10,570 research outputs found
Succinct Indexable Dictionaries with Applications to Encoding -ary Trees, Prefix Sums and Multisets
We consider the {\it indexable dictionary} problem, which consists of storing
a set for some integer , while supporting the
operations of \Rank(x), which returns the number of elements in that are
less than if , and -1 otherwise; and \Select(i) which returns
the -th smallest element in . We give a data structure that supports both
operations in O(1) time on the RAM model and requires bits to store a set of size , where {\cal B}(n,m) = \ceil{\lg
{m \choose n}} is the minimum number of bits required to store any -element
subset from a universe of size . Previous dictionaries taking this space
only supported (yes/no) membership queries in O(1) time. In the cell probe
model we can remove the additive term in the space bound,
answering a question raised by Fich and Miltersen, and Pagh.
We present extensions and applications of our indexable dictionary data
structure, including:
An information-theoretically optimal representation of a -ary cardinal
tree that supports standard operations in constant time,
A representation of a multiset of size from in bits that supports (appropriate generalizations of) \Rank
and \Select operations in constant time, and
A representation of a sequence of non-negative integers summing up to
in bits that supports prefix sum queries in constant
time.Comment: Final version of SODA 2002 paper; supersedes Leicester Tech report
2002/1
Succinct Representations of Permutations and Functions
We investigate the problem of succinctly representing an arbitrary
permutation, \pi, on {0,...,n-1} so that \pi^k(i) can be computed quickly for
any i and any (positive or negative) integer power k. A representation taking
(1+\epsilon) n lg n + O(1) bits suffices to compute arbitrary powers in
constant time, for any positive constant \epsilon <= 1. A representation taking
the optimal \ceil{\lg n!} + o(n) bits can be used to compute arbitrary powers
in O(lg n / lg lg n) time.
We then consider the more general problem of succinctly representing an
arbitrary function, f: [n] \rightarrow [n] so that f^k(i) can be computed
quickly for any i and any integer power k. We give a representation that takes
(1+\epsilon) n lg n + O(1) bits, for any positive constant \epsilon <= 1, and
computes arbitrary positive powers in constant time. It can also be used to
compute f^k(i), for any negative integer k, in optimal O(1+|f^k(i)|) time.
We place emphasis on the redundancy, or the space beyond the
information-theoretic lower bound that the data structure uses in order to
support operations efficiently. A number of lower bounds have recently been
shown on the redundancy of data structures. These lower bounds confirm the
space-time optimality of some of our solutions. Furthermore, the redundancy of
one of our structures "surpasses" a recent lower bound by Golynski [Golynski,
SODA 2009], thus demonstrating the limitations of this lower bound.Comment: Preliminary versions of these results have appeared in the
Proceedings of ICALP 2003 and 2004. However, all results in this version are
improved over the earlier conference versio
Enhanced mixing of a rectangular supersonic jet by natural and induced screech
The influence of shear layer excitation on the mixing of supersonic rectangular jets was studied experimentally. Two methods of excitation were used to control the jet mixing. The first used the natural screech of an underexpanded supersonic jet from a converging nozzle. The level of the screech excitation was controlled by the use of a pair of baffles located to block the acoustic feedback path between the downstream shock structure and the nozzle lip. A screech level variation of over 30 decibels was achieved and the mixing was completely determined by the level of screech attained at the nozzle lip. The second form of self-excitation used the induced screech caused by obstacles or paddles located in the shear layers on either long side of the rectangular jet. With sufficient immersion of the paddles intense jet mixing occurred and large flapping wave motion was observed using a strobed focused Schlieren system. Each paddle was instrumented with a total pressure tap and strain gages to determine the pressure and drag force on the square cross-section paddle. Considerable drag was observed in this initial exploratory study. Future studies using alternate paddle geometries will be conducted to maximize jet mixing with minimum drag
Gravitational Lorentz Violation and Superluminality via AdS/CFT Duality
A weak quantum mechanical coupling is constructed permitting superluminal
communication within a preferred region of a gravitating AdS_5 spacetime. This
is achieved by adding a spatially non-local perturbation of a special kind to
the Hamiltonian of a four-dimensional conformal field theory with a
weakly-coupled AdS dual, such as maximally supersymmetric Yang-Mills theory. In
particular, two issues are given careful treatment: (1) the UV-completeness of
our deformed CFT, guaranteeing the existence of a ``deformed string theory''
AdS dual, and (2) the demonstration that superluminal effects can take place in
AdS, both on its boundary as well as in the bulk. Exotic Lorentz-violating
properties such as these may have implications for tests of General Relativity,
addressing the cosmological constant problem, or probing "behind'' horizons.
