22,204 research outputs found
Multisequences with high joint nonlinear complexity
We introduce the new concept of joint nonlinear complexity for multisequences
over finite fields and we analyze the joint nonlinear complexity of two
families of explicit inversive multisequences. We also establish a
probabilistic result on the behavior of the joint nonlinear complexity of
random multisequences over a fixed finite field
On asymptotically good ramp secret sharing schemes
Asymptotically good sequences of linear ramp secret sharing schemes have been
intensively studied by Cramer et al. in terms of sequences of pairs of nested
algebraic geometric codes. In those works the focus is on full privacy and full
reconstruction. In this paper we analyze additional parameters describing the
asymptotic behavior of partial information leakage and possibly also partial
reconstruction giving a more complete picture of the access structure for
sequences of linear ramp secret sharing schemes. Our study involves a detailed
treatment of the (relative) generalized Hamming weights of the considered
codes
Construction of sequences with high Nonlinear Complexity from the Hermitian Function Field
We provide a sequence with high nonlinear complexity from the Hermitian
function field over . This sequence was
obtained using a rational function with pole divisor in certain
collinear rational places on , where . In
particular we improve the lower bounds on the th-order nonlinear complexity
obtained by H. Niederreiter and C. Xing; and O. Geil, F. \"Ozbudak and D.
Ruano
How to determine linear complexity and -error linear complexity in some classes of linear recurring sequences
Several fast algorithms for the determination of the linear complexity of -periodic sequences over a finite
field \F_q, i.e. sequences with characteristic polynomial , have been proposed in the literature.
In this contribution fast algorithms for determining the linear complexity of binary sequences with characteristic
polynomial for an arbitrary positive integer , and are presented.
The result is then utilized to establish a fast algorithm for determining the -error linear complexity of
binary sequences with characteristic polynomial
Finite Fields: Theory and Applications
Finite ïŹelds are the focal point of many interesting geometric, algorithmic and combinatorial problems. The workshop was devoted to progress on these questions, with an eye also on the important applications of ïŹnite ïŹeld techniques in cryptography, error correcting codes, and random number generation
Time-resolved magnetic sensing with electronic spins in diamond
Quantum probes can measure time-varying fields with high sensitivity and
spatial resolution, enabling the study of biological, material, and physical
phenomena at the nanometer scale. In particular, nitrogen-vacancy centers in
diamond have recently emerged as promising sensors of magnetic and electric
fields. Although coherent control techniques have measured the amplitude of
constant or oscillating fields, these techniques are not suitable for measuring
time-varying fields with unknown dynamics. Here we introduce a coherent
acquisition method to accurately reconstruct the temporal profile of
time-varying fields using Walsh sequences. These decoupling sequences act as
digital filters that efficiently extract spectral coefficients while
suppressing decoherence, thus providing improved sensitivity over existing
strategies. We experimentally reconstruct the magnetic field radiated by a
physical model of a neuron using a single electronic spin in diamond and
discuss practical applications. These results will be useful to implement
time-resolved magnetic sensing with quantum probes at the nanometer scale.Comment: 8+12 page
Predictability: a way to characterize Complexity
Different aspects of the predictability problem in dynamical systems are
reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy,
Shannon entropy and algorithmic complexity is discussed. In particular, we
emphasize how a characterization of the unpredictability of a system gives a
measure of its complexity. Adopting this point of view, we review some
developments in the characterization of the predictability of systems showing
different kind of complexity: from low-dimensional systems to high-dimensional
ones with spatio-temporal chaos and to fully developed turbulence. A special
attention is devoted to finite-time and finite-resolution effects on
predictability, which can be accounted with suitable generalization of the
standard indicators. The problems involved in systems with intrinsic randomness
is discussed, with emphasis on the important problems of distinguishing chaos
from noise and of modeling the system. The characterization of irregular
behavior in systems with discrete phase space is also considered.Comment: 142 Latex pgs. 41 included eps figures, submitted to Physics Reports.
Related information at this http://axtnt2.phys.uniroma1.i
On the critical nature of plastic flow: one and two dimensional models
Steady state plastic flows have been compared to developed turbulence because
the two phenomena share the inherent complexity of particle trajectories, the
scale free spatial patterns and the power law statistics of fluctuations. The
origin of the apparently chaotic and at the same time highly correlated
microscopic response in plasticity remains hidden behind conventional
engineering models which are based on smooth fitting functions. To regain
access to fluctuations, we study in this paper a minimal mesoscopic model whose
goal is to elucidate the origin of scale free behavior in plasticity. We limit
our description to fcc type crystals and leave out both temperature and rate
effects. We provide simple illustrations of the fact that complexity in rate
independent athermal plastic flows is due to marginal stability of the
underlying elastic system. Our conclusions are based on a reduction of an
over-damped visco-elasticity problem for a system with a rugged elastic energy
landscape to an integer valued automaton. We start with an overdamped one
dimensional model and show that it reproduces the main macroscopic
phenomenology of rate independent plastic behavior but falls short of
generating self similar structure of fluctuations. We then provide evidence
that a two dimensional model is already adequate for describing power law
statistics of avalanches and fractal character of dislocation patterning. In
addition to capturing experimentally measured critical exponents, the proposed
minimal model shows finite size scaling collapse and generates realistic shape
functions in the scaling laws.Comment: 72 pages, 40 Figures, International Journal of Engineering Science
for the special issue in honor of Victor Berdichevsky, 201
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