1,157 research outputs found
Dehn surgery, homology and hyperbolic volume
If a closed, orientable hyperbolic 3--manifold M has volume at most 1.22 then
H_1(M;Z_p) has dimension at most 2 for every prime p not 2 or 7, and H_1(M;Z_2)
and H_1(M;Z_7) have dimension at most 3. The proof combines several deep
results about hyperbolic 3--manifolds. The strategy is to compare the volume of
a tube about a shortest closed geodesic C in M with the volumes of tubes about
short closed geodesics in a sequence of hyperbolic manifolds obtained from M by
Dehn surgeries on C.Comment: This is the version published by Algebraic & Geometric Topology on 8
December 200
On abstract commensurators of groups
We prove that the abstract commensurator of a nonabelian free group, an
infinite surface group, or more generally of a group that splits appropriately
over a cyclic subgroup, is not finitely generated.
This applies in particular to all torsion-free word-hyperbolic groups with
infinite outer automorphism group and abelianization of rank at least 2.
We also construct a finitely generated, torsion-free group which can be
mapped onto Z and which has a finitely generated commensurator.Comment: 13 pages, no figur
Protective effects of total fraction of avocado/soybean unsaponifiables on the structural changes in experimental dog osteoarthritis: inhibition of nitric oxide synthase and matrix metalloproteinase-13
The resource theory of quantum reference frames: manipulations and monotones
Every restriction on quantum operations defines a resource theory,
determining how quantum states that cannot be prepared under the restriction
may be manipulated and used to circumvent the restriction. A superselection
rule is a restriction that arises through the lack of a classical reference
frame and the states that circumvent it (the resource) are quantum reference
frames. We consider the resource theories that arise from three types of
superselection rule, associated respectively with lacking: (i) a phase
reference, (ii) a frame for chirality, and (iii) a frame for spatial
orientation. Focussing on pure unipartite quantum states (and in some cases
restricting our attention even further to subsets of these), we explore
single-copy and asymptotic manipulations. In particular, we identify the
necessary and sufficient conditions for a deterministic transformation between
two resource states to be possible and, when these conditions are not met, the
maximum probability with which the transformation can be achieved. We also
determine when a particular transformation can be achieved reversibly in the
limit of arbitrarily many copies and find the maximum rate of conversion. A
comparison of the three resource theories demonstrates that the extent to which
resources can be interconverted decreases as the strength of the restriction
increases. Along the way, we introduce several measures of frameness and prove
that these are monotonically nonincreasing under various classes of operations
that are permitted by the superselection rule.Comment: 37 pages, 4 figures, Published Versio
Security Analysis of an Untrusted Source for Quantum Key Distribution: Passive Approach
We present a passive approach to the security analysis of quantum key
distribution (QKD) with an untrusted source. A complete proof of its
unconditional security is also presented. This scheme has significant
advantages in real-life implementations as it does not require fast optical
switching or a quantum random number generator. The essential idea is to use a
beam splitter to split each input pulse. We show that we can characterize the
source using a cross-estimate technique without active routing of each pulse.
We have derived analytical expressions for the passive estimation scheme.
Moreover, using simulations, we have considered four real-life imperfections:
Additional loss introduced by the "plug & play" structure, inefficiency of the
intensity monitor, noise of the intensity monitor, and statistical fluctuation
introduced by finite data size. Our simulation results show that the passive
estimate of an untrusted source remains useful in practice, despite these four
imperfections. Also, we have performed preliminary experiments, confirming the
utility of our proposal in real-life applications. Our proposal makes it
possible to implement the "plug & play" QKD with the security guaranteed, while
keeping the implementation practical.Comment: 35 pages, 19 figures. Published Versio
Breast MRI and tumour biology predict axillary lymph node response to neoadjuvant chemotherapy for breast cancer
Complete experimental toolbox for alignment-free quantum communication
Quantum communication employs the counter-intuitive features of quantum
physics to perform tasks that are im- possible in the classical world. It is
crucial for testing the foundations of quantum theory and promises to rev-
olutionize our information and communication technolo- gies. However, for two
or more parties to execute even the simplest quantum transmission, they must
establish, and maintain, a shared reference frame. This introduces a
considerable overhead in communication resources, par- ticularly if the parties
are in motion or rotating relative to each other. We experimentally demonstrate
how to circumvent this problem with the efficient transmission of quantum
information encoded in rotationally invariant states of single photons. By
developing a complete toolbox for the efficient encoding and decoding of
quantum infor- mation in such photonic qubits, we demonstrate the fea- sibility
of alignment-free quantum key-distribution, and perform a proof-of-principle
alignment-free entanglement distribution and violation of a Bell inequality.
Our scheme should find applications in fundamental tests of quantum mechanics
and satellite-based quantum communication.Comment: Main manuscript: 7 pages, 3 figures; Supplementary Information: 7
pages, 3 figure
Prosthetic overhang is the most effective way to prevent scapular conflict in a reverse total shoulder prosthesis
Methods An average and a "worst case scenario" shape in A-P view in a 2-D computer model of a scapula was created, using data from 200 "normal" scapulae, so that the position of the glenoid and humeral component could be changed as well as design features such as depth of the polyethylene insert, the size of glenosphere, the position of the center of rotation, and downward glenoid inclination. The model calculated the maximum adduction (notch angle) in the scapular plane when the cup of the humeral component was in conflict with the scapula.
Results A change in humeral neck shaft inclination from 155 degrees to 145 degrees gave a 10 degrees gain in notch angle. A change in cup depth from 8 mm to 5 mm gave a gain of 12 degrees. With no inferior prosthetic overhang, a lateralization of the center of rotation from 0 mm to 5 mm gained 16 degrees. With an inferior overhang of only 1 mm, no effect of lateralizing the center of rotation was noted. Downward glenoid inclination of 0 boolean OR to 10 boolean OR gained 10 degrees. A change in glenosphere radius from 18 mm to 21 mm gained 31 degrees due to the inferior overhang created by the increase in glenosphere. A prosthetic overhang to the bone from 0 mm to 5 mm gained 39 degrees.
Interpretation Of all 6 solutions tested, the prosthetic overhang created the biggest gain in notch angle and this should be considered when designing the reverse arthroplasty and defining optimal surgical technique
Self-assembly in solution of a reversible comb-shaped supramolecular polymer
We report a single step synthesis of a polyisobutene with a bis-urea moiety
in the middle of the chain. In low polarity solvents, this polymer
self-assembles by hydrogen bonding to form a combshaped polymer with a central
hydrogen bonded backbone and polyisobutene arms. The comb backbone can be
reversibly broken, and consequently, its length can be tuned by changing the
solvent, the concentration or the temperature. Moreover, we have proved that
the bulkiness of the side-chains have a strong influence on both the
self-assembly pattern and the length of the backbone. Finally, the density of
arms can be reduced, by simply mixing with a low molar mass bis-urea
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