9,966 research outputs found
Towards MKM in the Large: Modular Representation and Scalable Software Architecture
MKM has been defined as the quest for technologies to manage mathematical
knowledge. MKM "in the small" is well-studied, so the real problem is to scale
up to large, highly interconnected corpora: "MKM in the large". We contend that
advances in two areas are needed to reach this goal. We need representation
languages that support incremental processing of all primitive MKM operations,
and we need software architectures and implementations that implement these
operations scalably on large knowledge bases.
We present instances of both in this paper: the MMT framework for modular
theory-graphs that integrates meta-logical foundations, which forms the base of
the next OMDoc version; and TNTBase, a versioned storage system for XML-based
document formats. TNTBase becomes an MMT database by instantiating it with
special MKM operations for MMT.Comment: To appear in The 9th International Conference on Mathematical
Knowledge Management: MKM 201
The MMT API: A Generic MKM System
The MMT language has been developed as a scalable representation and
interchange language for formal mathematical knowledge. It permits natural
representations of the syntax and semantics of virtually all declarative
languages while making MMT-based MKM services easy to implement. It is
foundationally unconstrained and can be instantiated with specific formal
languages.
The MMT API implements the MMT language along with multiple backends for
persistent storage and frontends for machine and user access. Moreover, it
implements a wide variety of MMT-based knowledge management services. The API
and all services are generic and can be applied to any language represented in
MMT. A plugin interface permits injecting syntactic and semantic idiosyncrasies
of individual formal languages.Comment: Conferences on Intelligent Computer Mathematics (CICM) 2013 The final
publication is available at http://link.springer.com
A Stochastic Analysis of Autoregulation of Gene Expression
This paper analyzes, in the context of a prokaryotic cell, the stochastic
variability of the number of proteins when there is a control of gene
expression by an autoregulation scheme. The goal of this work is to estimate
the efficiency of the regulation to limit the fluctuations of the number of
copies of a given protein. The autoregulation considered in this paper relies
mainly on a negative feedback: the proteins are repressors of their own gene
expression. The efficiency of a production process without feedback control is
compared to a production process with an autoregulation of the gene expression
assuming that both of them produce the same average number of proteins. The
main characteristic used for the comparison is the standard deviation of the
number of proteins at equilibrium. With a Markovian representation and a simple
model of repression, we prove that, under a scaling regime, the repression
mechanism follows a Hill repression scheme with an hyperbolic control. An
explicit asymptotic expression of the variance of the number of proteins under
this regulation mechanism is obtained. Simulations are used to study other
aspects of autoregulation such as the rate of convergence to equilibrium of the
production process and the case where the control of the production process of
proteins is achieved via the inhibition of mRNAs
- …