21,930 research outputs found
A randomized polynomial kernel for Subset Feedback Vertex Set
The Subset Feedback Vertex Set problem generalizes the classical Feedback
Vertex Set problem and asks, for a given undirected graph , a set , and an integer , whether there exists a set of at most
vertices such that no cycle in contains a vertex of . It was
independently shown by Cygan et al. (ICALP '11, SIDMA '13) and Kawarabayashi
and Kobayashi (JCTB '12) that Subset Feedback Vertex Set is fixed-parameter
tractable for parameter . Cygan et al. asked whether the problem also admits
a polynomial kernelization.
We answer the question of Cygan et al. positively by giving a randomized
polynomial kernelization for the equivalent version where is a set of
edges. In a first step we show that Edge Subset Feedback Vertex Set has a
randomized polynomial kernel parameterized by with
vertices. For this we use the matroid-based tools of Kratsch and Wahlstr\"om
(FOCS '12) that for example were used to obtain a polynomial kernel for
-Multiway Cut. Next we present a preprocessing that reduces the given
instance to an equivalent instance where the size of
is bounded by . These two results lead to a polynomial kernel for
Subset Feedback Vertex Set with vertices
Stability Boundaries for Resonant Migrating Planet Pairs
Convergent migration allows pairs of planet to become trapped into mean
motion resonances. Once in resonance, the planets' eccentricities grow to an
equilibrium value that depends on the ratio of migration time scale to the
eccentricity damping timescale, , with higher values of
equilibrium eccentricity for lower values of . For low equilibrium
eccentricities, . The stability of a planet pair
depends on eccentricity so the system can become unstable before it reaches its
equilibrium eccentricity. Using a resonant overlap criterion that takes into
account the role of first and second order resonances and depends on
eccentricity, we find a function that defines the lowest
value for , as a function of the ratio of total planet mass to stellar mass
() and the period ratio of the resonance defined as ,
that allows two convergently migrating planets to remain stable in resonance at
their equilibrium eccentricities. We scaled the functions for each
resonance of the same order into a single function . The function
for planet pairs in first order resonances is linear with increasing planet
mass and quadratic for pairs in second order resonances with a coefficient
depending on the relative migration rate and strongly on the planet to planet
mass ratio. The linear relation continues until the mass approaches a critical
mass defined by the 2/7 resonance overlap instability law and .
We compared our analytic boundary with an observed sample of resonant two
planet systems. All but one of the first order resonant planet pair systems
found by radial velocity measurements are well inside the stability region
estimated by this model. We calculated for Kepler systems without
well-constrained eccentricities and found only weak constraints on .Comment: 11 pages, 7 figure
A new proof of a Nordgren, Rosenthal and Wintrobe Theorem on universal operators
A striking result by Nordgren, Rosenthal and Wintrobe states that the Invariant Subspace Problem is equivalent to the fact that any minimal invariant subspace for a composition operator Cφ induced by a hyperbolic automorphism φ of the unit disc D acting on the classical Hardy space H² is one dimensional. We provide a completely different proof of Nordgren, Rosenthal and Wintrobe’s Theorem based on analytic Toeplitz operators
A hyperbolic universal operator commuting with a compact operator
A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a non-trivial, quasinilpotent, injective, compact operator with dense range, but unlike other examples, it acts on the Bergman space instead of the Hardy space and this operator is associated with a `hyperbolic' composition operator
Effects of screened Coulomb impurities on autoionizing two-electron resonances in spherical quantum dots
In a recent paper (Phys. Rev. B {\bf 78}, 075316 (2008)), Sajeev and Moiseyev
demonstrated that the bound-to-resonant transitions and lifetimes of
autoionizing states in spherical quantum dots can be controlled by varying the
confinment strength. In the present paper, we report that such control can in
some cases be compromised by the presence of Coulomb impurities. It is
demonstrated that a screened Coulomb impurity placed in the vicinity of the dot
center can lead to bound-to-resonant transitions and to avoided crossings-like
behavior when the screening of the impurity charge is varied. It is argued that
these properties also can have impact on electron transport through quantum dot
arrays
The Likelihood Encoder for Lossy Source Compression
In this work, a likelihood encoder is studied in the context of lossy source
compression. The analysis of the likelihood encoder is based on a soft-covering
lemma. It is demonstrated that the use of a likelihood encoder together with
the soft-covering lemma gives alternative achievability proofs for classical
source coding problems. The case of the rate-distortion function with side
information at the decoder (i.e. the Wyner-Ziv problem) is carefully examined
and an application of the likelihood encoder to the multi-terminal source
coding inner bound (i.e. the Berger-Tung region) is outlined.Comment: 5 pages, 2 figures, ISIT 201
Mixed-state evolution in the presence of gain and loss
A model is proposed that describes the evolution of a mixed state of a
quantum system for which gain and loss of energy or amplitude are present.
Properties of the model are worked out in detail. In particular, invariant
subspaces of the space of density matrices corresponding to the fixed points of
the dynamics are identified, and the existence of a transition between the
phase in which gain and loss are balanced and the phase in which this balance
is lost is illustrated in terms of the time average of observables. The model
is extended to include a noise term that results from a uniform random
perturbation generated by white noise. Numerical studies of example systems
show the emergence of equilibrium states that suppress the phase transition.Comment: 5 pages, 2 figures (published version
A Rate-Distortion Based Secrecy System with Side Information at the Decoders
A secrecy system with side information at the decoders is studied in the
context of lossy source compression over a noiseless broadcast channel. The
decoders have access to different side information sequences that are
correlated with the source. The fidelity of the communication to the legitimate
receiver is measured by a distortion metric, as is traditionally done in the
Wyner-Ziv problem. The secrecy performance of the system is also evaluated
under a distortion metric. An achievable rate-distortion region is derived for
the general case of arbitrarily correlated side information. Exact bounds are
obtained for several special cases in which the side information satisfies
certain constraints. An example is considered in which the side information
sequences come from a binary erasure channel and a binary symmetric channel.Comment: 8 pages. Allerton 201
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