1,228 research outputs found
Completeness of Flat Coalgebraic Fixpoint Logics
Modal fixpoint logics traditionally play a central role in computer science,
in particular in artificial intelligence and concurrency. The mu-calculus and
its relatives are among the most expressive logics of this type. However,
popular fixpoint logics tend to trade expressivity for simplicity and
readability, and in fact often live within the single variable fragment of the
mu-calculus. The family of such flat fixpoint logics includes, e.g., LTL, CTL,
and the logic of common knowledge. Extending this notion to the generic
semantic framework of coalgebraic logic enables covering a wide range of logics
beyond the standard mu-calculus including, e.g., flat fragments of the graded
mu-calculus and the alternating-time mu-calculus (such as alternating-time
temporal logic ATL), as well as probabilistic and monotone fixpoint logics. We
give a generic proof of completeness of the Kozen-Park axiomatization for such
flat coalgebraic fixpoint logics.Comment: Short version appeared in Proc. 21st International Conference on
Concurrency Theory, CONCUR 2010, Vol. 6269 of Lecture Notes in Computer
Science, Springer, 2010, pp. 524-53
Instrumental polarisation at the Nasmyth focus of the E-ELT
The ~39-m European Extremely Large Telescope (E-ELT) will be the largest
telescope ever built. This makes it particularly suitable for sensitive
polarimetric observations, as polarimetry is a photon-starved technique.
However, the telescope mirrors may severely limit the polarimetric accuracy of
instruments on the Nasmyth platforms by creating instrumental polarisation
and/or modifying the polarisation signal of the object. In this paper we
characterise the polarisation effects of the two currently considered designs
for the E-ELT Nasmyth ports as well as the effect of ageing of the mirrors. By
means of the Mueller matrix formalism, we compute the response matrices of each
mirror arrangement for a range of zenith angles and wavelengths. We then
present two techniques to correct for these effects that require the addition
of a modulating device at the polarisation-free intermediate focus that acts
either as a switch or as a part of a two-stage modulator. We find that the
values of instrumental polarisation, Stokes transmission reduction and cross-
talk vary significantly with wavelength, and with pointing, for the lateral
Nasmyth case, often exceeding the accuracy requirements for proposed
polarimetric instruments. Realistic ageing effects of the mirrors after perfect
calibration of these effects may cause polarimetric errors beyond the
requirements. We show that the modulation approach with a polarimetric element
located in the intermediate focus reduces the instrumental polarisation effects
down to tolerable values, or even removes them altogether. The E-ELT will be
suitable for sensitive and accurate polarimetry, provided frequent calibrations
are carried out, or a dedicated polarimetric element is installed at the
intermediate focus.Comment: Accepted for publication in A&
Algorithmic correspondence and completeness in modal logic. I. The core algorithm SQEMA
Modal formulae express monadic second-order properties on Kripke frames, but
in many important cases these have first-order equivalents. Computing such
equivalents is important for both logical and computational reasons. On the
other hand, canonicity of modal formulae is important, too, because it implies
frame-completeness of logics axiomatized with canonical formulae.
Computing a first-order equivalent of a modal formula amounts to elimination
of second-order quantifiers. Two algorithms have been developed for
second-order quantifier elimination: SCAN, based on constraint resolution, and
DLS, based on a logical equivalence established by Ackermann.
