21,306 research outputs found
A constructive proof of the general Lovasz Local Lemma
The Lovasz Local Lemma [EL75] is a powerful tool to non-constructively prove
the existence of combinatorial objects meeting a prescribed collection of
criteria. In his breakthrough paper [Bec91], Beck demonstrated that a
constructive variant can be given under certain more restrictive conditions.
Simplifications of his procedure and relaxations of its restrictions were
subsequently exhibited in several publications [Alo91, MR98, CS00, Mos06,
Sri08, Mos08]. In [Mos09], a constructive proof was presented that works under
negligible restrictions, formulated in terms of the Bounded Occurrence
Satisfiability problem. In the present paper, we reformulate and improve upon
these findings so as to directly apply to almost all known applications of the
general Local Lemma.Comment: 8 page
Kruskal's Tree Theorem for Acyclic Term Graphs
In this paper we study termination of term graph rewriting, where we restrict
our attention to acyclic term graphs. Motivated by earlier work by Plump we aim
at a definition of the notion of simplification order for acyclic term graphs.
For this we adapt the homeomorphic embedding relation to term graphs. In
contrast to earlier extensions, our notion is inspired by morphisms. Based on
this, we establish a variant of Kruskal's Tree Theorem formulated for acyclic
term graphs. In proof, we rely on the new notion of embedding and follow
Nash-Williams' minimal bad sequence argument. Finally, we propose a variant of
the lexicographic path order for acyclic term graphs.Comment: In Proceedings TERMGRAPH 2016, arXiv:1609.0301
Fabrication of large addition energy quantum dots in graphene
We present a simple technique to fabricate graphene quantum dots in a
cryostat. It relies upon the controlled rupture of a suspended graphene sheet
subjected to the application of a large electron current. This results in the
in-situ formation of a clean and ultra-narrow constriction, which hosts one
quantum dot, and occasionally a few quantum dots in series. Conductance
spectroscopy indicates that individual quantum dots can possess an addition
energy as large as 180 meV and a level spacing as large as 25 meV. Our
technique has several assets: (i) the dot is suspended, thus the electrostatic
influence of the substrate is reduced, and (ii) contamination is minimized,
since the edges of the dot have only been exposed to the vacuum in the
cryostat.Comment: Improved version. To appear in Applied Physics Letter
Symmetry breaking in a mechanical resonator made from a carbon nanotube
Nanotubes behave as semi-flexible polymers in that they can bend by a
sizeable amount. When integrating a nanotube in a mechanical resonator, the
bending is expected to break the symmetry of the restoring potential. Here we
report on a new detection method that allows us to demonstrate such symmetry
breaking. The method probes the motion of the nanotube resonator at nearly
zero-frequency; this motion is the low-frequency counterpart of the second
overtone of resonantly excited vibrations. We find that symmetry breaking leads
to the spectral broadening of mechanical resonances, and to an apparent quality
factor that drops below 100 at room temperature. The low quality factor at room
temperature is a striking feature of nanotube resonators whose origin has
remained elusive for many years. Our results shed light on the role played by
symmetry breaking in the mechanics of nanotube resonators.Comment: manuscript and supplementary material, 7 figure
A few things I learnt from Jurgen Moser
A few remarks on integrable dynamical systems inspired by discussions with
Jurgen Moser and by his work.Comment: An article for the special issue of "Regular and Chaotic Dynamics"
dedicated to 80-th anniversary of Jurgen Mose
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