32,723 research outputs found
Folding, Tiling, and Multidimensional Coding
Folding a sequence into a multidimensional box is a method that is used
to construct multidimensional codes. The well known operation of folding is
generalized in a way that the sequence can be folded into various shapes.
The new definition of folding is based on lattice tiling and a direction in the
-dimensional grid. There are potentially different folding
operations. Necessary and sufficient conditions that a lattice combined with a
direction define a folding are given. The immediate and most impressive
application is some new lower bounds on the number of dots in two-dimensional
synchronization patterns. This can be also generalized for multidimensional
synchronization patterns. We show how folding can be used to construct
multidimensional error-correcting codes and to generate multidimensional
pseudo-random arrays
On the descriptional complexity of iterative arrays
The descriptional complexity of iterative arrays (lAs) is studied. Iterative arrays are a parallel computational model with a sequential processing of the input. It is shown that lAs when compared to deterministic finite automata or pushdown automata may provide savings in size which are not bounded by any recursive function, so-called non-recursive trade-offs. Additional non-recursive trade-offs are proven to exist between lAs working in linear time and lAs working in real time. Furthermore, the descriptional complexity of lAs is compared with cellular automata (CAs) and non-recursive trade-offs are proven between two restricted classes. Finally, it is shown that many decidability questions for lAs are undecidable and not semidecidable
Volumetric diffusers : pseudorandom cylinder arrays on a periodic lattice
Most conventional diffusers take the form of a surface based treatment, and as a result can only operate in hemispherical space. Placing a diffuser in the volume of a room might provide greater efficiency by allowing scattering into the whole space. A periodic cylinder array (or sonic crystal) produces periodicity lobes and uneven scattering. Introducing defects into an array, by removing or varying the size of some of the cylinders, can enhance their diffusing abilities. This paper applies number theoretic concepts to create cylinder arrays that have more even scattering. Predictions using a Boundary Element Method are compared to measurements to verify the model, and suitable metrics are adopted to evaluate performance. Arrangements with good aperiodic autocorrelation properties tend to produce the best results. At low frequency power is controlled by object size and at high frequency diffusion is dominated by lattice spacing and structural similarity. Consequently the operational bandwidth is rather small. By using sparse arrays and varying cylinder sizes, a wider bandwidth can be achieved
Toward the Jamming Threshold of Sphere Packings: Tunneled Crystals
We have discovered a new family of three-dimensional crystal sphere packings
that are strictly jammed (i.e., mechanically stable) and yet possess an
anomalously low density. This family constitutes an uncountably infinite number
of crystal packings that are subpackings of the densest crystal packings and
are characterized by a high concentration of self-avoiding "tunnels" (chains of
vacancies) that permeate the structures. The fundamental geometric
characteristics of these tunneled crystals command interest in their own right
and are described here in some detail. These include the lattice vectors (that
specify the packing configurations), coordination structure, Voronoi cells, and
density fluctuations. The tunneled crystals are not only candidate structures
for achieving the jamming threshold (lowest-density rigid packing), but may
have substantially broader significance for condensed matter physics and
materials science.Comment: 19 pages, 5 figure
High-resolution ab initio three-dimensional X-ray diffraction microscopy
Coherent X-ray diffraction microscopy is a method of imaging non-periodic
isolated objects at resolutions only limited, in principle, by the largest
scattering angles recorded. We demonstrate X-ray diffraction imaging with high
resolution in all three dimensions, as determined by a quantitative analysis of
the reconstructed volume images. These images are retrieved from the 3D
diffraction data using no a priori knowledge about the shape or composition of
the object, which has never before been demonstrated on a non-periodic object.
We also construct 2D images of thick objects with infinite depth of focus
(without loss of transverse spatial resolution). These methods can be used to
image biological and materials science samples at high resolution using X-ray
undulator radiation, and establishes the techniques to be used in
atomic-resolution ultrafast imaging at X-ray free-electron laser sources.Comment: 22 pages, 11 figures, submitte
Growing perfect cubes
AbstractAn (n,a,b)-perfect double cube is a b×b×b sized n-ary periodic array containing all possible a×a×a sized n-ary array exactly once as subarray. A growing cube is an array whose cj×cj×cj sized prefix is an (nj,a,cj)-perfect double cube for j=1,2,…, where cj=njv/3,v=a3 and n1<n2<⋯. We construct the smallest possible perfect double cube (a 256×256×256 sized 8-ary array) and growing cubes for any a
Improved measurements of the energy and shower maximum of cosmic rays with Tunka-Rex
The Tunka Radio Extension (Tunka-Rex) is an array of 63 antennas located in
the Tunka Valley, Siberia. It detects radio pulses in the 30-80 MHz band
produced during the air-shower development. As shown by Tunka-Rex, a sparse
radio array with about 200 m spacing is able to reconstruct the energy and the
depth of the shower maximum with satisfactory precision using simple methods
based on parameters of the lateral distribution of amplitudes. The LOFAR
experiment has shown that a sophisticated treatment of all individually
measured amplitudes of a dense antenna array can make the precision comparable
with the resolution of existing optical techniques. We develop these ideas
further and present a method based on the treatment of time series of measured
signals, i.e. each antenna station provides several points (trace) instead of a
single one (amplitude or power). We use the measured shower axis and energy as
input for CoREAS simulations: for each measured event we simulate a set of
air-showers with proton, helium, nitrogen and iron as primary particle (each
primary is simulated about ten times to cover fluctuations in the shower
maximum due to the first interaction). Simulated radio pulses are processed
with the Tunka-Rex detector response and convoluted with the measured signals.
A likelihood fit determines how well the simulated event fits to the measured
one. The positions of the shower maxima are defined from the distribution of
chi-square values of these fits. When using this improved method instead of the
standard one, firstly, the shower maximum of more events can be reconstructed,
secondly, the resolution is increased. The performance of the method is
demonstrated on the data acquired by the Tunka-Rex detector in 2012-2014.Comment: Proceedings of the 35th ICRC 2017, Busan, Kore
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