8,779 research outputs found
Switchable Genetic Oscillator Operating in Quasi-Stable Mode
Ring topologies of repressing genes have qualitatively different long-term
dynamics if the number of genes is odd (they oscillate) or even (they exhibit
bistability). However, these attractors may not fully explain the observed
behavior in transient and stochastic environments such as the cell. We show
here that even repressilators possess quasi-stable, travelling-wave periodic
solutions that are reachable, long-lived and robust to parameter changes. These
solutions underlie the sustained oscillations observed in even rings in the
stochastic regime, even if these circuits are expected to behave as switches.
The existence of such solutions can also be exploited for control purposes:
operation of the system around the quasi-stable orbit allows us to turn on and
off the oscillations reliably and on demand. We illustrate these ideas with a
simple protocol based on optical interference that can induce oscillations
robustly both in the stochastic and deterministic regimes.Comment: 24 pages, 5 main figure
HRTFs Measurement Based on Periodic Sequences Robust towards Nonlinearities in Automotive Audio
The head related transfer functions (HRTFs) represent the acoustic path transfer functions between sound sources in 3D space and the listener’s ear. They are used to create immersive audio scenarios or to subjectively evaluate sound systems according to a human-centric point of view. Cars are nowadays the most popular audio listening environment and the use of HRTFs in automotive audio has recently attracted the attention of researchers. In this context, the paper proposes a measurement method for HRTFs based on perfect or orthogonal periodic sequences. The proposed measurement method ensures robustness towards the nonlinearities that may affect the measurement system. The experimental results considering both an emulated scenario and real measurements in a controlled environment illustrate the effectiveness of the approach and compare the proposed method with other popular approaches
Kernel Analog Forecasting: Multiscale Test Problems
Data-driven prediction is becoming increasingly widespread as the volume of
data available grows and as algorithmic development matches this growth. The
nature of the predictions made, and the manner in which they should be
interpreted, depends crucially on the extent to which the variables chosen for
prediction are Markovian, or approximately Markovian. Multiscale systems
provide a framework in which this issue can be analyzed. In this work kernel
analog forecasting methods are studied from the perspective of data generated
by multiscale dynamical systems. The problems chosen exhibit a variety of
different Markovian closures, using both averaging and homogenization;
furthermore, settings where scale-separation is not present and the predicted
variables are non-Markovian, are also considered. The studies provide guidance
for the interpretation of data-driven prediction methods when used in practice.Comment: 30 pages, 14 figures; clarified several ambiguous parts, added
references, and a comparison with Lorenz' original method (Sec. 4.5
Construction of invariant whiskered tori by a parameterization method. Part II: Quasi-periodic and almost periodic breathers in coupled map lattices
We construct quasi-periodic and almost periodic solutions for coupled
Hamiltonian systems on an infinite lattice which is translation invariant. The
couplings can be long range, provided that they decay moderately fast with
respect to the distance. For the solutions we construct, most of the sites are
moving in a neighborhood of a hyperbolic fixed point, but there are oscillating
sites clustered around a sequence of nodes. The amplitude of these oscillations
does not need to tend to zero. In particular, the almost periodic solutions do
not decay at infinity. We formulate an invariance equation. Solutions of this
equation are embeddings of an invariant torus on which the motion is conjugate
to a rotation. We show that, if there is an approximate solution of the
invariance equation that satisfies some non-degeneracy conditions, there is a
true solution close by. The proof of this \emph{a-posteriori} theorem is based
on a Nash-Moser iteration, which does not use transformation theory. Simpler
versions of the scheme were developed in E. Fontich, R. de la Llave,Y. Sire
\emph{J. Differential. Equations.} {\bf 246}, 3136 (2009). One technical tool,
important for our purposes, is the use of weighted spaces that capture the idea
that the maps under consideration are local interactions. Using these weighted
spaces, the estimates of iterative steps are similar to those in finite
dimensional spaces. In particular, the estimates are independent of the number
of nodes that get excited. Using these techniques, given two breathers, we can
place them apart and obtain an approximate solution, which leads to a true
solution nearby. By repeating the process infinitely often, we can get
solutions with infinitely many frequencies which do not tend to zero at
infinity.Comment: This is a revised version of the paper located at
http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=12-2
Design of sequences with good correlation properties
This thesis is dedicated to exploring sequences with good correlation properties. Periodic sequences with desirable correlation properties have numerous applications in communications. Ideally, one would like to have a set of sequences whose out-of-phase auto-correlation magnitudes and cross-correlation magnitudes are very small, preferably zero. However, theoretical bounds show that the maximum magnitudes of auto-correlation and cross-correlation of a sequence set are mutually constrained, i.e., if a set of sequences possesses good auto-correlation properties, then the cross-correlation properties are not good and vice versa. The design of sequence sets that achieve those theoretical bounds is therefore of great interest. In addition, instead of pursuing the least possible correlation values within an entire period, it is also interesting to investigate families of sequences with ideal correlation in a smaller zone around the origin. Such sequences are referred to as sequences with zero correlation zone or ZCZ sequences, which have been extensively studied due to their applications in 4G LTE and 5G NR systems, as well as quasi-synchronous code-division multiple-access communication systems.
Paper I and a part of Paper II aim to construct sequence sets with low correlation within a whole period. Paper I presents a construction of sequence sets that meets the Sarwate bound. The construction builds a connection between generalised Frank sequences and combinatorial objects, circular Florentine arrays. The size of the sequence sets is determined by the existence of circular Florentine arrays of some order. Paper II further connects circular Florentine arrays to a unified construction of perfect polyphase sequences, which include generalised Frank sequences as a special case. The size of a sequence set that meets the Sarwate bound, depends on a divisor of the period of the employed sequences, as well as the existence of circular Florentine arrays.
Paper III-VI and a part of Paper II are devoted to ZCZ sequences.
Papers II and III propose infinite families of optimal ZCZ sequence sets with respect to some bound, which are used to eliminate interference within a single cell in a cellular network. Papers V, VI and a part of Paper II focus on constructions of multiple optimal ZCZ sequence sets with favorable inter-set cross-correlation, which can be used in multi-user communication environments to minimize inter-cell interference. In particular, Paper~II employs circular Florentine arrays and improves the number of the optimal ZCZ sequence sets with optimal inter-set cross-correlation property in some cases.Doktorgradsavhandlin
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