254 research outputs found
Foundation of Fractional Langevin Equation: Harmonization of a Many Body Problem
In this study we derive a single-particle equation of motion, from
first-principles, starting out with a microscopic description of a tracer
particle in a one-dimensional many-particle system with a general two-body
interaction potential. Using a new harmonization technique, we show that the
resulting dynamical equation belongs to the class of fractional Langevin
equations, a stochastic framework which has been proposed in a large body of
works as a means of describing anomalous dynamics. Our work sheds light on the
fundamental assumptions of these phenomenological models.Comment: 8 pages, 2 figures, REVTeX, revised with 4 appendices added, to
appear in Physical Review E
The Iterative Signature Algorithm for the analysis of large scale gene expression data
We present a new approach for the analysis of genome-wide expression data.
Our method is designed to overcome the limitations of traditional techniques,
when applied to large-scale data. Rather than alloting each gene to a single
cluster, we assign both genes and conditions to context-dependent and
potentially overlapping transcription modules. We provide a rigorous definition
of a transcription module as the object to be retrieved from the expression
data. An efficient algorithm, that searches for the modules encoded in the data
by iteratively refining sets of genes and conditions until they match this
definition, is established. Each iteration involves a linear map, induced by
the normalized expression matrix, followed by the application of a threshold
function. We argue that our method is in fact a generalization of Singular
Value Decomposition, which corresponds to the special case where no threshold
is applied. We show analytically that for noisy expression data our approach
leads to better classification due to the implementation of the threshold. This
result is confirmed by numerical analyses based on in-silico expression data.
We discuss briefly results obtained by applying our algorithm to expression
data from the yeast S. cerevisiae.Comment: Latex, 36 pages, 8 figure
Chemotaxis When Bacteria Remember: Drift versus Diffusion
{\sl Escherichia coli} ({\sl E. coli}) bacteria govern their trajectories by
switching between running and tumbling modes as a function of the nutrient
concentration they experienced in the past. At short time one observes a drift
of the bacterial population, while at long time one observes accumulation in
high-nutrient regions. Recent work has viewed chemotaxis as a compromise
between drift toward favorable regions and accumulation in favorable regions. A
number of earlier studies assume that a bacterium resets its memory at tumbles
-- a fact not borne out by experiment -- and make use of approximate
coarse-grained descriptions. Here, we revisit the problem of chemotaxis without
resorting to any memory resets. We find that when bacteria respond to the
environment in a non-adaptive manner, chemotaxis is generally dominated by
diffusion, whereas when bacteria respond in an adaptive manner, chemotaxis is
dominated by a bias in the motion. In the adaptive case, favorable drift occurs
together with favorable accumulation. We derive our results from detailed
simulations and a variety of analytical arguments. In particular, we introduce
a new coarse-grained description of chemotaxis as biased diffusion, and we
discuss the way it departs from older coarse-grained descriptions.Comment: Revised version, journal reference adde
Fractional transport equations for Levy stable processes
The influence functional method of Feynman and Vernon is used to obtain a
quantum master equation for a Brownian system subjected to a Levy stable random
force. The corresponding classical transport equations for the Wigner function
are then derived, both in the limit of weak and strong friction. These are
fractional extensions of the Klein-Kramers and the Smoluchowski equations. It
is shown that the fractional character acquired by the position in the
Smoluchowski equation follows from the fractional character of the momentum in
the Klein-Kramers equation. Connections among fractional transport equations
recently proposed are clarified.Comment: 4 page
Scaling and Asymptotic Scaling in the SU(2) Gauge Theory
We determine the critical couplings for the deconfinement phase transition in
gauge theory on lattices with
and 16 and varying between 16 and 48. A comparison with string
tension data shows scaling of the ratio in the entire
coupling regime , while the individual quantities still
exhibit large scaling violations. We find . We
also discuss in detail the extrapolation of and to the continuum
limit. Our result, which is consistent with the above ratio, is and . We also comment upon corresponding
results for gauge theory and four flavour QCD.Comment: 27 pages with 9 postscript figures included. Plain TeX file (needed
macros are included). BI-TP 92-26, FSU-SCRI-92-103, HLRZ-92-39 (Quote of
UKQCD string tension, and accordingly Figs. 5 and 7a, plus a few typo's
corrected.
