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, $\lambda$ and $\lambda^\star$ respectively. We discuss the numerical difficulties that arise in the numerical calculation of $\lambda^\star$ in the case of strong intermittency. When the frequency corresponds to a Ornstein-Uhlenbeck process, we compute analytically $\lambda^\star$ 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