Possible Exotic Phases in the One-Dimensional Extended Hubbard Model

We investigate numerically the ground state phase diagram of the one-dimensional extended Hubbard model, including an on--site interaction U and a nearest--neighbor interaction V. We focus on the ground state phases of the model in the V >> U region, where previous studies have suggested the possibility of dominant superconducting pairing fluctuations before the system phase separates at a critical value V=V_PS. Using quantum Monte Carlo methods on lattices much larger than in previous Lanczos diagonalization studies, we determine the boundary of phase separation, the Luttinger Liquid correlation exponent K_rho, and other correlation functions in this region. We find that phase separation occurs for V significantly smaller than previously reported. In addition, for negative U, we find that a uniform state re-enters from phase separation as the electron density is increased towards half filling. For V < V_PS, our results show that superconducting fluctuations are not dominant. The system behaves asymptotically as a Luttinger Liquid with K_rho < 1, but we also find strong low-energy (but gapped) charge-density fluctuations at a momentum not expected for a standard Luttinger Liquid.

Intersubject Regularity in the Intrinsic Shape of Human V1

Previous studies have reported considerable intersubject variability in the three-dimensional geometry of the human primary visual cortex (V1). Here we demonstrate that much of this variability is due to extrinsic geometric features of the cortical folds, and that the intrinsic shape of V1 is similar across individuals. V1 was imaged in ten ex vivo human hemispheres using high-resolution (200 μm) structural magnetic resonance imaging at high field strength (7 T). Manual tracings of the stria of Gennari were used to construct a surface representation, which was computationally flattened into the plane with minimal metric distortion. The instrinsic shape of V1 was determined from the boundary of the planar representation of the stria. An ellipse provided a simple parametric shape model that was a good approximation to the boundary of flattened V1. The aspect ration of the best-fitting ellipse was found to be consistent across subject, with a mean of 1.85 and standard deviation of 0.12. Optimal rigid alignment of size-normalized V1 produced greater overlap than that achieved by previous studies using different registration methods. A shape analysis of published macaque data indicated that the intrinsic shape of macaque V1 is also stereotyped, and similar to the human V1 shape. Previoud measurements of the functional boundary of V1 in human and macaque are in close agreement with these results.

Protein Docking by the Underestimation of Free Energy Funnels in the Space of Encounter Complexes

Similarly to protein folding, the association of two proteins is driven by a free energy funnel, determined by favorable interactions in some neighborhood of the native state. We describe a docking method based on stochastic global minimization of funnel-shaped energy functions in the space of rigid body motions (SE(3)) while accounting for flexibility of the interface side chains. The method, called semi-definite programming-based underestimation (SDU), employs a general quadratic function to underestimate a set of local energy minima and uses the resulting underestimator to bias further sampling. While SDU effectively minimizes functions with funnel-shaped basins, its application to docking in the rotational and translational space SE(3) is not straightforward due to the geometry of that space. We introduce a strategy that uses separate independent variables for side-chain optimization, center-to-center distance of the two proteins, and five angular descriptors of the relative orientations of the molecules. The removal of the center-to-center distance turns out to vastly improve the efficiency of the search, because the five-dimensional space now exhibits a well-behaved energy surface suitable for underestimation. This algorithm explores the free energy surface spanned by encounter complexes that correspond to local free energy minima and shows similarity to the model of macromolecular association that proceeds through a series of collisions. Results for standard protein docking benchmarks establish that in this space the free energy landscape is a funnel in a reasonably broad neighborhood of the native state and that the SDU strategy can generate docking predictions with less than 5 � ligand interface Ca root-mean-square deviation while achieving an approximately 20-fold efficiency gain compared to Monte Carlo methods.