Photon Statistics; Nonlinear Spectroscopy of Single Quantum Systems
A unified description of multitime correlation functions, nonlinear response
functions, and quantum measurements is developed using a common generating
function which allows a direct comparison of their information content. A
general formal expression for photon counting statistics from single quantum
objects is derived in terms of Liouville space correlation functions of the
material system by making a single assumption that spontaneous emission is
described by a master equation
Synchronization and clustering of synthetic genetic networks: A role for cis-regulatory modules
The effect of signal integration through cis-regulatory modules (CRMs) on
synchronization and clustering of populations of two-component genetic
oscillators coupled by quorum sensing is in detail investigated. We find that
the CRMs play an important role in achieving synchronization and clustering.
For this, we investigate 6 possible cis-regulatory input functions (CRIFs) with
AND, OR, ANDN, ORN, XOR, and EQU types of responses in two possible kinds of
cell-to-cell communications: activator-regulated communication (i.e., the
autoinducer regulates the activator) and repressor-regulated communication
(i.e., the autoinducer regulates the repressor). Both theoretical analysis and
numerical simulation show that different CRMs drive fundamentally different
cellular patterns, such as complete synchronization, various cluster-balanced
states and several cluster-nonbalanced states.Comment: 30 pages, 8 figure
Asmparts: assembly of biological model parts
We propose a new computational tool to produce models of biological systems by assembling models from biological parts. Our software not only takes advantage of modularity, but it also enforces standardisation in part characterisation by considering a model of each part. We have used model parts in SBML to design transcriptional networks. Our software is open source, it works in linux and windows platforms, and it could be used to automatically produce models in a server. Our tool not only facilitates model design, but it will also help to promote the establishment of a registry of model parts
Evolution of Robustness to Noise and Mutation in Gene Expression Dynamics
Phenotype of biological systems needs to be robust against mutation in order
to sustain themselves between generations. On the other hand, phenotype of an
individual also needs to be robust against fluctuations of both internal and
external origins that are encountered during growth and development. Is there a
relationship between these two types of robustness, one during a single
generation and the other during evolution? Could stochasticity in gene
expression have any relevance to the evolution of these robustness? Robustness
can be defined by the sharpness of the distribution of phenotype; the variance
of phenotype distribution due to genetic variation gives a measure of `genetic
robustness' while that of isogenic individuals gives a measure of
`developmental robustness'. Through simulations of a simple stochastic gene
expression network that undergoes mutation and selection, we show that in order
for the network to acquire both types of robustness, the phenotypic variance
induced by mutations must be smaller than that observed in an isogenic
population. As the latter originates from noise in gene expression, this
signifies that the genetic robustness evolves only when the noise strength in
gene expression is larger than some threshold. In such a case, the two
variances decrease throughout the evolutionary time course, indicating increase
in robustness. The results reveal how noise that cells encounter during growth
and development shapes networks' robustness to stochasticity in gene
expression, which in turn shapes networks' robustness to mutation. The
condition for evolution of robustness as well as relationship between genetic
and developmental robustness is derived through the variance of phenotypic
fluctuations, which are measurable experimentally.Comment: 25 page
Sensory Measurements: Coordination and Standardization
Do sensory measurements deserve the label of “measurement”? We argue that they do. They fit with an epistemological view of measurement held in current philosophy of science, and they face the same kinds of epistemological challenges as physical measurements do: the problem of coordination and the problem of standardization. These problems are addressed through the process of “epistemic iteration,” for all measurements. We also argue for distinguishing the problem of standardization from the problem of coordination. To exemplify our claims, we draw on olfactory performance tests, especially studies linking olfactory decline to neurodegenerative disorders
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