1,174 research outputs found
A relational-constructionist account of protein macrostructure and function
info:eu-repo/semantics/publishedVersio
Lyapunov exponent of the random frequency oscillator: cumulant expansion approach
We consider a one-dimensional harmonic oscillator with a random frequency,
focusing on both the standard and the generalized Lyapunov exponents,
and respectively. We discuss the numerical difficulties that
arise in the numerical calculation of in the case of strong
intermittency. When the frequency corresponds to a Ornstein-Uhlenbeck process,
we compute analytically by using a cumulant expansion including
up to the fourth order. Connections with the problem of finding an analytical
estimate for the largest Lyapunov exponent of a many-body system with smooth
interactions are discussed.Comment: 6 pages, 4 figures, to appear in J. Phys. Conf. Series - LAWNP0
Correcting the Mean-Variance Dependency for Differential Variability Testing Using Single-Cell RNA Sequencing Data.
Cell-to-cell transcriptional variability in otherwise homogeneous cell populations plays an important role in tissue function and development. Single-cell RNA sequencing can characterize this variability in a transcriptome-wide manner. However, technical variation and the confounding between variability and mean expression estimates hinder meaningful comparison of expression variability between cell populations. To address this problem, we introduce an analysis approach that extends the BASiCS statistical framework to derive a residual measure of variability that is not confounded by mean expression. This includes a robust procedure for quantifying technical noise in experiments where technical spike-in molecules are not available. We illustrate how our method provides biological insight into the dynamics of cell-to-cell expression variability, highlighting a synchronization of biosynthetic machinery components in immune cells upon activation. In contrast to the uniform up-regulation of the biosynthetic machinery, CD4+ T cells show heterogeneous up-regulation of immune-related and lineage-defining genes during activation and differentiation.NE was funded by the European Molecular Biology Laboratory (EMBL) international PhD programme. ACR was funded by the MRC Skills Development Fellowship (MR/P014178/1). SR was funded by MRC grant MC_UP_0801/1. JCM was funded by core support of Cancer Research UK and EMBL. CAV was funded by The Alan Turing Institute, EPSRC grant EP/N510129/1
On the semiclassical theory for universal transmission fluctuations in chaotic systems: the importance of unitarity
The standard semiclassical calculation of transmission correlation functions
for chaotic systems is severely influenced by unitarity problems. We show that
unitarity alone imposes a set of relationships between cross sections
correlation functions which go beyond the diagonal approximation. When these
relationships are properly used to supplement the semiclassical scheme we
obtain transmission correlation functions in full agreement with the exact
statistical theory and the experiment. Our approach also provides a novel
prediction for the transmission correlations in the case where time reversal
symmetry is present
Lyapunov exponent of many-particle systems: testing the stochastic approach
The stochastic approach to the determination of the largest Lyapunov exponent
of a many-particle system is tested in the so-called mean-field
XY-Hamiltonians. In weakly chaotic regimes, the stochastic approach relates the
Lyapunov exponent to a few statistical properties of the Hessian matrix of the
interaction, which can be calculated as suitable thermal averages. We have
verified that there is a satisfactory quantitative agreement between theory and
simulations in the disordered phases of the XY models, either with attractive
or repulsive interactions. Part of the success of the theory is due to the
possibility of predicting the shape of the required correlation functions,
because this permits the calculation of correlation times as thermal averages.Comment: 11 pages including 6 figure
Semiclassical approach to fidelity amplitude
The fidelity amplitude is a quantity of paramount importance in echo type
experiments. We use semiclassical theory to study the average fidelity
amplitude for quantum chaotic systems under external perturbation. We explain
analytically two extreme cases: the random dynamics limit --attained
approximately by strongly chaotic systems-- and the random perturbation limit,
which shows a Lyapunov decay. Numerical simulations help us bridge the gap
between both extreme cases.Comment: 10 pages, 9 figures. Version closest to published versio
Semiclassical Description of Wavepacket Revival
We test the ability of semiclassical theory to describe quantitatively the
revival of quantum wavepackets --a long time phenomena-- in the one dimensional
quartic oscillator (a Kerr type Hamiltonian). Two semiclassical theories are
considered: time-dependent WKB and Van Vleck propagation. We show that both
approaches describe with impressive accuracy the autocorrelation function and
wavefunction up to times longer than the revival time. Moreover, in the Van
Vleck approach, we can show analytically that the range of agreement extends to
arbitrary long times.Comment: 10 pages, 6 figure
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