Efficient parametric inference for stochastic biological systems with measured variability

Stochastic systems in biology often exhibit substantial variability within and between cells. This variability, as well as having dramatic functional consequences, provides information about the underlying details of the system's behaviour. It is often desirable to infer properties of the parameters governing such systems given experimental observations of the mean and variance of observed quantities. In some circumstances, analytic forms for the likelihood of these observations allow very efficient inference: we present these forms and demonstrate their usage. When likelihood functions are unavailable or difficult to calculate, we show that an implementation of approximate Bayesian computation (ABC) is a powerful tool for parametric inference in these systems. However, the calculations required to apply ABC to these systems can also be computationally expensive, relying on repeated stochastic simulations. We propose an ABC approach that cheaply eliminates unimportant regions of parameter space, by addressing computationally simple mean behaviour before explicitly simulating the more computationally demanding variance behaviour. We show that this approach leads to a substantial increase in speed when applied to synthetic and experimental datasets.Comment: 11 pages, 4 fig

Embedded density functional theory for covalently bonded and strongly interacting subsystems

Embedded density functional theory (e-DFT) is used to describe the electronic structure of strongly interacting molecular subsystems. We present a general implementation of the Exact Embedding (EE) method [J. Chem. Phys. 133, 084103 (2010)] to calculate the large contributions of the nonadditive kinetic potential (NAKP) in such applications. Potential energy curves are computed for the dissociation of Li^+–Be, CH_3–CF_3, and hydrogen-bonded water clusters, and e-DFT results obtained using the EE method are compared with those obtained using approximate kinetic energy functionals. In all cases, the EE method preserves excellent agreement with reference Kohn–Sham calculations, whereas the approximate functionals lead to qualitative failures in the calculated energies and equilibrium structures. We also demonstrate an accurate pairwise approximation to the NAKP that allows for efficient parallelization of the EE method in large systems; benchmark calculations on molecular crystals reveal ideal, size-independent scaling of wall-clock time with increasing system size

Swift heat transfer by fast-forward driving in open quantum systems

Typically, time-dependent thermodynamic protocols need to run asymptotically slowly in order to avoid dissipative losses. By adapting ideas from counter-diabatic driving and Floquet engineering to open systems, we develop fast-forward protocols for swiftly thermalizing a system oscillator locally coupled to an optical phonon bath. These protocols control the system frequency and the system-bath coupling to induce a resonant state exchange between the system and the bath. We apply the fast-forward protocols to realize a fast approximate Otto engine operating at high power near the Carnot Efficiency. Our results suggest design principles for swift cooling protocols in coupled many-body systems.Comment: 16 pages, 10 figure