152 research outputs found
Dynamics of Triangulations
We study a few problems related to Markov processes of flipping
triangulations of the sphere. We show that these processes are ergodic and
mixing, but find a natural example which does not satisfy detailed balance. In
this example, the expected distribution of the degrees of the nodes seems to
follow the power law
Irreversible and reversible modes of operation of deterministic ratchets
We discuss a problem of optimization of the energetic efficiency of a simple
rocked ratchet. We concentrate on a low-temperature case in which the
particle's motion in a ratchet potential is deterministic. We show that the
energetic efficiency of a ratchet working adiabatically is bounded from above
by a value depending on the form of ratchet potential. The ratchets with
strongly asymmetric potentials can achieve ideal efficiency of unity without
approaching reversibility. On the other hand we show that for any form of the
ratchet potential a set of time-protocols of the outer force exist under which
the operation is reversible and the ideal value of efficiency is also achieved.
The mode of operation of the ratchet is still quasistatic but not adiabatic.
The high values of efficiency can be preserved even under elevated
temperatures
The Cochlear Tuning Curve
The tuning curve of the cochlea measures how large an input is required to
elicit a given output level as a function of the frequency. It is a fundamental
object of auditory theory, for it summarizes how to infer what a sound was on
the basis of the cochlear output. A simple model is presented showing that only
two elements are sufficient for establishing the cochlear tuning curve: a
broadly tuned traveling wave, moving unidirectionally from high to low
frequencies, and a set of mechanosensors poised at the threshold of an
oscillatory (Hopf) instability. These two components suffice to generate the
various frequency-response regimes which are needed for a cochlear tuning curve
with a high slope
Brownian Motors driven by Particle Exchange
We extend the Langevin dynamics so that particles can be exchanged with a
particle reservoir. We show that grand canonical ensembles are realized at
equilibrium and derive the relations of thermodynamics for processes between
equilibrium states. As an application of the proposed evolution rule, we devise
a simple model of Brownian motors driven by particle exchange. KEYWORDS:
Langevin Dynamics, Thermodynamics, Open SystemsComment: 5 pages, late
Harshlight: a "corrective make-up" program for microarray chips
BACKGROUND: Microscopists are familiar with many blemishes that fluorescence images can have due to dust and debris, glass flaws, uneven distribution of fluids or surface coatings, etc. Microarray scans do show similar artifacts, which might affect subsequent analysis. Although all but the starkest blemishes are hard to find by the unaided eye, particularly in high-density oligonucleotide arrays (HDONAs), few tools are available to help with the detection of those defects. RESULTS: We develop a novel tool, Harshlight, for the automatic detection and masking of blemishes in HDONA microarray chips. Harshlight uses a combination of statistic and image processing methods to identify three different types of defects: localized blemishes affecting a few probes, diffuse defects affecting larger areas, and extended defects which may invalidate an entire chip. CONCLUSION: We demonstrate the use of Harshlight can materially improve analysis of HDONA chips, especially for experiments with subtle changes between samples. For the widely used MAS5 algorithm, we show that compact blemishes cause an average of 8 gene expression values per chip to change by more than 50%, two of them by more than twofold; our masking algorithm restores about two thirds of this damage. Large-scale artifacts are successfully detected and eliminated
Efficiency, selectivity and robustness of the nuclear pore complex transport
All materials enter or exit the cell nucleus through nuclear pore complexes
(NPCs), efficient transport devices that combine high selectivity and
throughput. A central feature of this transport is the binding of
cargo-carrying soluble transport factors to flexible, unstructured
proteinaceous filaments called FG-nups that line the NPC. We have modeled the
dynamics of transport factors and their interaction with the flexible FG-nups
as diffusion in an effective potential, using both analytical theory and
computer simulations. We show that specific binding of transport factors to the
FG-nups facilitates transport and provides the mechanism of selectivity. We
show that the high selectivity of transport can be accounted for by competition
for both binding sites and space inside the NPC, which selects for transport
factors over other macromolecules that interact only non-specifically with the
NPC. We also show that transport is relatively insensitive to changes in the
number and distribution of FG-nups in the NPC, due mainly to their flexibility;
this accounts for recent experiments where up to half of the total mass of the
NPC has been deleted, without abolishing the transport. Notably, we demonstrate
that previously established physical and structural properties of the NPC can
account for observed features of nucleocytoplasmic transport. Finally, our
results suggest strategies for creation of artificial nano-molecular sorting
devices.Comment: 38 pages, six figure
Feynman's ratchet and pawl: an exactly solvable model
We introduce a simple, discrete model of Feynman's ratchet and pawl,
operating between two heat reservoirs. We solve exactly for the steady-state
directed motion and heat flows produced, first in the absence and then in the
presence of an external load. We show that the model can act both as a heat
engine and as a refrigerator. We finally investigate the behavior of the system
near equilibrium, and use our model to confirm general predictions based on
linear response theory.Comment: 19 pages + 10 figures; somewhat tighter presentatio
Noise in neurons is message-dependent
Neuronal responses are conspicuously variable. We focus on one particular
aspect of that variability: the precision of action potential timing. We show
that for common models of noisy spike generation, elementary considerations
imply that such variability is a function of the input, and can be made
arbitrarily large or small by a suitable choice of inputs. Our considerations
are expected to extend to virtually any mechanism of spike generation, and we
illustrate them with data from the visual pathway. Thus, a simplification
usually made in the application of information theory to neural processing is
violated: noise {\sl is not independent of the message}. However, we also show
the existence of {\sl error-correcting} topologies, which can achieve better
timing reliability than their components.Comment: 6 pages,6 figures. Proceedings of the National Academy of Sciences
(in press
Quantum Ratchets
The concept of thermal ratchets is extended to the system governed by quantum
mechanics. We study a tight-binding model with an asymmetric periodic potential
contacting with a heat bath under an external oscillating field as a specific
example of quantum ratchet. Dynamics of a density operator of this system is
studied numerically by using the quantum Liouville equation. Finite net current
is found in the non-equilibrium steady state. The direction of the current
varies with parameters, in contrast with the classical thermal ratchets.Comment: 7 pages, Latex, 4 ps figures; No change in the text by this
replacement. only the figures are replaced with higher quality ones (but
smaller size
Fluctuation Dissipation Relation for a Langevin Model with Multiplicative Noise
A random multiplicative process with additive noise is described by a
Langevin equation. We show that the fluctuation-dissipation relation is
satisfied in the Langevin model, if the noise strength is not so strong.Comment: 11 pages, 6 figures, other comment
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