Carrolljarvis2281

Gene regulation in a cellular environment is a stochastic phenomenon leading to a large variability in mRNAs and protein numbers that are often produced in bursts. The regulation leading to varied protein dynamics can be ascribed to transcriptional or post-transcriptional mechanisms. In transcriptional regulation, the gene dynamically switches between an active and an inactive state, while in the post-transcriptional regulation small RNAs tune the activity of mRNAs. In either scenario, it is possible to calculate the time-dependent probability distribution of proteins and address the interesting question pertaining to their first passage time statistics. The coefficient of variation of first passage time can be considered to be an indicator of efficiency in controlling regulatory pathways and we show that post-transcriptional regulation performs better than simple transcriptional regulation for comparable protein yields.By conditioning a stochastic process on the value of an observable, one obtains a new stochastic process with different properties. We apply this idea in the context of active matter and condition interacting self-propelled particles on their individual motility. Using the effective process formalism from dynamical large deviations theory, we derive the interactions that actuate the imposed mobility against jamming interactions in two toy models-the totally asymmetric exclusion process and run-and-tumble particles, in the case of two or three particles. We provide a framework which takes into account the energy-consumption required for self-propulsion and address the question of how energy-efficient the emergent interactions are. Upon conditioning, run-and-tumble particles develop an alignment interaction and achieve a higher gain in efficiency than TASEP particles. A point of diminishing returns in efficiency is reached beyond a certain level of conditioning. With recourse to a general formula for the change in energy efficiency upon conditioning, we conclude that the most significant gains occur when there are large fluctuations in mobility to exploit. From a detailed comparison of the emergent effective interaction in a two- versus a three-body scenario, we discover evidence of a screening effect which suggests that conditioning can produce topological rather than metric interactions.The time-dependent variational principle is used to optimize the linear and nonlinear parameters of Gaussian basis functions to solve the time-dependent Schrödinger equation in one and three dimensions for a one-body soft Coulomb potential in a laser field. The accuracy is tested comparing the solution to finite difference grid calculations using several examples. Linsitinib concentration The approach is not limited to one particle systems and the example presented for two electrons demonstrates the potential to tackle larger systems using correlated basis functions.Here, we propose a class of scale-free networks G(t;m) with intriguing properties, which cannot be simultaneously held by all the theoretical models with power-law degree distribution in the existing literature, including the following (i) average degrees 〈k〉 of all the generated networks are no longer constant in the limit of large graph size, implying that they are not sparse but dense; (ii) power-law parameters γ of these networks are precisely calculated equal to 2; and (iii) their diameters D are all invariant in the growth process of models. While our models have deterministic structure with clustering coefficients equivalent to zero, we might be able to obtain various candidates with nonzero clustering coefficients based on original networks using reasonable approaches, for instance, randomly adding new edges under the premise of keeping the three important properties above unchanged. In addition, we study the trapping problem on networks G(t;m) and then obtain a closed-form solution to mean hitting time 〈H〉_t. As opposed to other previous models, our results show an unexpected phenomenon that the analytic value for 〈H〉_t is approximately close to the logarithm of the vertex number of networks G(t;m). From the theoretical point of view, these networked models considered here can be thought of as counterexamples for most of the published models obeying power-law distribution in current study.In finite-time quantum heat engines, some work is consumed to drive a working fluid accompanying coherence, which is called "friction." To understand the role of friction in quantum thermodynamics, we present a couple of finite-time quantum Otto cycles with two different baths Agarwal versus Lindbladian. We solve them exactly and compare the performance of the Agarwal engine with that of the Lindbladian engine. In particular, we find remarkable and counterintuitive results that the performance of the Agarwal engine due to friction can be much higher than that in the quasistatic limit with the Otto efficiency, and the power of the Lindbladian engine can be nonzero in the short-time limit. Based on additional numerical calculations of these outcomes, we discuss possible origins of such differences between two engines and reveal them. Our results imply that, even with an equilibrium bath, a nonequilibrium working fluid brings on the higher performance than what an equilibrium working fluid does.The entanglement of eigenstates in two coupled, classically chaotic kicked tops is studied in dependence of their interaction strength. The transition from the noninteracting and unentangled system toward full random matrix behavior is governed by a universal scaling parameter. Using suitable random matrix transition ensembles we express this transition parameter as a function of the subsystem sizes and the coupling strength for both unitary and orthogonal symmetry classes. The universality is confirmed for the level spacing statistics of the coupled kicked tops and a perturbative description is in good agreement with numerical results. The statistics of Schmidt eigenvalues and entanglement entropies of eigenstates is found to follow a universal scaling as well. Remarkably, this is not only the case for large subsystems of equal size but also if one of them is much smaller. For the entanglement entropies a perturbative description is obtained, which can be extended to large couplings and provides very good agreement with numerical results.