9,095 research outputs found
Adiabatic reduction of models of stochastic gene expression with bursting
This paper considers adiabatic reduction in both discrete and continuous
models of stochastic gene expression. In gene expression models, the concept of
bursting is a production of several molecules simultaneously and is generally
represented as a compound Poisson process of random size. In a general
two-dimensional birth and death discrete model, we prove that under specific
assumptions and scaling (that are characteristics of the mRNA-protein system)
an adiabatic reduction leads to a one-dimensional discrete-state space model
with bursting production. The burst term appears through the reduction of the
first variable. In a two-dimensional continuous model, we also prove that an
adiabatic reduction can be performed in a stochastic slow/fast system. In this
gene expression model, the production of mRNA (the fast variable) is assumed to
be bursty and the production of protein (the slow variable) is linear as a
function of mRNA. When the dynamics of mRNA is assumed to be faster than the
protein dynamics (due to a mRNA degradation rate larger than for the protein)
we prove that, with the appropriate scaling, the bursting phenomena can be
transmitted to the slow variable. We show that the reduced equation is either a
stochastic differential equation with a jump Markov process or a deterministic
ordinary differential equation depending on the scaling that is appropriate.
These results are significant because adiabatic reduction techniques seem to
have not been applied to a stochastic differential system containing a jump
Markov process. Last but not least, for our particular system, the adiabatic
reduction allows us to understand what are the necessary conditions for the
bursting production-like of protein to occur.Comment: 24 page
On regression adjustments in experiments with several treatments
Regression adjustments are often made to experimental data. Since
randomization does not justify the models, bias is likely; nor are the usual
variance calculations to be trusted. Here, we evaluate regression adjustments
using Neyman's nonparametric model. Previous results are generalized, and more
intuitive proofs are given. A bias term is isolated, and conditions are given
for unbiased estimation in finite samples.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS143 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Diffusion approximations in collective risk theory
Collective risk theory concerned with random fluctuations of total assets of insurance compan
Law without law or "just" limit theorems?
About 35 years ago Wheeler introduced the motto `law without law' to
highlight the possibility that (at least a part of) Physics may be understood
only following {\em regularity principles} and few relevant facts, rather than
relying on a treatment in terms of fundamental theories. Such a proposal can be
seen as part of a more general attempt (including the maximum entropy approach)
summarized by the slogan `it from bit', which privileges the information as the
basic ingredient. Apparently it seems that it is possible to obtain, without
the use of physical laws, some important results in an easy way, for instance,
the probability distribution of the canonical ensemble. In this paper we will
present a general discussion on those ideas of Wheeler's that originated the
motto `law without law'. In particular we will show how the claimed simplicity
is only apparent and it is rather easy to produce wrong results. We will show
that it is possible to obtain some of the results treated by Wheeler in the
realm of the statistical mechanics, using precise assumptions and nontrivial
results of probability theory, mainly concerning ergodicity and limit theorems.Comment: 9 pages, 3 figure
Is Brownian motion necessary to model high-frequency data?
This paper considers the problem of testing for the presence of a continuous
part in a semimartingale sampled at high frequency. We provide two tests, one
where the null hypothesis is that a continuous component is present, the other
where the continuous component is absent, and the model is then driven by a
pure jump process. When applied to high-frequency individual stock data, both
tests point toward the need to include a continuous component in the model.Comment: Published in at http://dx.doi.org/10.1214/09-AOS749 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Consequences of a Goedel's misjudgment
The fundamental aim of the paper is to correct an harmful way to interpret a
Goedel's erroneous remark at the Congress of Koenigsberg in 1930. Despite the
Goedel's fault is rather venial, its misreading has produced and continues to
produce dangerous fruits, as to apply the incompleteness Theorems to the full
second-order Arithmetic and to deduce the semantic incompleteness of its
language by these same Theorems. The first three paragraphs are introductory
and serve to define the languages inherently semantic and its properties, to
discuss the consequences of the expression order used in a language and some
question about the semantic completeness: in particular is highlighted the fact
that a non-formal theory may be semantically complete despite using a language
semantically incomplete. Finally, an alternative interpretation of the Goedel's
unfortunate comment is proposed. KEYWORDS: semantic completeness, syntactic
incompleteness, categoricity, arithmetic, second-order languages, paradoxesComment: English version, 19 pages. Fixed and improved terminolog
Z2SAL: a translation-based model checker for Z
Despite being widely known and accepted in industry, the Z formal specification language has not so far been well supported by automated verification tools, mostly because of the challenges in handling the abstraction of the language. In this paper we discuss a novel approach to building a model-checker for Z, which involves implementing a translation from Z into SAL, the input language for the Symbolic Analysis Laboratory, a toolset which includes a number of model-checkers and a simulator. The Z2SAL translation deals with a number of important issues, including: mapping unbounded, abstract specifications into bounded, finite models amenable to a BDD-based symbolic checker; converting a non-constructive and piecemeal style of functional specification into a deterministic, automaton-based style of specification; and supporting the rich set-based vocabulary of the Z mathematical toolkit. This paper discusses progress made towards implementing as complete and faithful a translation as possible, while highlighting certain assumptions, respecting certain limitations and making use of available optimisations. The translation is illustrated throughout with examples; and a complete working example is presented, together with performance data
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