41,222 research outputs found
Large deviations for two scale chemical kinetic processes
We formulate the large deviations for a class of two scale chemical kinetic
processes motivated from biological applications. The result is successfully
applied to treat a genetic switching model with positive feedbacks. The
corresponding Hamiltonian is convex with respect to the momentum variable as a
by-product of the large deviation theory. This property ensures its superiority
in the rare event simulations compared with the result obtained by formal WKB
asymptotics. The result is of general interest to understand the large
deviations for multiscale problems
Two-scale large deviations for chemical reaction kinetics through second quantization path integral
Motivated by the study of rare events for a typical genetic switching model
in systems biology, in this paper we aim to establish the general two-scale
large deviations for chemical reaction systems. We build a formal approach to
explicitly obtain the large deviation rate functionals for the considered
two-scale processes based upon the second-quantization path integral technique.
We get three important types of large deviation results when the underlying two
times scales are in three different regimes. This is realized by singular
perturbation analysis to the rate functionals obtained by path integral. We
find that the three regimes possess the same deterministic mean-field limit but
completely different chemical Langevin approximations. The obtained results are
natural extensions of the classical large volume limit for chemical reactions.
We also discuss its implication on the single-molecule Michaelis-Menten
kinetics. Our framework and results can be applied to understand general
multi-scale systems including diffusion processes
Entanglement renormalization and integral geometry
We revisit the applications of integral geometry in AdS and argue that
the metric of the kinematic space can be realized as the entanglement contour,
which is defined as the additive entanglement density. From the renormalization
of the entanglement contour, we can holographically understand the operations
of disentangler and isometry in multi-scale entanglement renormalization
ansatz. Furthermore, a renormalization group equation of the long-distance
entanglement contour is then derived. We then generalize this integral
geometric construction to higher dimensions and in particular demonstrate how
it works in bulk space of homogeneity and isotropy.Comment: 40 pages, 7 figures. v2: discussions on the general measure added,
typos fixed; v3: sections reorganized, various points clarified, to appear in
JHE
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