the Gutzwiller projected d-wave superconducting (SC) state of the t-J-type models are studied numerically on finite lattices. Restrict to the uniform system but treat exactly the strong correlation between electrons, we show that the product of weights is equal to the pairing amplitude squared, same as in the weakly coupled case. In addition, we derive a rigorous relation of SW with doping in the electron doped system and obtain particle-hole asymmetry of the conductance-proportional quantity within the SC gap energy and, also, the anti-correlation between gap sizes and peak heights observed in tunneling spectroscopy on high Tc cuprates.Comment: 4 Revtex pages and 4 .eps figures. Published versio

Dimerized and trimerized phases for spin-2 Bosons in a one-dimensional optical lattice

We study the phase diagram for spin-2 bosons loaded in a one-dimensional optical lattice. By using non-Abelian density matrix renormalization group (DMRG) method we identify three possible phases: ferromagnetic, dimerized, and trimerized phases. We sketch the phase boundaries based on DMRG. We illustrate two methods for identifying the phases. The first method is based on the spin-spin correlation function while in the second method one observes the excitation gap as a dimerization or a trimerization superlattice is imposed. The advantage of the second method is that it can also be easily implemented in experiments. By using the scattering lengths in the literature we estimate that $^{83}$Rb, $^{23}$Na, and $^{87}$Rb be ferromagnetic, dimerized, and trimerized respectively.Comment: 4 pages, 3 figures. Add acknowledgemen

Quantum Critical Spin-2 Chain with Emergent SU(3) Symmetry

We study the quantum critical phase of a SU(2) symmetric spin-2 chain obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling of the entanglement entropy and finite-size energies by exact diagonalization and density-matrix renormalization group methods. From the numerical results of the energy spectrum, central charge, and scaling dimension we identify the conformal field theory describing the whole critical phase to be the SU(3)$_1$ Wess-Zumino-Witten model. We find that while in the whole critical phase the Hamiltonian is only SU(2) invariant, there is an emergent SU(3) symmetry in the thermodynamic limit

Parallel symbolic state-space exploration is difficult, but what is the alternative?

State-space exploration is an essential step in many modeling and analysis problems. Its goal is to find the states reachable from the initial state of a discrete-state model described. The state space can used to answer important questions, e.g., "Is there a dead state?" and "Can N become negative?", or as a starting point for sophisticated investigations expressed in temporal logic. Unfortunately, the state space is often so large that ordinary explicit data structures and sequential algorithms cannot cope, prompting the exploration of (1) parallel approaches using multiple processors, from simple workstation networks to shared-memory supercomputers, to satisfy large memory and runtime requirements and (2) symbolic approaches using decision diagrams to encode the large structured sets and relations manipulated during state-space generation. Both approaches have merits and limitations. Parallel explicit state-space generation is challenging, but almost linear speedup can be achieved; however, the analysis is ultimately limited by the memory and processors available. Symbolic methods are a heuristic that can efficiently encode many, but not all, functions over a structured and exponentially large domain; here the pitfalls are subtler: their performance varies widely depending on the class of decision diagram chosen, the state variable order, and obscure algorithmic parameters. As symbolic approaches are often much more efficient than explicit ones for many practical models, we argue for the need to parallelize symbolic state-space generation algorithms, so that we can realize the advantage of both approaches. This is a challenging endeavor, as the most efficient symbolic algorithm, Saturation, is inherently sequential. We conclude by discussing challenges, efforts, and promising directions toward this goal

Considerations to Model Heart Disease in Women with Preeclampsia and Cardiovascular Disease

Preeclampsia is a multifactorial cardiovascular disorder diagnosed after 20 weeks of gestation, and is the leading cause of death for both mothers and babies in pregnancy. The pathophysiology remains poorly understood due to the variability and unpredictability of disease manifestation when studied in animal models. After preeclampsia, both mothers and offspring have a higher risk of cardiovascular disease (CVD), including myocardial infarction or heart attack and heart failure (HF). Myocardial infarction is an acute myocardial damage that can be treated through reperfusion; however, this therapeutic approach leads to ischemic/reperfusion injury (IRI), often leading to HF. In this review, we compared the current in vivo, in vitro and ex vivo model systems used to study preeclampsia, IRI and HF. Future studies aiming at evaluating CVD in preeclampsia patients could benefit from novel models that better mimic the complex scenario described in this article

Density Matrices for a Chain of Oscillators

We consider chains with an optical phonon spectrum and study the reduced density matrices which occur in density-matrix renormalization group (DMRG) calculations. Both for one site and for half of the chain, these are found to be exponentials of bosonic operators. Their spectra, which are correspondingly exponential, are determined and discussed. The results for large systems are obtained from the relation to a two-dimensional Gaussian model.Comment: 15 pages,8 figure

Density-Matrix Spectra of Solvable Fermionic Systems

We consider non-interacting fermions on a lattice and give a general result for the reduced density matrices corresponding to parts of the system. This allows to calculate their spectra, which are essential in the DMRG method, by diagonalizing small matrices. We discuss these spectra and their typical features for various fermionic quantum chains and for the two-dimensional tight-binding model.Comment: 12 pages and 9 figure

Rho Kinases Regulate the Renewal and Neural Differentiation of Embryonic Stem Cells in a Cell Plating Density–Dependent Manner

[[abstract]]BACKGROUND: Rho kinases (ROCKs) mediate cell contraction, local adhesion, and cell motility, which are considered to be important in cell differentiation. We postulated that ROCKs are involved in controlling embryonic stem (ES) cell renewal and differentiation. METHODOLOGY/PRINCIPAL FINDINGS: CCE, a murine ES cell, was treated with Y-27632 for 48 to 96 hours and colony formation was evaluated. Y-27632 blocked CCE colony formation and induced CCE to grow as individual cells, regardless of the initial seeding cell density either at 10(4)/cm(2) ("high" seeding density) or 2x10(3)/cm(2) ("low" density). However, at high seeding density, Y-27632-treated cells exhibited reduction of alkaline phosphatase (AP) staining and Oct3/4 expression. They expressed SOX-1, nestin, and MAP2c, but not betaIII-tubulin or NG-2. They did not express endoderm or mesoderm lineage markers. After removal of Y-27632, the cells failed to form colonies or regain undifferentiated state. Silencing of ROCK-1 or ROCK-2 with selective small interference RNA induced CCE morphological changes similar to Y-27632. Silencing of ROCK-1 or ROCK-2 individually was sufficient to cause reduction of AP and Oct3/4, and expression of SOX-1, nestin, and MAP2c; and combined silencing of both ROCKs did not augment the effects exerted by individual ROCK siRNA. Y-27632-treated CCE cells seeded at 2x10(3) or 6.6x10(3) cells/cm(2) did not lose renewal factors or express differentiation markers. Furthermore, they were able to form AP-positive colonies after removal of Y-27632 and reseeding. Similar to ROCK inhibition by Y-27632, silencing of ROCK-1 or ROCK-2 in cells seeded at 2x10(3)/cm(2) did not change renewal factors. CONCLUSIONS/SIGNIFICANCE: We conclude that ROCKs promote ES cell colony formation, maintain them at undifferentiated state, and prevent them from neural differentiation at high seeding density. ROCK inhibition represents a new strategy for preparing large numbers of neural progenitor cells