6,208 research outputs found
Data Structure Lower Bounds for Document Indexing Problems
We study data structure problems related to document indexing and pattern
matching queries and our main contribution is to show that the pointer machine
model of computation can be extremely useful in proving high and unconditional
lower bounds that cannot be obtained in any other known model of computation
with the current techniques. Often our lower bounds match the known space-query
time trade-off curve and in fact for all the problems considered, there is a
very good and reasonable match between the our lower bounds and the known upper
bounds, at least for some choice of input parameters. The problems that we
consider are set intersection queries (both the reporting variant and the
semi-group counting variant), indexing a set of documents for two-pattern
queries, or forbidden- pattern queries, or queries with wild-cards, and
indexing an input set of gapped-patterns (or two-patterns) to find those
matching a document given at the query time.Comment: Full version of the conference version that appeared at ICALP 2016,
25 page
Multiple-scale structures: from Faraday waves to soft-matter quasicrystals
For many years, quasicrystals were observed only as solid-state metallic
alloys, yet current research is now actively exploring their formation in a
variety of soft materials, including systems of macromolecules, nanoparticles
and colloids. Much effort is being invested in understanding the thermodynamic
properties of these soft-matter quasicrystals in order to predict and possibly
control the structures that form, and hopefully to shed light on the broader
yet unresolved general questions of quasicrystal formation and stability.
Moreover, the ability to control the self-assembly of soft quasicrystals may
contribute to the development of novel photonic or other applications based on
self-assembled metamaterials. Here a path is followed, leading to quantitative
stability predictions, that starts with a model developed two decades ago to
treat the formation of multiple-scale quasiperiodic Faraday waves (standing
wave patterns in vibrated fluid surfaces) and which was later mapped onto
systems of soft particles, interacting via multiple-scale pair potentials. The
article reviews, and substantially expands, the quantitative predictions of
these models, while correcting a few discrepancies in earlier calculations, and
presents new analytical methods for treating the models. In so doing, a number
of new stable quasicrystalline structures with octagonal, octadecagonal and
higher-order symmetries, some of which may, it is hoped, be observed in future
experiments.Comment: 22 pages, 22 figures, 1 table. Comments welcom
An Improved Bound for Weak Epsilon-Nets in the Plane
We show that for any finite set of points in the plane and
there exist
points in , for arbitrary small , that pierce every
convex set with . This is the first improvement
of the bound of that was
obtained in 1992 by Alon, B\'{a}r\'{a}ny, F\"{u}redi and Kleitman for general
point sets in the plane.Comment: A preliminary version to appear in the proceedings of FOCS 201
Regional differences in APD restitution can initiate wavebreak and re-entry in cardiac tissue: A computational study
Background
Regional differences in action potential duration (APD) restitution in the heart favour arrhythmias, but the mechanism is not well understood.
Methods
We simulated a 150 × 150 mm 2D sheet of cardiac ventricular tissue using a simplified computational model. We investigated wavebreak and re-entry initiated by an S1S2S3 stimulus protocol in tissue sheets with two regions, each with different APD restitution. The two regions had a different APD at short diastolic interval (DI), but similar APD at long DI. Simulations were performed twice; once with both regions having steep (slope > 1), and once with both regions having flat (slope < 1) APD restitution.
Results
Wavebreak and re-entry were readily initiated using the S1S2S3 protocol in tissue sheets with two regions having different APD restitution properties. Initiation occurred irrespective of whether the APD restitution slopes were steep or flat. With steep APD restitution, the range of S2S3 intervals resulting in wavebreak increased from 1 ms with S1S2 of 250 ms, to 75 ms (S1S2 180 ms). With flat APD restitution, the range of S2S3 intervals resulting in wavebreak increased from 1 ms (S1S2 250 ms), to 21 ms (S1S2 340 ms) and then 11 ms (S1S2 400 ms).
Conclusion
Regional differences in APD restitution are an arrhythmogenic substrate that can be concealed at normal heart rates. A premature stimulus produces regional differences in repolarisation, and a further premature stimulus can then result in wavebreak and initiate re-entry. This mechanism for initiating re-entry is independent of the steepness of the APD restitution curve
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