1,057 research outputs found
Aspects of (2+1) dimensional gravity: AdS3 asymptotic dynamics in the framework of Fefferman-Graham-Lee theorems
Using the Chern-Simon formulation of (2+1) gravity, we derive, for the
general asymptotic metrics given by the Fefferman-Graham-Lee theorems, the
emergence of the Liouville mode associated to the boundary degrees of freedom
of (2+1) dimensional anti de Sitter geometries.Comment: 6 pages, Latex, presented at the Journees Relativistes 99, Weimar,
September 12-17, 1999; revised version with minor modifications and 1
reference adde
Insights into the relation between noise and biological complexity
Understanding under which conditions the increase of systems complexity is
evolutionary advantageous, and how this trend is related to the modulation of
the intrinsic noise, are fascinating issues of utmost importance for synthetic
and systems biology. To get insights into these matters, we analyzed chemical
reaction networks with different topologies and degrees of complexity,
interacting or not with the environment. We showed that the global level of
fluctuations at the steady state, as measured by the sum of the Fano factors of
the number of molecules of all species, is directly related to the topology of
the network. For systems with zero deficiency, this sum is constant and equal
to the rank of the network. For higher deficiencies, we observed an increase or
decrease of the fluctuation levels according to the values of the reaction
fluxes that link internal species, multiplied by the associated stoichiometry.
We showed that the noise is reduced when the fluxes all flow towards the
species of higher complexity, whereas it is amplified when the fluxes are
directed towards lower complexity species.Comment: 5 pages, 3 figure
Stochastic noise reduction upon complexification: positively correlated birth-death type systems
Cell systems consist of a huge number of various molecules that display
specific patterns of interactions, which have a determining influence on the
cell's functioning. In general, such complexity is seen to increase with the
complexity of the organism, with a concomitant increase of the accuracy and
specificity of the cellular processes. The question thus arises how the
complexification of systems - modeled here by simple interacting birth-death
type processes - can lead to a reduction of the noise - described by the
variance of the number of molecules. To gain understanding of this issue, we
investigated the difference between a single system containing molecules that
are produced and degraded, and the same system - with the same average number
of molecules - connected to a buffer. We modeled these systems using Ito
stochastic differential equations in discrete time, as they allow
straightforward analytical developments. In general, when the molecules in the
system and the buffer are positively correlated, the variance on the number of
molecules in the system is found to decrease compared to the equivalent system
without a buffer. Only buffers that are too noisy by themselves tend to
increase the noise in the main system. We tested this result on two model
cases, in which the system and the buffer contain proteins in their active and
inactive state, or protein monomers and homodimers. We found that in the second
test case, where the interconversion terms are non-linear in the number of
molecules, the noise reduction is much more pronounced; it reaches up to 20%
reduction of the Fano factor with the parameter values tested in numerical
simulations on an unperturbed birth-death model. We extended our analysis to
two arbitrary interconnected systems.Comment: 38 pages, 5 figures, to appear in J. Theor. Bio
Optimality of the genetic code with respect to protein stability and amino acid frequencies
How robust is the natural genetic code with respect to mistranslation errors?
It has long been known that the genetic code is very efficient in limiting the
effect of point mutation. A misread codon will commonly code either for the
same amino acid or for a similar one in terms of its biochemical properties, so
the structure and function of the coded protein remain relatively unaltered.
