13,356 research outputs found
Tight Bounds for the Randomized and Quantum Communication Complexities of Equality with Small Error
We investigate the randomized and quantum communication complexities of the
well-studied Equality function with small error probability , getting
the optimal constant factors in the leading terms in a number of different
models.
In the randomized model,
1) we give a general technique to convert public-coin protocols to
private-coin protocols by incurring a small multiplicative error, at a small
additive cost. This is an improvement over Newman's theorem [Inf. Proc.
Let.'91] in the dependence on the error parameter.
2) Using this we obtain a -cost private-coin
communication protocol that computes the -bit Equality function, to error
. This improves upon the upper bound
implied by Newman's theorem, and matches the best known lower bound, which
follows from Alon [Comb. Prob. Comput.'09], up to an additive
.
In the quantum model,
1) we exhibit a one-way protocol of cost , that uses only
pure states and computes the -bit Equality function to error .
This bound was implicitly already shown by Nayak [PhD thesis'99].
2) We show that any -error one-way protocol for -bit Equality
that uses only pure states communicates at least
qubits.
3) We exhibit a one-way protocol of cost , that
uses mixed states and computes the -bit Equality function to error
. This is also tight up to an additive ,
which follows from Alon's result.
Our upper bounds also yield upper bounds on the approximate rank and related
measures of the Identity matrix. This also implies improved upper bounds on
these measures for the distributed SINK function, which was recently used to
refute the randomized and quantum versions of the log-rank conjecture.Comment: 16 page
A close look into the carbon disk at the core of the planetary nebula CPD-568032
We present high spatial resolution observations of the dusty core of the
Planetary Nebula with Wolf-Rayet central star CPD-568032. These observations
were taken with the mid-infrared interferometer VLTI/MIDI in imaging mode
providing a typical 300 mas resolution and in interferometric mode using
UT2-UT3 47m baseline providing a typical spatial resolution of 20 mas. The
visible HST images exhibit a complex multilobal geometry dominated by faint
lobes. The farthest structures are located at 7" from the star. The mid-IR
environment of CPD-568032 is dominated by a compact source, barely resolved by
a single UT telescope in a 8.7 micron filter. The infrared core is almost fully
resolved with the three 40-45m projected baselines ranging from -5 to 51 degree
but smooth oscillating fringes at low level have been detected in spectrally
dispersed visibilities. This clear signal is interpreted in terms of a ring
structure which would define the bright inner rim of the equatorial disk.
Geometric models allowed us to derive the main geometrical parameters of the
disk. For instance, a reasonably good fit is reached with an achromatic and
elliptical truncated Gaussian with a radius of 97+/-11 AU, an inclination of
28+/-7 degree and a PA for the major axis at 345+/-7 degree. Furthermore, we
performed some radiative transfer modeling aimed at further constraining the
geometry and mass content of the disk, by taking into account the MIDI
dispersed visibilities, spectra, and the large aperture SED of the source.
These models show that the disk is mostly optically thin in the N band and
highly flared.Comment: Paper accepted in A&
Hydraulische invloed van structurele ingrepen tegen de verzanding van het Zwin
The specific fauna and flora of the natural reserve "Het Zwin" are generated by the seawater that streams in and out of the channels of the reserve at each tide. This water transports sand and mud, that are deposited in the channels and on the inundated surfaces. This way the chanels and saltmarshes are silting up gradually.The international Belgian-Dutch Commission of the Zwin has decided to stop the silting up and to maintain the Zwin as a salty tidal area.In 1987 a technical committee was established to deliberate on the mesures that had to be taken. In 1989 the main channel was deepened and a sandtrap introduced.This article represents mainly the calculations on mathematical model by Flanders Hydraulics to estimate the influence of different proposed solutions.Alternative managements are examined concerning their effect on the ecological values, the landscape and the recreational values of the Zwin.The international Commission of the Zwin has approuved a project in phases, where alternatives are combined to maintain and fortify the natural values of the Zwin
Simultaneous Communication Protocols with Quantum and Classical Messages
We study the simultaneous message passing (SMP) model of communication
complexity, for the case where one party is quantum and the other is classical.
We show that in an SMP protocol that computes some function with the first
party sending q qubits and the second sending c classical bits, the quantum
message can be replaced by a randomized message of O(qc) classical bits, as
well as by a deterministic message of O(q c log q) classical bits. Our proofs
rely heavily on earlier results due to Scott Aaronson.
