20,696 research outputs found
Deleting and Testing Forbidden Patterns in Multi-Dimensional Arrays
Understanding the local behaviour of structured multi-dimensional data is a
fundamental problem in various areas of computer science. As the amount of data
is often huge, it is desirable to obtain sublinear time algorithms, and
specifically property testers, to understand local properties of the data.
We focus on the natural local problem of testing pattern freeness: given a
large -dimensional array and a fixed -dimensional pattern over a
finite alphabet, we say that is -free if it does not contain a copy of
the forbidden pattern as a consecutive subarray. The distance of to
-freeness is the fraction of entries of that need to be modified to make
it -free. For any and any large enough pattern over
any alphabet, other than a very small set of exceptional patterns, we design a
tolerant tester that distinguishes between the case that the distance is at
least and the case that it is at most , with query
complexity and running time , where and
depend only on .
To analyze the testers we establish several combinatorial results, including
the following -dimensional modification lemma, which might be of independent
interest: for any large enough pattern over any alphabet (excluding a small
set of exceptional patterns for the binary case), and any array containing
a copy of , one can delete this copy by modifying one of its locations
without creating new -copies in .
Our results address an open question of Fischer and Newman, who asked whether
there exist efficient testers for properties related to tight substructures in
multi-dimensional structured data. They serve as a first step towards a general
understanding of local properties of multi-dimensional arrays, as any such
property can be characterized by a fixed family of forbidden patterns
Array operators using multiple dispatch: a design methodology for array implementations in dynamic languages
Arrays are such a rich and fundamental data type that they tend to be built
into a language, either in the compiler or in a large low-level library.
Defining this functionality at the user level instead provides greater
flexibility for application domains not envisioned by the language designer.
Only a few languages, such as C++ and Haskell, provide the necessary power to
define -dimensional arrays, but these systems rely on compile-time
abstraction, sacrificing some flexibility. In contrast, dynamic languages make
it straightforward for the user to define any behavior they might want, but at
the possible expense of performance.
As part of the Julia language project, we have developed an approach that
yields a novel trade-off between flexibility and compile-time analysis. The
core abstraction we use is multiple dispatch. We have come to believe that
while multiple dispatch has not been especially popular in most kinds of
programming, technical computing is its killer application. By expressing key
functions such as array indexing using multi-method signatures, a surprising
range of behaviors can be obtained, in a way that is both relatively easy to
write and amenable to compiler analysis. The compact factoring of concerns
provided by these methods makes it easier for user-defined types to behave
consistently with types in the standard library.Comment: 6 pages, 2 figures, workshop paper for the ARRAY '14 workshop, June
11, 2014, Edinburgh, United Kingdo
Plasmon-phonon coupling in large-area graphene dot and antidot arrays
Nanostructured graphene on SiO2 substrates pave the way for enhanced
light-matter interactions and explorations of strong plasmon-phonon
hybridization in the mid-infrared regime. Unprecedented large-area graphene
nanodot and antidot optical arrays are fabricated by nanosphere lithography,
with structural control down to the sub-100 nanometer regime. The interaction
between graphene plasmon modes and the substrate phonons is experimentally
demonstrated and structural control is used to map out the hybridization of
plasmons and phonons, showing coupling energies of the order 20 meV. Our
findings are further supported by theoretical calculations and numerical
simulations.Comment: 7 pages including 6 figures. Supporting information is available upon
request to author
Large-area, wide-angle, spectrally selective plasmonic absorber
A simple metamaterial-based wide-angle plasmonic absorber is introduced,
fabricated, and experimentally characterized using angle-resolved infrared
spectroscopy. The metamaterials are prepared by nano-imprint lithography, an
attractive low-cost technology for making large-area samples. The matching of
the metamaterial's impedance to that of vacuum is responsible for the observed
spectrally selective "perfect" absorption of infrared light. The impedance is
theoretically calculated in the single-resonance approximation, and the
responsible resonance is identified as a short-range surface plasmon. The
spectral position of the absorption peak (which is as high as 95%) is
experimentally shown to be controlled by the metamaterial's dimensions. The
persistence of "perfect" absorption with variable metamaterial parameters is
theoretically explained. The wide-angle nature of the absorber can be utilized
for sub-diffraction-scale infrared pixels exhibiting spectrally selective
absorption/emissivity.Comment: 7 pages, 6 figures, submitted to Phys. Rev.
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