Previous studies have attempted to address this question more quantitatively,
namely by statistically estimating the fraction of randomly generated codes
that do better than the genetic code regarding its overall robustness. In this
paper, we extend these results by investigating the role of amino acid
frequencies in the optimality of the genetic code. When measuring the relative
fitness of the natural code with respect to a random code, it is indeed natural
to assume that a translation error affecting a frequent amino acid is less
favorable than that of a rare one, at equal mutation cost. We find that taking
the amino acid frequency into account accordingly decreases the fraction of
random codes that beat the natural code, making the latter comparatively even
more robust. This effect is particularly pronounced when more refined measures
of the amino acid substitution cost are used than hydrophobicity. To show this,
we devise a new cost function by evaluating with computer experiments the
change in folding free energy caused by all possible single-site mutations in a
set of known protein structures. With this cost function, we estimate that of
the order of one random code out of 100 millions is more fit than the natural
code when taking amino acid frequencies into account. The genetic code seems
therefore structured so as to minimize the consequences of translation errors
on the 3D structure and stability of proteins.Comment: 31 pages, 2 figures, postscript fil
Star products on extended massive non-rotating BTZ black holes
space-time admits a foliation by two-dimensional twisted conjugacy
classes, stable under the identification subgroup yielding the non-rotating
massive BTZ black hole. Each leaf constitutes a classical solution of the
space-time Dirac-Born-Infeld action, describing an open D-string in or
a D-string winding around the black hole. We first describe two nonequivalent
maximal extensions of the non-rotating massive BTZ space-time and observe that
in one of them, each D-string worldsheet admits an action of a two-parameter
subgroup (\ca \cn) of \SL. We then construct non-formal, \ca
\cn-invariant, star products that deform the classical algebra of functions on
the D-string worldsheets and on their embedding space-times. We end by giving
the first elements towards the definition of a Connes spectral triple on
non-commutative space-times.Comment: 25 pages, 1 figur
Noncommutative Locally Anti-de Sitter Black Holes
We give a review of our joint work on strict deformation of BHTZ 2+1 black
holes \cite{BRS02,BDHRS03}. However some results presented here are not
published elsewhere, and an effort is made for enlightening the instrinsical
aspect of the constructions. This shows in particular that the three
dimensional case treated here could be generalized to an anti-de Sitter space
of arbitrary dimension provided one disposes of a universal deformation formula
for the actions of a parabolic subgroup of its isometry group.Comment: 10 pages, based on a talk given by P.B., to appear in the proceedings
of the workshop `Noncommutative Geometry and Physics 2004' (Feb. 2004, Keio
University, Japan) (World Scientific
Global geometry of the 2+1 rotating black hole
The generic rotating BTZ black hole, obtained by identifications in AdS3
space through a discrete subgroup of its isometry group, is investigated within
a Lie theoretical context. This space is found to admit a foliation by
two-dimensional leaves, orbits of a two-parameter subgroup of SL(2,R) and
invariant under the BTZ identification subgroup. A global expression for the
metric is derived, allowing a better understanding of the causal structure of
the black hole.Comment: 9 pages, 1 figur
Uniqueness of the asymptotic AdS3 geometry
We explicitly show that in (2+1) dimensions the general solution of the
Einstein equations with negative cosmological constant on a neigbourhood of
timelike spatial infinity can be obtained from BTZ metrics by coordinate
transformations corresponding geometrically to deformations of their spatial
infinity surface. Thus, whatever the topology and geometry of the bulk, the
metric on the timelike extremities is BTZ.Comment: LaTeX, 8 pages, no figures, version that will appear in Class. Quant.
Gra
Deciphering noise amplification and reduction in open chemical reaction networks
The impact of random fluctuations on the dynamical behavior a complex
biological systems is a longstanding issue, whose understanding would shed
light on the evolutionary pressure that nature imposes on the intrinsic noise
levels and would allow rationally designing synthetic networks with controlled
noise. Using the It\=o stochastic differential equation formalism, we performed
both analytic and numerical analyses of several model systems containing
different molecular species in contact with the environment and interacting
with each other through mass-action kinetics. These systems represent for
example biomolecular oligomerization processes, complex-breakage reactions,
signaling cascades or metabolic networks. For chemical reaction networks with
zero deficiency values, which admit a detailed- or complex-balanced steady
state, all molecular species are uncorrelated. The number of molecules of each
species follow a Poisson distribution and their Fano factors, which measure the
intrinsic noise, are equal to one. Systems with deficiency one have an
unbalanced non-equilibrium steady state and a non-zero S-flux, defined as the
flux flowing between the complexes multiplied by an adequate stoichiometric
coefficient. In this case, the noise on each species is reduced if the flux
flows from the species of lowest to highest complexity, and is amplified is the
flux goes in the opposite direction. These results are generalized to systems
of deficiency two, which possess two independent non-vanishing S-fluxes, and we
conjecture that a similar relation holds for higher deficiency systems
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