2,367 research outputs found
Getting Feasible Variable Estimates From Infeasible Ones: MRF Local Polytope Study
This paper proposes a method for construction of approximate feasible primal
solutions from dual ones for large-scale optimization problems possessing
certain separability properties. Whereas infeasible primal estimates can
typically be produced from (sub-)gradients of the dual function, it is often
not easy to project them to the primal feasible set, since the projection
itself has a complexity comparable to the complexity of the initial problem. We
propose an alternative efficient method to obtain feasibility and show that its
properties influencing the convergence to the optimum are similar to the
properties of the Euclidean projection. We apply our method to the local
polytope relaxation of inference problems for Markov Random Fields and
demonstrate its superiority over existing methods.Comment: 20 page, 4 figure
Weyl structures with positive Ricci tensor
We prove the vanishing of the first Betti number on compact manifolds
admitting a Weyl structure whose Ricci tensor satisfies certain positivity
conditions, thus obtaining a Bochner-type vanishing theorem in Weyl geometry.
We also study compact Hermitian-Weyl manifolds with non-negative symmetric part
of the Ricci tensor of the canonical Weyl connection and show that every such
manifold has first Betti number and Hodge numbers for
, , for .Comment: 8 pages, Latex format, no figures; added section; to appear in Diff.
Geom. App
Emergence of Bloch oscillations in one-dimensional systems
Electrons in periodic potentials exhibit oscillatory motion in presence of an
electric field. Such oscillations are known as Bloch oscillations. In this
article we theoretically investigate the emergence of Bloch oscillations for
systems where the electric field is confined to a finite region, like in
typical electronic devices. We use a one-dimensional tight-binding model within
the single-band approximation to numerically study the dynamics of electrons
after a sudden switching-on of the electric field. We find a transition from a
regime with direct current to Bloch oscillations when increasing the system
size or decreasing the field strength. We propose a pump-probe scheme to
observe the oscillations by measuring the accumulated charge as a function of
the pulse-length
A Spectral Gap Estimate and Applications
We consider the Schr\"odinger operator -\frac{d^2}{d x^2} + V \qquad
\mbox{on an interval}~~[a,b]~\mbox{with Dirichlet boundary conditions}, where
is bounded from below and prove a lower bound on the first eigenvalue
in terms of sublevel estimates: if then The
result is sharp up to a universal constant if is an interval for the value of solving the minimization problem.
An immediate application is as follows: let be a
convex domain with inradius and diameter and let be the first eigenfunction of the Laplacian
on with Dirichlet boundary conditions on . We prove
which answers a question of van den Berg in the
special case of two dimensions
Seismic waves damping with arrays of inertial resonators
We investigate the elastic stop band properties of a theoretical cubic array
of iron spheres connected to a bulk of concrete via iron or rubber ligaments.
Each sphere can move freely within a surrounding air cavity, but ligaments
couple it to the bulk and further facilitate bending and rotational motions.
Associated low frequency local resonances are well predicted by an asymptotic
formula. We find complete stop bands (for all wave-polarizations) in the
frequency range Hertz (resp. Hertz) for -meter (resp.
-meter) diameter iron spheres with a -meter (resp. -meter)
center-to-center spacing, when they are connected to concrete via steel (resp.
rubber) ligaments. The scattering problem shows that only bending modes are
responsible for damping and that rotational modes are totally overwritten by
bending modes. Regarding seismic applications, we further consider soil as a
bulk medium, in which case the relative bandwidth of the low frequency stop
band can be enlarged through ligaments of different sizes that allow for well
separated bending and rotational modes. We finally achieve some damping of
elastodynamic waves from to Hertz (relative stop band of
percent) for iron spheres -meter in diameter that are connected to soil
with six rubber ligaments of optimized shapes. These results represent a
preliminary step in the design of seismic shields placed around, or underneath,
the foundations of large civil infrastructures
Aerodynamic Stability of Satellites in Elliptic Low Earth Orbits
Topical observations of the thermosphere at altitudes below are
of great benefit in advancing the understanding of the global distribution of
mass, composition, and dynamical responses to geomagnetic forcing, and momentum
transfer via waves. The perceived risks associated with such low altitude and
short duration orbits has prohibited the launch of Discovery-class missions.
Miniaturization of instruments such as mass spectrometers and advances in the
nano-satellite technology, associated with relatively low cost of
nano-satellite manufacturing and operation, open an avenue for performing low
altitude missions. The time dependent coefficients of a second order
non-homogeneous ODE which describes the motion have a double periodic shape.
Hence, they will be approximated using Jacobi elliptic functions. Through a
change of variables the original ODE will be converted into Hill's ODE for
stability analysis using Floquet theory. We are interested in how changes in
the coefficients of the ODE affect the stability of the solution. The expected
result will be an allowable range of parameters for which the motion is
dynamically stable. A possible extension of the application is a computational
tool for the rapid evaluation of the stability of entry or re-entry vehicles in
rarefied flow regimes and of satellites flying in relatively low orbits.Comment: 18 pages, 16 figure
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