2,490 research outputs found
A statistical view on exchanges in Quickselect
In this paper we study the number of key exchanges required by Hoare's FIND
algorithm (also called Quickselect) when operating on a uniformly distributed
random permutation and selecting an independent uniformly distributed rank.
After normalization we give a limit theorem where the limit law is a perpetuity
characterized by a recursive distributional equation. To make the limit theorem
usable for statistical methods and statistical experiments we provide an
explicit rate of convergence in the Kolmogorov--Smirnov metric, a numerical
table of the limit law's distribution function and an algorithm for exact
simulation from the limit distribution. We also investigate the limit law's
density. This case study provides a program applicable to other cost measures,
alternative models for the rank selected and more balanced choices of the pivot
element such as median-of- versions of Quickselect as well as further
variations of the algorithm.Comment: Theorem 4.4 revised; accepted for publication in Analytic
Algorithmics and Combinatorics (ANALCO14
Computational Tools for Cohomology of Toric Varieties
In this review, novel non-standard techniques for the computation of
cohomology classes on toric varieties are summarized. After an introduction of
the basic definitions and properties of toric geometry, we discuss a specific
computational algorithm for the determination of the dimension of line-bundle
valued cohomology groups on toric varieties. Applications to the computation of
chiral massless matter spectra in string compactifications are discussed and,
using the software package cohomCalg, its utility is highlighted on a new
target space dual pair of (0,2) heterotic string models.Comment: 17 pages, 4 tables; prepared for the special issue "Computational
Algebraic Geometry in String and Gauge Theory" of Advances in High Energy
Physics, cohomCalg implementation available at
http://wwwth.mppmu.mpg.de/members/blumenha/cohomcalg
Feynman Categories
In this paper we give a new foundational, categorical formulation for
operations and relations and objects parameterizing them. This generalizes and
unifies the theory of operads and all their cousins including but not limited
to PROPs, modular operads, twisted (modular) operads, properads, hyperoperads,
their colored versions, as well as algebras over operads and an abundance of
other related structures, such as crossed simplicial groups, the augmented
simplicial category or FI--modules.
The usefulness of this approach is that it allows us to handle all the
classical as well as more esoteric structures under a common framework and we
can treat all the situations simultaneously. Many of the known constructions
simply become Kan extensions.
In this common framework, we also derive universal operations, such as those
underlying Deligne's conjecture, construct Hopf algebras as well as perform
resolutions, (co)bar transforms and Feynman transforms which are related to
master equations. For these applications, we construct the relevant model
category structures. This produces many new examples.Comment: Expanded version. New introduction, new arrangement of text, more
details on several constructions. New figure
Acquisition of the concept of friction
Thesis (Ed. D.)--Boston University. This item was digitized by the Internet Archive
Flight Dynamics Operations of the TanDEM-X Formation
Since end of 2010 the German TerraSAR-X and TanDEM-X satellites are routinely operated as the first configurable single-pass Synthetic Aperture Radar interferometer in space. The two 1340 kg satellites fly in a 514 km sun-synchronous orbit. In order to collect sufficient measurements for the generation of a global digital elevation model and to demonstrate new interferometric SAR techniques and applications, more than three years of formation flying are foreseen with flexible baselines ranging from 150 m to few kilometers. As a prerequisite for the close formation flight an extensive flight dynamics system was established at DLR/GSOC, which comprises of GPS-based absolute and relative navigation and impulsive orbit and formation control. Daily formation maintenance maneuvers are performed by TanDEM-X to counterbalance natural and artificial disturbances. The paper elaborates on the routine flight dynamics operations and its interactions with mission planning and ground-station network. The navigation and formation control concepts and the achieved control accuracy are briefly outlined. Furthermore, the paper addresses non-routine operations experienced during formation acquisition, frequent formation reconfiguration, formation maintenance problems and space debris collision avoidance, which is even more challenging than for single-satellite operations. In particular two close approaches of debris are presented, which were experienced in March 2011 and April 2012. Finally, a formation break-up procedure is discussed which could be executed in case of severe onboard failures
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Nanocomposites and methods for synthesis and use thereof
Nanocomposite compositions and methods of synthesis of the compositions are described. In particular, liquid crystal-functionalized nanoparticles, liquid crystal-templated nanoparticles, nanocomposite compositions including the nanoparticles, and composite compositions including the nanocomposites are detailed.Board of Regents, University of Texas Syste
Cohomology of Line Bundles: A Computational Algorithm
We present an algorithm for computing line bundle valued cohomology classes
over toric varieties. This is the basic starting point for computing massless
modes in both heterotic and Type IIB/F-theory compactifications, where the
manifolds of interest are complete intersections of hypersurfaces in toric
varieties supporting additional vector bundles.Comment: 11 pages, 1 figure, 2 tables; v2: typos and references corrected; v3:
proof-related statements updated, cohomCalg implementation available at
http://wwwth.mppmu.mpg.de/members/blumenha/cohomcalg
Mechanisms of Supraventricular Tachycardia
In summary, we have found a close association between the stress of A-V nodal conduction and the occurrence of atrial dispersion or aberration. We could not explain atrial dispersion on the basis of incomplete recovery of atrial activity, slowing of atrial conduction, or the occurrence of atrial fusion. We postulate that the phenomenon of dispersion of atrial activation is related to the functional dissociation within the A-V node seen during situations which stress A-V conduction. This phenomenon may represent a mechanism whereby a second area of turnaround other than the A-V node is involved in reentry atrial tachyarrhythmias. Indeed, such a mechanism could provide a physiological basis for the concept of the atrial bridge being involved in supraventricular tachycardias and reciprocal beating
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