42,809 research outputs found
Curvature of Co-Links Uncovers Hidden Thematic Layers in the World Wide Web
Beyond the information stored in pages of the World Wide Web, novel types of
``meta-information'' are created when they connect to each other. This
information is a collective effect of independent users writing and linking
pages, hidden from the casual user. Accessing it and understanding the
inter-relation of connectivity and content in the WWW is a challenging problem.
We demonstrate here how thematic relationships can be located precisely by
looking only at the graph of hyperlinks, gleaning content and context from the
Web without having to read what is in the pages. We begin by noting that
reciprocal links (co-links) between pages signal a mutual recognition of
authors, and then focus on triangles containing such links, since triangles
indicate a transitive relation. The importance of triangles is quantified by
the clustering coefficient (Watts) which we interpret as a curvature
(Gromov,Bridson-Haefliger). This defines a Web-landscape whose connected
regions of high curvature characterize a common topic. We show experimentally
that reciprocity and curvature, when combined, accurately capture this
meta-information for a wide variety of topics. As an example of future
directions we analyze the neural network of C. elegans (White, Wood), using the
same methods.Comment: 8 pages, 5 figures, expanded version of earlier submission with more
example
Complete Constant Mean Curvature surfaces and Bernstein type Theorems in
In this paper we study constant mean curvature surfaces in a product
space, , where is a complete
Riemannian manifold. We assume the angle function \nu = \meta{N}{\partial_t}
does not change sign on . We classify these surfaces according to the
infimum of the Gaussian curvature of the projection of .
When and , then is a cylinder over a
complete curve with curvature 2H. If H=0 and , then
must be a vertical plane or is a slice , or
with the flat metric and is a
tilted plane (after possibly passing to a covering space).
When , then is a vertical
cylinder over a complete curve of of constant geodesic curvature
. This result is optimal.
We also prove a non-existence result concerning complete multi-graphs in
, when
Nanoscale Equilibrium Crystal Shapes
The finite size and interface effects on equilibrium crystal shape (ECS) have
been investigated for the case of a surface free energy density including step
stiffness and inverse-square step-step interactions. Explicitly including the
curvature of a crystallite leads to an extra boundary condition in the solution
of the crystal shape, yielding a family of crystal shapes, governed by a shape
parameter c. The total crystallite free energy, including interface energy, is
minimized for c=0, yielding in all cases the traditional PT shape (z x3/2).
Solutions of the crystal shape for c≠0 are presented and discussed in the
context of meta-stable states due to the energy barrier for nucleation.
Explicit scaled relationships for the ECS and meta-stable states in terms of
the measurable step parameters and the interfacial energy are presented.Comment: 35 page
Stability Constraints on Classical de Sitter Vacua
We present further no-go theorems for classical de Sitter vacua in Type II
string theory, i.e., de Sitter constructions that do not invoke
non-perturbative effects or explicit supersymmetry breaking localized sources.
By analyzing the stability of the 4D potential arising from compactification on
manfiolds with curvature, fluxes, and orientifold planes, we found that
additional ingredients, beyond the minimal ones presented so far, are necessary
to avoid the presence of unstable modes. We enumerate the minimal setups for
(meta)stable de Sitter vacua to arise in this context.Comment: 18 pages; v2: argument improved, references adde
Exchange functionals based on finite uniform electron gases
We show how one can construct \alert{a simple} exchange functional by
extending the well-know local-density approximation (LDA) to finite uniform
electron gases. This new generalized local-density approximation (GLDA)
functional uses only two quantities: the electron density and the
curvature of the Fermi hole . This alternative "rung 2" functional can
be easily coupled with generalized-gradient approximation (GGA) functionals to
form a new family of "rung 3" meta-GGA (MGGA) functionals that we have named
factorizable MGGAs (FMGGAs). Comparisons are made with various LDA, GGA and
MGGA functionals for atoms and molecules.Comment: 20 pages, 5 figures and 2 table
Surface and curvature energies from jellium spheres: Density functional hierarchy and quantum Monte Carlo
We consider spherical jellium clusters with up to 200 electrons as a testing ground for density functional approximations to the exchange-correlation energy of a many-electron ground state. As nearly-exact standards, we employ HartreeâFock energies at the exchange-only level and the diffusion Monte Carlo (DMC) energies of Sottile and Ballone (2001) at the correlated level. The density functionals tested are the local spin density (LSD), generalized gradient (GGA), and meta-generalized gradient (meta-GGA) approximations; the latter gives the most accurate results. By fitting the deviation from the LSD energy of closed-shell clusters to the predictions of the liquid drop model, we extract the exchange-correlation surface energies and curvature energies of a semi-infinite jellium from the energies of finite clusters. For the density functionals, the surface energies so extracted agree closely with those calculated directly for a single planar surface. But for the diffusion Monte Carlo method, the surface energies so extracted are considerably lower (and we suspect more accurate) than those extrapolated by Acioli and Ceperley (1996) from their DMC supercell calculations. The errors of the LSD, GGA, and meta-GGA surface and curvature energies are estimated, and are found to be consistently small for both properties only at the meta-GGA level. These errors are qualitatively related to relative performances of the various density functionals for the calculation of atomization energies: the proper self-interaction correction to the LSD for a one-electron atom is in the curvature energy (as it is in meta-GGA), not in the surface energy (as it is in GGA). Additionally, a formula is given for the interpolation and extrapolation of the surface energy Ïxc as a function of the bulk density parameter r
Absence of a True Vortex-Glass Phase above the Bragg Glass Transition Line in Bi-2212
In magnetic measurements on BiSrCaCuO (Bi-2212)
single crystals, a general peak with a dynamical feature on both and
curves was found with S the magnetic relaxation rate. At higher fields,
the characteristic exponent becomes negative, together with the positive
curvature of vs. and the scaling based on the 2D vortex glass
theory or plastic creep theory, we conclude that the vortex motion above the
second peak is plastic when and there is no vortex glass phase at
finite temperatures in Bi-2212. The peak of S is then explained as the
crossover between different meta-stable vortex states.Comment: 10 pages, 5 figures, To appear in Physica
Exploring eternal stability with the simple harmonic universe
We construct nonsingular cyclic cosmologies that respect the null energy
condition, have a large hierarchy between the minimum and maximum size of the
universe, and are stable under linearized fluctuations. The models are
supported by a combination of positive curvature, a negative cosmological
constant, cosmic strings and matter that at the homogeneous level behaves as a
perfect fluid with equation of state -1 < w < -1/3. We investigate analytically
the stability of the perturbation equations and discuss the role of parametric
resonances and nonlinear corrections. Finally, we argue that Casimir energy
contributions associated to the compact spatial slices can become important at
short scales and lift nonperturbative decays towards vanishing size. This class
of models (particularly in the static limit) can then provide a useful
framework for studying the question of the ultimate (meta)stability of an
eternal universe.Comment: 22 pages, 2 figure
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