Our construction may give insight into the interpretation of wormhole solutions
in Euclidean AdS gravity.Comment: 23 pages LaTex. Typo in Eq. (37) corrected. References adde
Naturally occurring and forced azimuthal modes in a turbulent jet
Naturally occurring instability modes in an axisymmetric jet were studied using the modal frequency technique. The evolution of the modal spectrum was obtained for a jet with a Reynolds number based on a diameter of 400,000 for both laminar and turbulent nozzle boundary layers. In the early evolution of the jet the axisymmetric mode was predominant, with the azimuthal modes growing rapidly but dominating only the end of the potential core. The growth of the azimuthal was observed closer to the nozzle exit for the jet in the laminar boundary layer case than for the turbulent. Target modes for efficient excitation of the jet were determined and two cases of excitation were studied. First, a jet was excited simultaneously by two helical modes, m equals plus 1 and m equals minus 1 at a Strouhal number based on jet diameter of 0.15 and the axisymmetric mode, m equals 0 at a jet diameter of 0.6. Second, m equals plus one and m equals minus 1 at jet diameter equals 0.3 and m equals 0 at jet diameter equals 0.6 were excited simultaneously. The downstream evolution of the hydrodynamic modes and the spreading rate of the jet were documented for each case. Higher jet spreading rates, accompanied by distorted jet cross sections were observed for the cases where combinations of axisymmetric and helical forcings were applied
Control of an axisymmetric turbulent jet by multi-modal excitation
Experimental measurements of naturally occurring instability modes in the axisymmetric shear layer of high Reynolds number turbulent jet are presented. The region up to the end of the potential core was dominated by the axisymmetric mode. The azimuthal modes dominated only downstream of the potential core region. The energy content of the higher order modes (m is greater than 1) was significantly lower than that of the axisymmeteric and m = + or - 1 modes. Under optimum conditions, two-frequency excitation (both at m = 0) was more effective than single frequency excitation (at m = 0) for jet spreading enhancement. An extended region of the jet was controlled by forcing combinations of both axisymmetric (m = 0) and helical modes (m = + or - 1). Higher spreading rates were obtained when multi-modal forcing was applied
Quantum and Classical Dynamics of a BEC in a Large-Period Optical Lattice
We experimentally investigate diffraction of a Rb-87 Bose-Einstein condensate
from a 1D optical lattice. We use a range of lattice periods and timescales,
including those beyond the Raman-Nath limit. We compare the results to quantum
mechanical and classical simulations, with quantitative and qualitative
agreement, respectively. The classical simulation predicts that the envelope of
the time-evolving diffraction pattern is shaped by caustics: singularities in
the phase space density of classical trajectories. This behavior becomes
increasingly clear as the lattice period grows.Comment: 7 pages, 6 figure
Perturbation Theory for Plasmonic Modulation and Sensing
We develop a general perturbation theory to treat small parameter changes in
dispersive plasmonic nanostructures and metamaterials. We specifically apply it
to dielectric refractive index, and metallic plasma frequency modulation in
metal- dielectric nanostructures. As a numerical demonstration, we verify the
theory's accu- racy against direct calculations, for a system of plasmonic rods
in air where the metal is defined by a two-pole fit of silver's dielectric
function. We also discuss new optical behavior related to plasma frequency
modulation in such systems. Our approach provides new physical insight for the
design of plasmonic devices for biochemical sensing and optical modulation, and
future active metamaterial applications.Comment: 17 pages, 6 figure
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