In particular, our results imply that quantum-classical protocols need to
send Omega(sqrt{n/log n}) bits/qubits to compute Equality on n-bit strings, and
hence are not significantly better than classical-classical protocols (and are
much worse than quantum-quantum protocols such as quantum fingerprinting). This
essentially answers a recent question of Wim van Dam. Our results also imply,
more generally, that there are no superpolynomial separations between
quantum-classical and classical-classical SMP protocols for functional
problems. This contrasts with the situation for relational problems, where
exponential gaps between quantum-classical and classical-classical SMP
protocols are known. We show that this surprising situation cannot arise in
purely classical models: there, an exponential separation for a relational
problem can be converted into an exponential separation for a functional
problem.Comment: 11 pages LaTeX. 2nd version: author added and some changes to the
writin
A silicate disk in the heart of the Ant
We aim at getting high spatial resolution information on the dusty core of
bipolar planetary nebulae to directly constrain the shaping process. Methods:
We present observations of the dusty core of the extreme bipolar planetary
nebula Menzel 3 (Mz 3, Hen 2-154, the Ant) taken with the mid-infrared
interferometer MIDI/VLTI and the adaptive optics NACO/VLT. The core of Mz 3 is
clearly resolved with MIDI in the interferometric mode, whereas it is
unresolved from the Ks to the N bands with single dish 8.2 m observations on a
scale ranging from 60 to 250 mas. A striking dependence of the dust core size
with the PA angle of the baselines is observed, that is highly suggestive of an
edge-on disk whose major axis is perpendicular to the axis of the bipolar
lobes. The MIDI spectrum and the visibilities of Mz 3 exhibit a clear signature
of amorphous silicate, in contrast to the signatures of crystalline silicates
detected in binary post-AGB systems, suggesting that the disk might be
relatively young. We used radiative-transfer Monte Carlo simulations of a
passive disk to constrain its geometrical and physical parameters. Its
inclination (74 degrees 3 degrees) and position angle (5 degrees 5
degrees) are in accordance with the values derived from the study of the lobes.
The inner radius is 9 1 AU and the disk is relatively flat. The dust mass
stored in the disk, estimated as 1 x 10-5Msun, represents only a small fraction
of the dust mass found in the lobes and might be a kind of relic of an
essentially polar ejection process
Assessment of recent outbreaks of Dickeya sp (syn. Erwinia chrysanthemi) slow wilt in potato crops in Israel
Suspected Dickeya sp. strains were obtained from potato plants and tubers collected from commercial plots. The disease was observed on crops of various cultivars grown from seed tubers imported from the Netherlands during the spring seasons of 2004-2006, with disease incidence of 2-30% ( 10% in average). In addition to typical wilting symptoms on the foliage, in cases of severe infection, progeny tubers were rotten in the soil. Six strains were characterised by biochemical, serological and PCR amplification. All tests verified the strains as Dickeya sp. The repPCR and the biochemical assays showed that the strains isolated from blackleg diseased plants in Israel were very similar, if not identical to strains isolated from Dutch seed potatoes, suggesting that the infection in Israel originated from the Dutch seed. The strains were distantly related to D. dianthicola strains, typically found in potatoes in Western Europe, and were similar to biovar 3 D. dadanti or D. zeae. This is the first time that the presence of biovar 3 strains in potato in the Netherlands is described. One of the strains was used for pathogenicity assays on potato cvs Nicola and Mondial. Symptoms appeared 2 to 3 days after stem inoculation, and 7 to 10 days after soil inoculation. The control plants treated with water, or plants inoculated with Pectobacterium carotovorum, did not develop any symptoms with either method of inoculation. The identity of Dickeya sp. and P. carotovorum re- isolated from inoculated plants was confirmed by PCR and ELISA
Following the Problem Organisation: A Design Strategy for Engineering Emergence
To support the development of self-organising systems, we explain and rationalise the following architectural strategy: directly mapping the solution decomposition on the problem organisation and only relying on the problem abstractions for the design. We illustrate this with an example from swarm robotics
GIRAFFE multiple integral field units at VLT: a unique tool to recover velocity fields of distant galaxies
The GIRAFFE spectrograph is unique in providing the integral field
spectroscopy of fifteen distant galaxies at the same time. It has been
successfully implemented at the second VLT unit within the FLAMES facility. We
present GIRAFFE observations acquired during the Guaranteed Time Observation of
the Paris Observatory, using total exposure times ranging from 6 to 12 hours.
The reduced 3D cube of each galaxy has been deconvolved using our new package
DisGal3D. This software has been written using the only assumption that UV
light traces the emission line regions. The comparison between GIRAFFE spectra
and HST imagery allows us to recover details on velocity fields as small as
0.3-0.4 arcsec. It has been successfully tested using Fabry Perot observations
of nearby galaxies purposely redshifted to large distances. We present here
preliminary results for three distant galaxies at 0.45< z < 0.65, whose
velocity fields have been derived with exquisite spectral (R=10000) and spatial
resolutions. Observed velocity fields range from disturbed fields expected in
major merger events to those of regular spiral with minor perturbations. For
the latter, one could accurately derive the dynamical major axis and the
maximal rotational velocity. We conclude that dynamical properties of a large
number of distant galaxies can be routinely derived at VLT. This opens a new
avenue towards the understanding of the galaxy formation and evolution during
the last 8 Gyr.Comment: 4 pages, 3 jpeg figures. to appear in A&
The Fractal Properties of the Source and BEC
Using simple space-time implementation of the random cascade model we
investigate numerically influence of the possible fractal structure of the
emitting source on Bose-Einstein correlations between identical particles. The
results are then discussed in terms of the non-extensive Tsallis statistics.Comment: LaTeX file and 2 PS files with figures, 8 pages altogether. Talk
presented at the 12th Indian Summer School "Relativistic Heavy Ion Physics,
Prague, Czech Republic, 30 August-3 Sept. 1999; to be published in Czech J.
Phys. (1999). Some typos correcte
- âŠ