2,477 research outputs found
Dynamic Programming for Graphs on Surfaces
We provide a framework for the design and analysis of dynamic programming
algorithms for surface-embedded graphs on n vertices and branchwidth at most k.
Our technique applies to general families of problems where standard dynamic
programming runs in 2^{O(k log k)} n steps. Our approach combines tools from
topological graph theory and analytic combinatorics. In particular, we
introduce a new type of branch decomposition called "surface cut
decomposition", generalizing sphere cut decompositions of planar graphs
introduced by Seymour and Thomas, which has nice combinatorial properties.
Namely, the number of partial solutions that can be arranged on a surface cut
decomposition can be upper-bounded by the number of non-crossing partitions on
surfaces with boundary. It follows that partial solutions can be represented by
a single-exponential (in the branchwidth k) number of configurations. This
proves that, when applied on surface cut decompositions, dynamic programming
runs in 2^{O(k)} n steps. That way, we considerably extend the class of
problems that can be solved in running times with a single-exponential
dependence on branchwidth and unify/improve most previous results in this
direction.Comment: 28 pages, 3 figure
Dynamic programming for graphs on surfaces
We provide a framework for the design and analysis of dynamic
programming algorithms for surface-embedded graphs on n vertices
and branchwidth at most k. Our technique applies to general families
of problems where standard dynamic programming runs in 2O(k·log k).
Our approach combines tools from topological graph theory and
analytic combinatorics.Postprint (updated version
Coordinate representation of particle dynamics in AdS and in generic static spacetimes
We discuss the quantum dynamics of a particle in static curved spacetimes in
a coordinate representation. The scheme is based on the analysis of the squared
energy operator E^2, which is quadratic in momenta and contains a scalar
curvature term. Our main emphasis is on AdS spaces, where this term is fixed by
the isometry group. As a byproduct the isometry generators are constructed and
the energy spectrum is reproduced. In the massless case the conformal symmetry
is realized as well. We show the equivalence between this quantization and the
covariant quantization, based on the Klein-Gordon type equation in AdS. We
further demonstrate that the two quantization methods in an arbitrary
(N+1)-dimensional static spacetime are equivalent to each other if the scalar
curvature terms both in the operator E^2 and in the Klein-Gordon type equation
have the same coefficient equal to (N-1)/(4N).Comment: 14 pages, no figures, typos correcte
Season-Long Volatile Emissions from Peach and Pear Trees In Situ , Overlapping Profiles, and Olfactory Attraction of an Oligophagous Fruit Moth in the Laboratory
Insect herbivores that have more than one generation per year and reproduce on different host plants are confronted with substantial seasonal variation in the volatile blends emitted by their hosts. One way to deal with such variation is to respond to a specific set of compounds common to all host plants. The oriental fruit moth Cydia (=Grapholita) molesta is a highly damaging invasive pest. The stone fruit peach (Prunus persica) is its primary host, whereas pome fruits such as pear (Pyrus communis) are considered secondary hosts. In some parts of their geographic range, moth populations switch from stone to pome fruit orchards during the growing season. Here, we tested whether this temporal switch is facilitated by female responses to plant volatiles. We collected volatiles from peach and pear trees in situ and characterized their seasonal dynamics by gas chromatography-mass spectrometry. We also assessed the effects of the natural volatile blends released by the two plant species on female attraction by using Y-tube olfactometry. Finally, we related variations in volatile emissions to female olfactory responses. Our results indicate that the seasonal host switch from peach to pear is facilitated by the changing olfactory effect of the natural volatile blends being emitted. Peach volatiles were only attractive early and mid season, whereas pear volatiles were attractive from mid to late season. Blends from the various attractive stages shared a common set of five aldehydes, which are suggested to play an essential role in female attraction to host plants. Particular attention should be given to these aldehydes when designing candidate attractants for oriental fruit moth female
Properties of branes in curved spacetimes
A generic property of curved manifolds is the existence of focal points. We
show that branes located at focal points of the geometry satisfy special
properties. Examples of backgrounds to which our discussion applies are AdS_m x
S^n and plane wave backgrounds. As an example, we show that a pair of AdS_2
branes located at the north and south pole of the S^5 in AdS_5 x S^5 are half
supersymmetric and that they are dual to a two-monopole solution of N=4 SU(N)
SYM theory. Our second example involves spacelike branes in the (Lorentzian)
plane wave. We develop a modified lightcone gauge for the open string channel,
analyze in detail the cylinder diagram and establish open-closed duality. When
the branes are located at focal points of the geometry the amplitude acquires
most of the characteristics of flat space amplitudes. In the open string
channel the special properties are due to stringy modes that become massless.Comment: 41 pages; v2:typos corrected, ref adde
Electron impact double ionization of helium from classical trajectory calculations
With a recently proposed quasiclassical ansatz [Geyer and Rost, J. Phys. B 35
(2002) 1479] it is possible to perform classical trajectory ionization
calculations on many electron targets. The autoionization of the target is
prevented by a M\o{}ller type backward--forward propagation scheme and allows
to consider all interactions between all particles without additional
stabilization. The application of the quasiclassical ansatz for helium targets
is explained and total and partially differential cross sections for electron
impact double ionization are calculated. In the high energy regime the
classical description fails to describe the dominant TS1 process, which leads
to big deviations, whereas for low energies the total cross section is
reproduced well. Differential cross sections calculated at 250 eV await their
experimental confirmation.Comment: LaTeX, 22 pages, 10 figures, submitted to J. Phys.
Multi giant graviton systems, SUSY breaking and CFT
In this article, we describe giant gravitons in AdS_5 x S^5 moving along
generic trajectories in AdS_5. The giant graviton dynamics is solved by proving
that the D3-brane effective action reduces to that of a massive point particle
in AdS_5 and therefore the solutions are in one to one correspondence with
timelike geodesics of AdS_5. All these configurations are related via
isometries of the background, which induce target space symmetries in the world
volume theory of the D-brane. Hence, all these configurations preserve the same
amount of supersymmetry as the original giant graviton, i.e. half of the
maximal supersymmetry. Multiparticle configurations of two or more giant
gravitons are also considered. In particular, a binary system preserving one
quarter of the supersymmetries is found, providing a non trivial time-dependent
supersymmetric solution. A short study on the dual CFT description of all the
above states is given, including a derivation of the exact induced isometry map
in the CFT side of the correspondence.Comment: latex, 27+1 pages. v2: comment on mixing of states in section 4.3
added, reference added, typos corrected, final versio
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