759 research outputs found
Kernels for Below-Upper-Bound Parameterizations of the Hitting Set and Directed Dominating Set Problems
In the {\sc Hitting Set} problem, we are given a collection of
subsets of a ground set and an integer , and asked whether has a
-element subset that intersects each set in . We consider two
parameterizations of {\sc Hitting Set} below tight upper bounds: and
. In both cases is the parameter. We prove that the first
parameterization is fixed-parameter tractable, but has no polynomial kernel
unless coNPNP/poly. The second parameterization is W[1]-complete,
but the introduction of an additional parameter, the degeneracy of the
hypergraph , makes the problem not only fixed-parameter
tractable, but also one with a linear kernel. Here the degeneracy of
is the minimum integer such that for each the
hypergraph with vertex set and edge set containing all edges of
without vertices in , has a vertex of degree at most
In {\sc Nonblocker} ({\sc Directed Nonblocker}), we are given an undirected
graph (a directed graph) on vertices and an integer , and asked
whether has a set of vertices such that for each vertex there is an edge (arc) from a vertex in to . {\sc Nonblocker} can be
viewed as a special case of {\sc Directed Nonblocker} (replace an undirected
graph by a symmetric digraph). Dehne et al. (Proc. SOFSEM 2006) proved that
{\sc Nonblocker} has a linear-order kernel. We obtain a linear-order kernel for
{\sc Directed Nonblocker}
A mechanistic model of connector hubs, modularity, and cognition
The human brain network is modular--comprised of communities of tightly
interconnected nodes. This network contains local hubs, which have many
connections within their own communities, and connector hubs, which have
connections diversely distributed across communities. A mechanistic
understanding of these hubs and how they support cognition has not been
demonstrated. Here, we leveraged individual differences in hub connectivity and
cognition. We show that a model of hub connectivity accurately predicts the
cognitive performance of 476 individuals in four distinct tasks. Moreover,
there is a general optimal network structure for cognitive
performance--individuals with diversely connected hubs and consequent modular
brain networks exhibit increased cognitive performance, regardless of the task.
Critically, we find evidence consistent with a mechanistic model in which
connector hubs tune the connectivity of their neighbors to be more modular
while allowing for task appropriate information integration across communities,
which increases global modularity and cognitive performance
Microwave state transfer and adiabatic dynamics of magnetically trapped polar molecules
Cold and ultracold polar molecules with nonzero electronic angular momentum
are of great interest for studies in quantum chemistry and control,
investigations of novel quantum systems, and precision measurement. However, in
mixed electric and magnetic fields, these molecules are generically subject to
a large set of avoided crossings among their Zeeman sublevels; in magnetic
traps, these crossings lead to distorted potentials and trap loss from electric
bias fields. We have characterized these crossings in OH by
microwave-transferring trapped OH molecules from the upper |f; M = +3/2> parity
state to the lower |e; +3/2> state and observing their trap dynamics under an
applied electric bias field. Our observations are very well described by a
simple Landau-Zener model, yielding insight to the rich spectra and dynamics of
polar radicals in mixed external fields.Comment: 5 pages, 4 figures plus supplementary materia
Low-energy molecular collisions in a permanent magnetic trap
Cold, neutral hydroxyl radicals are Stark decelerated and confined within a
magnetic trap consisting of two permanent ring magnets. The OH molecules are
trapped in the ro-vibrational ground state at a density of
cm and temperature of 70 mK. Collisions between the trapped OH sample
and supersonic beams of atomic He and molecular D are observed and
absolute collision cross sections measured. The He--OH and D--OH
center-of-mass collision energies are tuned from 60 cm to 230 cm
and 145 cm to 510 cm, respectively, yielding evidence of reduced
He--OH inelastic cross sections at energies below 84 cm, the OH ground
rotational level spacing.Comment: 4 pages, 4 figure
- β¦