In this paper we introduce a new algorithm, SQEMA, for computing first-order
equivalents (using a modal version of Ackermann's lemma) and, moreover, for
proving canonicity of modal formulae. Unlike SCAN and DLS, it works directly on
modal formulae, thus avoiding Skolemization and the subsequent problem of
unskolemization. We present the core algorithm and illustrate it with some
examples. We then prove its correctness and the canonicity of all formulae on
which the algorithm succeeds. We show that it succeeds not only on all
Sahlqvist formulae, but also on the larger class of inductive formulae,
introduced in our earlier papers. Thus, we develop a purely algorithmic
approach to proving canonical completeness in modal logic and, in particular,
establish one of the most general completeness results in modal logic so far.Comment: 26 pages, no figures, to appear in the Logical Methods in Computer
Scienc
Mid-Infrared Instrumentation for the European Extremely Large Telescope
MIDIR is the proposed thermal/mid-IR imager and spectrograph for the European
Extremely Large Telescope (E-ELT). It will cover the wavelength range of 3 to
at least 20 microns. Designed for diffraction-limited performance over the
entire wavelength range, MIDIR will require an adaptive optics system; a
cryogenically cooled system could offer optimal performance in the IR, and this
is a critical aspect of the instrument design. We present here an overview of
the project, including a discussion of MIDIR's science goals and a comparison
with other infrared (IR) facilities planned in the next decade; top level
requirements derived from these goals are outlined. We describe the optical and
mechanical design work carried out in the context of a conceptual design study,
and discuss some important issues to emerge from this work, related to the
design, operation and calibration of the instrument. The impact of telescope
optical design choices on the requirements for the MIDIR instrument is
demonstrated.Comment: for publication in SPIE Proceedings vol. 6692, Cryogenic Optical
Systems and Instrumentation XII, eds. J.B. Heaney and L.G. Burriesci, San
Diego, Aug 200
Imaging Electron Wave Functions of Quantized Energy Levels in Carbon Nanotubes
Carbon nanotubes provide a unique system to study one-dimensional
quantization phenomena. Scanning tunneling microscopy is used to observe the
electronic wave functions that correspond to quantized energy levels in short
metallic carbon nanotubes. Discrete electron waves are apparent from periodic
oscillations in the differential conductance as a function of the position
along the tube axis, with a period that differs from that of the atomic
lattice. Wave functions can be observed for several electron states at adjacent
discrete energies. The measured wavelengths are in good agreement with the
calculated Fermi wavelength for armchair nanotubes.Comment: 11 pages, 4 figures in seperate PDF fil
Local Spectral Weight of a Luttinger Liquid: Effects from Edges and Impurities
We calculate the finite-temperature local spectral weight (LSW) of a
Luttinger liquid with an "open" (hard wall) boundary. Close to the boundary the
LSW exhibits characteristic oscillations indicative of spin-charge separation.
The line shape of the LSW is also found to have a Fano-like asymmetry, a
feature originating from the interplay between electron-electron interaction
and scattering off the boundary. Our results can be used to predict how edges
and impurities influence scanning tunneling microscopy (STM) of one-dimensional
electron systems at low temperatures and voltage bias. Applications to STM on
single-walled carbon nanotubes are discussed.Comment: 15 pages, 10 figues, The latest version in pdf format is available at
http://www.physik.uni-kl.de/eggert/papers/LSW-LL.pd
Quantum Conductance Steps in Solutions of Multiwalled Carbon Nanotubes
We have prepared solutions of multiwalled carbon nanotubes in Aroclor 1254, a
mixture of polychlorinated biphenyls. The solutions are stable at room
temperature. Transport measurements were performed using a scanning--tunneling
probe on a sample prepared by spin--coating of the solution on gold substrates.
Conductance steps were clearly seen. An histogram of a high number of traces
shows maximum peaks at integer values of the conductance quantum , demonstrating ballistic transport at room temperature along the carbon
nanotube over distances longer than .Comment: 4 pages and 2 figure
Mechanism of Transcription Activation at the comG Promoter by the Competence Transcription Factor ComK of Bacillus subtilis
The development of genetic competence in Bacillus subtilis is regulated by a complex signal transduction cascade, which results in the synthesis of the competence transcription factor, encoded by comK. ComK is required for the transcription of the late competence genes that encode the DNA binding and uptake machinery and of genes required for homologous recombination. In vivo and in vitro experiments have shown that ComK is responsible for transcription activation at the comG promoter. In this study, we investigated the mechanism of this transcription activation. The intrinsic binding characteristics of RNA polymerase with and without ComK at the comG promoter were determined, demonstrating that ComK stabilizes the binding of RNA polymerase to the comG promoter. This stabilization probably occurs through interactions with the upstream DNA, since a deletion of the upstream DNA resulted in an almost complete abolishment of stabilization of RNA polymerase binding. Furthermore, a strong requirement for the presence of an extra AT box in addition to the common ComK-binding site was shown. In vitro transcription with B. subtilis RNA polymerase reconstituted with wild-type -subunits and with C-terminal deletion mutants of the -subunits was performed, demonstrating that these deletions do not abolish transcription activation by ComK. This indicates that ComK is not a type I activator. We also show that ComK is not required for open complex formation. A possible mechanism for transcription activation is proposed, implying that the major stimulatory effect of ComK is on binding of RNA polymerase.Peer reviewe
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