3,839 research outputs found
Hypergraphic LP Relaxations for Steiner Trees
We investigate hypergraphic LP relaxations for the Steiner tree problem,
primarily the partition LP relaxation introduced by Koenemann et al. [Math.
Programming, 2009]. Specifically, we are interested in proving upper bounds on
the integrality gap of this LP, and studying its relation to other linear
relaxations. Our results are the following. Structural results: We extend the
technique of uncrossing, usually applied to families of sets, to families of
partitions. As a consequence we show that any basic feasible solution to the
partition LP formulation has sparse support. Although the number of variables
could be exponential, the number of positive variables is at most the number of
terminals. Relations with other relaxations: We show the equivalence of the
partition LP relaxation with other known hypergraphic relaxations. We also show
that these hypergraphic relaxations are equivalent to the well studied
bidirected cut relaxation, if the instance is quasibipartite. Integrality gap
upper bounds: We show an upper bound of sqrt(3) ~ 1.729 on the integrality gap
of these hypergraph relaxations in general graphs. In the special case of
uniformly quasibipartite instances, we show an improved upper bound of 73/60 ~
1.216. By our equivalence theorem, the latter result implies an improved upper
bound for the bidirected cut relaxation as well.Comment: Revised full version; a shorter version will appear at IPCO 2010
Open vent volcanoes fuelled by depth-integrated magma degassing
Open-vent, persistently degassing volcanoesâsuch as Stromboli and Etna (Italy), Villarrica (Chile), Bagana and Manam (Papua New Guinea), Fuego and Pacaya (Guatemala) volcanoesâproduce high gas fluxes and infrequent violent strombolian or âparoxysmalâ eruptions that erupt very little magma. Here we draw on examples of open-vent volcanic systems to highlight the principal characteristics of their degassing regimes and develop a generic model to explain open-vent degassing in both high and low viscosity magmas and across a range of tectonic settings. Importantly, gas fluxes from open-vent volcanoes are far higher than can be supplied by erupting magma and independent migration of exsolved volatiles is integral to the dynamics of such systems. The composition of volcanic gases emitted from open-vent volcanoes is consistent with its derivation from magma stored over a range of crustal depths that in general requires contributions from both magma decompression (magma ascent and/or convection) and iso- and polybaric second boiling processes. Prolonged crystallisation of water-rich basalts in crustal reservoirs produces a segregated exsolved hydrous volatile phase that may flux through overlying shallow magma reservoirs, modulating heat flux and generating overpressure in the shallow conduit. Small fraction water-rich melts generated in the lower and mid-crust may play an important role in advecting volatiles to subvolcanic reservoirs. Excessive gas fluxes at the surface are linked to extensive intrusive magmatic activity and endogenous crustal growth, aided in many cases by extensional tectonics in the crust, which may control the longevity and activity of open-vent volcanoes. There is emerging abundant geophysical evidence for the existence of a segregated exsolved magmatic volatile phase in magma storage regions in the crust. Here we provide a conceptual picture of gas-dominated volcanoes driven by magmatic intrusion and degassing throughout the crust
Imaginary in all directions: an elegant formulation of special relativity and classical electrodynamics
A suitable parameterization of space-time in terms of one complex and three
quaternionic imaginary units allows Lorentz transformations to be implemented
as multiplication by complex-quaternionic numbers rather than matrices.
Maxwell's equations reduce to a single equation.Comment: 8 page
Capillary interactions in Pickering emulsions
The effective capillary interaction potentials for small colloidal particles
trapped at the surface of liquid droplets are calculated analytically. Pair
potentials between capillary monopoles and dipoles, corresponding to particles
floating on a droplet with a fixed center of mass and subjected to external
forces and torques, respectively, exhibit a repulsion at large angular
separations and an attraction at smaller separations, with the latter
resembling the typical behavior for flat interfaces. This change of character
is not observed for quadrupoles, corresponding to free particles on a
mechanically isolated droplet. The analytical results for quadrupoles are
compared with the numerical minimization of the surface free energy of the
droplet in the presence of ellipsoidal particles.Comment: twocolumn, 8 pages, 3 figures, submitted to Phys. Rev.
Entanglement in SO(3)-invariant bipartite quantum systems
The structure of the state spaces of bipartite (N tensor N) quantum systems
which are invariant under product representations of the group SO(3) of
three-dimensional proper rotations is analyzed. The subsystems represent
particles of arbitrary spin j which transform according to an irreducible
representation of the rotation group. A positive map theta is introduced which
describes the time reversal symmetry of the local states and which is unitarily
equivalent to the transposition of matrices. It is shown that the partial time
reversal transformation theta_2 = (I tensor theta) acting on the composite
system can be expressed in terms of the invariant 6-j symbols introduced by
Wigner into the quantum theory of angular momentum. This fact enables a
complete geometrical construction of the manifold of states with positive
partial transposition and of the sets of separable and entangled states of (4
tensor 4) systems. The separable states are shown to form a three-dimensional
prism and a three-dimensional manifold of bound entangled states is identified.
A positive maps is obtained which yields, together with the time reversal, a
necessary and sufficient condition for the separability of states of (4 tensor
4) systems. The relations to the reduction criterion and to the recently
proposed cross norm criterion for separability are discussed.Comment: 15 pages, 3 figure
Reorientation Transition in Single-Domain (Ga,Mn)As
We demonstrate that the interplay of in-plane biaxial and uniaxial anisotropy
fields in (Ga,Mn)As results in a magnetization reorientation transition and an
anisotropic AC susceptibility which is fully consistent with a simple single
domain model. The uniaxial and biaxial anisotropy constants vary respectively
as the square and fourth power of the spontaneous magnetization across the
whole temperature range up to T_C. The weakening of the anisotropy at the
transition may be of technological importance for applications involving
thermally-assisted magnetization switching.Comment: 4 pages, 4 figure
Solving a "Hard" Problem to Approximate an "Easy" One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems
We consider geometric instances of the Maximum Weighted Matching Problem
(MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000
vertices. Making use of a geometric duality relationship between MWMP, MTSP,
and the Fermat-Weber-Problem (FWP), we develop a heuristic approach that yields
in near-linear time solutions as well as upper bounds. Using various
computational tools, we get solutions within considerably less than 1% of the
optimum.
An interesting feature of our approach is that, even though an FWP is hard to
compute in theory and Edmonds' algorithm for maximum weighted matching yields a
polynomial solution for the MWMP, the practical behavior is just the opposite,
and we can solve the FWP with high accuracy in order to find a good heuristic
solution for the MWMP.Comment: 20 pages, 14 figures, Latex, to appear in Journal of Experimental
Algorithms, 200
- âŠ