DNA methylation variability arises due to concurrent genetic and environmental influences. Each of them is a mixture of regular and noisy sources, whose relative contribution has not been satisfactorily understood yet. We conduct a systematic assessment of the age-dependent methylation by the signal-to-noise ratio and identify a wealth of “deterministic” CpG probes (about 90%), whose methylation variability likely originates due to genetic and general environmental factors. The remaining 10% of “stochastic” CpG probes are arguably governed by the biological noise or incidental environmental factors. Investigating the mathematical functional relationship between methylation levels and variability, we find that in about 90% of the age-associated differentially methylated positions, the variability changes as the square of the methylation level, whereas in the most of the remaining cases the dependence is linear. Furthermore, we demonstrate that the methylation level itself in more than 15% cases varies nonlinearly with age (according to the power law), in contrast to the previously assumed linear changes. Our findings present ample evidence of the ubiquity of strong DNA methylation regulation, resulting in the individual age-dependent and nonlinear methylation trajectories, whose divergence explains the cross-sectional variability. It may also serve a basis for constructing novel nonlinear epigenetic clocks.
Quantum systems, when interacting with their environments, can exhibit complex non-equilibrium states that are tempting to be interpreted as quantum versions of chaotic attractors. Here we propose an approach to open cavity dynamics based on the unraveling of the corresponding master equation into an ensemble of quantum trajectories. By using the concept of "quantum Lyapunov exponents" [I. I. Yusipov et al., arxiv: 1806.09295], we demonstrate that 'chaotic' and 'regular' regimes of the intra-cavity dynamics can be identified. The chaotic regimes are marked by the emergence of power-law intermediate asymptotics in the distribution of photon waiting times. The photon counting statistics can be retrieved by monitoring photon emission in experiment. Therefore, chaotic regimes can be identified without additional measurements (and thus disturbance) of the intra-cavity dynamics.
DNA methylation variability arises due to concurrent genetic and environmental influences. Each of them is a mixture of regular and noisy sources, whose relative contribution has not been satisfactorily understood yet. We conduct a systematic assessment of the age-dependent methylation by the signal-to-noise ratio and identify a wealth of “deterministic” CpG probes (about 90%), whose methylation variability likely originates due to genetic and general environmental factors. The remaining 10% of “stochastic” CpG probes are arguably governed by the biological noise or incidental environmental factors. Investigating the mathematical functional relationship between methylation levels and variability, we find that in about 90% of the age-associated differentially methylated positions, the variability changes as the square of the methylation level, whereas in the most of the remaining cases the dependence is linear. Furthermore, we demonstrate that the methylation level itself in more than 15% cases varies nonlinearly with age (according to the power law), in contrast to the previously assumed linear changes. Our findings present ample evidence of the ubiquity of strong DNA methylation regulation, resulting in the individual age-dependent and nonlinear methylation trajectories, whose divergence explains the cross-sectional variability. It may also serve a basis for constructing novel nonlinear epigenetic clocks.
We investigate the possibility to control localization properties of the asymptotic state of an open quantum system with a tunable synthetic dissipation. The control mechanism relies on the matching between properties of dissipative operators, acting on neighboring sites and specified by a single control parameter, and the spatial phase structure of eigenstates of the system Hamiltonian. As a result, the latter coincide (or near coincide) with the dark states of the operators. In a disorder-free Hamiltonian with a flat band, one can either obtain a localized asymptotic state or populate whole flat and/or dispersive bands, depending on the value of the control parameter. In a disordered Anderson system, the asymptotic state can be localized anywhere in the spectrum of the Hamiltonian. The dissipative control is robust with respect to an additional local dephasing.
Quantum systems, when interacting with their environments, may exhibit non-equilibrium states that are tempting to be interpreted as quantum analogs of chaotic attractors. However, different from the Hamiltonian case, the toolbox for quantifying dissipative quantum chaos remains limited. In particular, quantum generalizations of Lyapunov exponents, the main quantifiers of classical chaos, are established only within the framework of continuous measurements. We propose an alternative generalization based on the unraveling of quantum master equation into an ensemble of 'quantum trajectories', by using the so-called Monte Carlo wave-function method. We illustrate the idea with a periodically modulated open quantum dimer and demonstrate that the transition to quantum chaos matches the period-doubling route to chaos in the corresponding mean-field system.It is one of the pillar concepts of Chaos theory that complex deterministic dynamics is rooted in the local instability which forces two initially close trajectories to diverge. This divergence is conventionally quantified with Lyapunov exponents (LEs), a powerful tool to quantify dynamical chaos. The history of attempts to generalize LEs to quantum dynamics is nearly as old as the history of Quantum Chaos. Most of this history is about the Hamiltonian limit, where the spectral theory of Quantum Chaos [1] was established first. The corresponding generalizations range from early ideas to use quasi-probability functions and define quantum LEs in terms of a "distance" between them [2-4] to very recent advances based on out-of-time correlation functions [5][6][7]. When a quantum system is open and its dynamics is modeled with a quantum master equation [8], the evolution of the system's density operator can be unraveled into an ensemble of evolving trajectories, each one described by a wave function [8]. Dynamics of these wave functions is essentially stochastic; therefore, LEs could be introduced in a more intuitive way than in the Hamiltonian limit. But will so-defined exponents make sense? Here we define a particular type of quantum LEs and give a positive answer to this question. Since quantum trajectories [9] are not just a formal trick but a part of reality, e.g., in optical [10] and microwave [11] cavity systems, we believe that our results will be of interest to the theoreticians (and, hopefully, to the experimentalists) dealing with these systems.
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