7,109 research outputs found
On the ground states of the Bernasconi model
The ground states of the Bernasconi model are binary +1/-1 sequences of
length N with low autocorrelations. We introduce the notion of perfect
sequences, binary sequences with one-valued off-peak correlations of minimum
amount. If they exist, they are ground states. Using results from the
mathematical theory of cyclic difference sets, we specify all values of N for
which perfect sequences do exist and how to construct them. For other values of
N, we investigate almost perfect sequences, i.e. sequences with two-valued
off-peak correlations of minimum amount. Numerical and analytical results
support the conjecture that almost perfect sequences do exist for all values of
N, but that they are not always ground states. We present a construction for
low-energy configurations that works if N is the product of two odd primes.Comment: 12 pages, LaTeX2e; extended content, added references; submitted to
J.Phys.
Enumeration of Linear Transformation Shift Registers
We consider the problem of counting the number of linear transformation shift
registers (TSRs) of a given order over a finite field. We derive explicit
formulae for the number of irreducible TSRs of order two. An interesting
connection between TSRs and self-reciprocal polynomials is outlined. We use
this connection and our results on TSRs to deduce a theorem of Carlitz on the
number of self-reciprocal irreducible monic polynomials of a given degree over
a finite field.Comment: 16 page
Rates of DNA Sequence Profiles for Practical Values of Read Lengths
A recent study by one of the authors has demonstrated the importance of
profile vectors in DNA-based data storage. We provide exact values and lower
bounds on the number of profile vectors for finite values of alphabet size ,
read length , and word length .Consequently, we demonstrate that for
and , the number of profile vectors is at least
with very close to one.In addition to enumeration
results, we provide a set of efficient encoding and decoding algorithms for
each of two particular families of profile vectors
Pseudorandom Number Generators and the Square Site Percolation Threshold
A select collection of pseudorandom number generators is applied to a Monte
Carlo study of the two dimensional square site percolation model. A generator
suitable for high precision calculations is identified from an application
specific test of randomness. After extended computation and analysis, an
ostensibly reliable value of pc = 0.59274598(4) is obtained for the percolation
threshold.Comment: 11 pages, 6 figure
From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals
Conventional sub-Nyquist sampling methods for analog signals exploit prior
information about the spectral support. In this paper, we consider the
challenging problem of blind sub-Nyquist sampling of multiband signals, whose
unknown frequency support occupies only a small portion of a wide spectrum. Our
primary design goals are efficient hardware implementation and low
computational load on the supporting digital processing. We propose a system,
named the modulated wideband converter, which first multiplies the analog
signal by a bank of periodic waveforms. The product is then lowpass filtered
and sampled uniformly at a low rate, which is orders of magnitude smaller than
Nyquist. Perfect recovery from the proposed samples is achieved under certain
necessary and sufficient conditions. We also develop a digital architecture,
which allows either reconstruction of the analog input, or processing of any
band of interest at a low rate, that is, without interpolating to the high
Nyquist rate. Numerical simulations demonstrate many engineering aspects:
robustness to noise and mismodeling, potential hardware simplifications,
realtime performance for signals with time-varying support and stability to
quantization effects. We compare our system with two previous approaches:
periodic nonuniform sampling, which is bandwidth limited by existing hardware
devices, and the random demodulator, which is restricted to discrete multitone
signals and has a high computational load. In the broader context of Nyquist
sampling, our scheme has the potential to break through the bandwidth barrier
of state-of-the-art analog conversion technologies such as interleaved
converters.Comment: 17 pages, 12 figures, to appear in IEEE Journal of Selected Topics in
Signal Processing, the special issue on Compressed Sensin
Data dependent energy modelling for worst case energy consumption analysis
Safely meeting Worst Case Energy Consumption (WCEC) criteria requires
accurate energy modeling of software. We investigate the impact of instruction
operand values upon energy consumption in cacheless embedded processors.
Existing instruction-level energy models typically use measurements from random
input data, providing estimates unsuitable for safe WCEC analysis.
We examine probabilistic energy distributions of instructions and propose a
model for composing instruction sequences using distributions, enabling WCEC
analysis on program basic blocks. The worst case is predicted with statistical
analysis. Further, we verify that the energy of embedded benchmarks can be
characterised as a distribution, and compare our proposed technique with other
methods of estimating energy consumption
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