7,291 research outputs found
Continued fraction for formal laurent series and the lattice structure of sequences
Besides equidistribution properties and statistical independence the lattice profile, a generalized version of Marsaglia's lattice test, provides another quality measure for pseudorandom sequences over a (finite) field. It turned out that the lattice profile is closely related with the linear complexity profile. In this article we give a survey of several features of the linear complexity profile and the lattice profile, and we utilize relationships to completely describe the lattice profile of a sequence over a finite field in terms of the continued fraction expansion of its generating function. Finally we describe and construct sequences with a certain lattice profile, and introduce a further complexity measure
Order in glassy systems
A directly measurable correlation length may be defined for systems having a
two-step relaxation, based on the geometric properties of density profile that
remains after averaging out the fast motion. We argue that the length diverges
if and when the slow timescale diverges, whatever the microscopic mechanism at
the origin of the slowing down. Measuring the length amounts to determining
explicitly the complexity from the observed particle configurations. One may
compute in the same way the Renyi complexities K_q, their relative behavior for
different q characterizes the mechanism underlying the transition. In
particular, the 'Random First Order' scenario predicts that in the glass phase
K_q=0 for q>x, and K_q>0 for q<x, with x the Parisi parameter. The hypothesis
of a nonequilibrium effective temperature may also be directly tested directly
from configurations.Comment: Typos corrected, clarifications adde
Quantum Noise Correlation Experiments with Ultracold Atoms
Noise correlation analysis is a detection tool for spatial structures and
spatial correlations in the in-trap density distribution of ultracold atoms. In
this book chapter, we discuss the implementation, properties and limitations of
the method applied to ensembles of ultracold atoms in optical lattices, and
describe some instances where it has been applied.Comment: 26 pages, 14 figures - To appear as Chapter 8 in "Quantum gas
experiments - exploring many-body states," P. T\"orm\"a, K. Sengstock, eds.
(Imperial College Press, to be published 2014
Error linear complexity measures for multisequences
Complexity measures for sequences over finite fields, such as the linear complexity and the k-error linear complexity, play an important role in cryptology. Recent developments in stream ciphers point towards an interest in word-based stream ciphers, which require the study of the complexity of multisequences. We introduce various options for error linear complexity measures for multisequences. For finite multisequences as well as for periodic multisequences with prime period, we present formulas for the number of multisequences with given error linear complexity for several cases, and we present lower bounds for the expected error linear complexity
A helicoidal transfer matrix model for inhomogeneous DNA melting
An inhomogeneous helicoidal nearest-neighbor model with continuous degrees of
freedom is shown to predict the same DNA melting properties as traditional
long-range Ising models, for free DNA molecules in solution, as well as
superhelically stressed DNA with a fixed linking number constraint. Without
loss of accuracy, the continuous degrees of freedom can be discretized using a
minimal number of discretization points, yielding an effective transfer matrix
model of modest dimension (d=36). The resulting algorithms to compute DNA
melting profiles are both simple and efficient.Comment: v3: Matlab toolbox included with source file; article unchanged, 12
pages, 11 figures, RevTe
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