1,259 research outputs found
Burch ideals and Burch rings
We introduce the notion of Burch ideals and Burch rings. They are easy to
define, and can be viewed as generalization of many well-known concepts, for
example integrally closed ideals of finite colength and Cohen--Macaulay rings
of minimal multiplicity. We give several characterizations of these objects. We
show that they satisfy many interesting and desirable properties:
ideal-theoretic, homological, categorical. We relate them to other classes of
ideals and rings in the literature.Comment: 23 pages, add Example 2.2, Prop 5.5 and Example 5.
Feedback Regulation and its Efficiency in Biochemical Networks
Intracellular biochemical networks fluctuate dynamically due to various
internal and external sources of fluctuation. Dissecting the fluctuation into
biologically relevant components is important for understanding how a cell
controls and harnesses noise and how information is transferred over apparently
noisy intracellular networks. While substantial theoretical and experimental
advancement on the decomposition of fluctuation was achieved for feedforward
networks without any loop, we still lack a theoretical basis that can
consistently extend such advancement to feedback networks. The main obstacle
that hampers is the circulative propagation of fluctuation by feedback loops.
In order to define the relevant quantity for the impact of feedback loops for
fluctuation, disentanglement of the causally interlocked influence between the
components is required. In addition, we also lack an approach that enables us
to infer non-perturbatively the influence of the feedback to fluctuation as the
dual reporter system does in the feedforward network. In this work, we resolve
these problems by extending the work on the fluctuation decomposition and the
dual reporter system. For a single-loop feedback network with two components,
we define feedback loop gain as the feedback efficiency that is consistent with
the fluctuation decomposition for feedforward networks. Then, we clarify the
relation of the feedback efficiency with the fluctuation propagation in an
open-looped FF network. Finally, by extending the dual reporter system, we
propose a conjugate feedback and feedforward system for estimating the feedback
efficiency only from the statistics of the system non-perturbatively
- …