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 $\epsilon$, 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 $(\log(n/\epsilon^2)+4)$-cost private-coin communication protocol that computes the $n$-bit Equality function, to error $\epsilon$. This improves upon the $\log(n/\epsilon^3)+O(1)$ 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 $\log\log(1/\epsilon)+O(1)$. In the quantum model, 1) we exhibit a one-way protocol of cost $\log(n/\epsilon)+4$, that uses only pure states and computes the $n$-bit Equality function to error $\epsilon$. This bound was implicitly already shown by Nayak [PhD thesis'99]. 2) We show that any $\epsilon$-error one-way protocol for $n$-bit Equality that uses only pure states communicates at least $\log(n/\epsilon)-\log\log(1/\epsilon)-O(1)$ qubits. 3) We exhibit a one-way protocol of cost $\log(\sqrt{n}/\epsilon)+3$, that uses mixed states and computes the $n$-bit Equality function to error $\epsilon$. This is also tight up to an additive $\log\log(1/\epsilon)+O(1)$, 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 $\pm$ 3 degrees) and position angle (5 degrees $\pm$ 5 degrees) are in accordance with the values derived from the study of the lobes. The inner radius is 9$\pm$ 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