2,848 research outputs found
Guess & Check Codes for Deletions and Synchronization
We consider the problem of constructing codes that can correct
deletions occurring in an arbitrary binary string of length bits.
Varshamov-Tenengolts (VT) codes can correct all possible single deletions
with an asymptotically optimal redundancy. Finding similar codes
for deletions is an open problem. We propose a new family of
codes, that we call Guess & Check (GC) codes, that can correct, with high
probability, a constant number of deletions occurring at uniformly
random positions within an arbitrary string. The GC codes are based on MDS
codes and have an asymptotically optimal redundancy that is . We provide deterministic polynomial time encoding and decoding schemes for
these codes. We also describe the applications of GC codes to file
synchronization.Comment: Accepted in ISIT 201
Cold reactive and non-reactive collisions of Li and Rb with C: implications for hybrid trap experiments
We present a theoretical investigation of cold reactive and non-reactive
collisions of Li and Rb atoms with C. The potential energy surfaces
for the singlet and triplet states of the Li--C and Rb--C
systems have been obtained using the CASSCF/ic-MRCI+Q approach with extended
basis sets. The potential energy surfaces are then used to investigate the
associative detachment reaction and to calculate rotationally inelastic cross
sections by means of the close-coupling method. The effect of the core
correlation on the potential energy surfaces is discussed and we estimate the
error on the collisional cross sections induced by freezing the orbitals
of the carbon atoms. The results are compared to those obtained for the
Rb-OH system and the applications for hybrid trap experiments are
explored. Furthermore, we discuss the possibility to perform Doppler
thermometry on the C anion and investigate the collision process
involving excited states. The implications for sympathetic cooling experiments
are also discussed
A stable classification of Lefschetz fibrations
We study the classification of Lefschetz fibrations up to stabilization by
fiber sum operations. We show that for each genus there is a `universal'
fibration f^0_g with the property that, if two Lefschetz fibrations over S^2
have the same Euler-Poincare characteristic and signature, the same numbers of
reducible singular fibers of each type, and admit sections with the same
self-intersection, then after repeatedly fiber summing with f^0_g they become
isomorphic. As a consequence, any two compact integral symplectic 4-manifolds
with the same values of (c_1^2, c_2, c_1.[w], [w]^2) become symplectomorphic
after blowups and symplectic sums with f^0_g.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol9/paper6.abs.htm
Reactivity of hydrated hydroxide anion cluster OH(HO) with H and Rb: an ab initio study
We present a theoretical investigation of the hydrated hydroxide anion
clusters OH(HO) and of the collisional complexes
H-OH(HO) and Rb-OH(HO) (with n). The MP2
and CCSD(T) methods are used to calculate interaction energies, optimized
geometries and vertical detachment energies. Part of the potential energy
surfaces are explored with a focus on the autodetachment region. We point out
the importance of diffuse functions to correctly describe the latter. We use
our results to discuss the different water loss and electronic detachment
channels which are the main reaction routes at room temperature. In particular,
we have considered a direct and an indirect process for the electronic
detachment, depending on whether water loss follows or precedes the detachment
of the excess electron. We use our results to discuss the implication for
astrochemistry and hybrid trap experiments in the context of cold chemistry
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