7,817 research outputs found
A simple model for DNA denaturation
Following Poland and Scheraga, we consider a simplified model for the
denaturation transition of DNA. The two strands are modeled as interacting
polymer chains. The attractive interactions, which mimic the pairing between
the four bases, are reduced to a single short range binding term. Furthermore,
base-pair misalignments are forbidden, implying that this binding term exists
only for corresponding (same curvilinear abscissae) monomers of the two chains.
We take into account the excluded volume repulsion between monomers of the two
chains, but neglect intra-chain repulsion. We find that the excluded volume
term generates an effective repulsive interaction between the chains, which
decays as . Due to this long-range repulsion between the chains, the
denaturation transition is first order in any dimension, in agreement with
previous studies.Comment: 10 page
X-ray rocking curve study of Si-implanted GaAs, Si, and Ge
Crystalline properties of Si-implanted GaAs, Si, and Ge have been studied by Bragg case double-crystal x-ray diffraction. Sharp qualitative and quantitative differences were found between the damage in GaAs on one hand and Si and Ge on the other. In Si and Ge the number of defects and the strain increase linearly with dose up to the amorphous threshold. In GaAs the increase in these quantities is neither linear nor monotonic with dose. At a moderate damage level the GaAs crystal undergoes a transition from elastic to plastic behavior. This transition is accompanied by the creation of extended defects, which are not detected in Si or Ge
Noise Effects on the Complex Patterns of Abnormal Heartbeats
Patients at high risk for sudden death often exhibit complex heart rhythms in
which abnormal heartbeats are interspersed with normal heartbeats. We analyze
such a complex rhythm in a single patient over a 12-hour period and show that
the rhythm can be described by a theoretical model consisting of two
interacting oscillators with stochastic elements. By varying the magnitude of
the noise, we show that for an intermediate level of noise, the model gives
best agreement with key statistical features of the dynamics.Comment: 4 pages, 4 figures, RevTe
Regulatory Dynamics on Random Networks: Asymptotic Periodicity and Modularity
We study the dynamics of discrete-time regulatory networks on random
digraphs. For this we define ensembles of deterministic orbits of random
regulatory networks, and introduce some statistical indicators related to the
long-term dynamics of the system. We prove that, in a random regulatory
network, initial conditions converge almost surely to a periodic attractor. We
study the subnetworks, which we call modules, where the periodic asymptotic
oscillations are concentrated. We proof that those modules are dynamically
equivalent to independent regulatory networks.Comment: 23 pages, 3 figure
Theoretical Isochrones with Extinction in the K Band. II. J - K versus K
We calculate theoretical isochrones in a consistent way for five filter pairs
near the J and K band atmospheric windows (J-K, J-K', J-Ks, F110W-F205W, and
F110W-F222M) using the Padova stellar evolutionary models of Girardi et al. We
present magnitude transformations between various K-band filters as a function
of color. Isochrones with extinction of up to 6 mag in the K band are also
presented. As found for the filter pairs composed of H & K band filters, we
find that the reddened isochrones of different filter pairs behave as if they
follow different extinction laws, and that the extinction curves of Hubble
Space Telescope NICMOS filter pairs in the color-magnitude diagram are
considerably nonlinear. Because of these problems, extinction values estimated
with NICMOS filters can be in error by up to 1.3 mag. Our calculation suggests
that the extinction law implied by the observations of Rieke et al for
wavelengths between the J and K bands is better described by a power-law
function with an exponent of 1.66 instead of 1.59, which is commonly used with
an assumption that the transmission functions of J and K filters are Dirac
delta functions.Comment: Published in PASP, 118, 62 (Jan. 2006
Investigation of single crystal ferrite thin films
Materials suitable for use in magnetic bubble domain memories were developed for aerospace applications. Practical techniques for the preparation of such materials in forms required for fabrication of computer memory devices were considered. The materials studied were epitaxial films of various compositions of the gallium-substituted yttrium gadolinium iron garnet system. The major emphasis was to determine their bubble properties and the conditions necessary for growing uncracked, high quality films
Optimal synchronization of directed complex networks
We study optimal synchronization of networks of coupled phase oscillators. We
extend previous theory for optimizing the synchronization properties of
undirected networks to the important case of directed networks. We derive a
generalized synchrony alignment function that encodes the interplay between
network structure and the oscillators' natural frequencies and serves as an
objective measure for the network's degree of synchronization. Using the
generalized synchrony alignment function, we show that a network's
synchronization properties can be systematically optimized. This framework also
allows us to study the properties of synchrony-optimized networks, and in
particular, investigate the role of directed network properties such as nodal
in- and out-degrees. For instance, we find that in optimally rewired networks
the heterogeneity of the in-degree distribution roughly matches the
heterogeneity of the natural frequency distribution, but no such relationship
emerges for out-degrees. We also observe that a network's synchronization
properties are promoted by a strong correlation between the nodal in-degrees
and the natural frequencies of oscillators, whereas the relationship between
the nodal out-degrees and the natural frequencies has comparatively little
effect. This result is supported by our theory, which indicates that
synchronization is promoted by a strong alignment of the natural frequencies
with the left singular vectors corresponding to the largest singular values of
the Laplacian matrix
A core genetic module : the Mixed Feedback Loop
The so-called Mixed Feedback Loop (MFL) is a small two-gene network where
protein A regulates the transcription of protein B and the two proteins form a
heterodimer. It has been found to be statistically over-represented in
statistical analyses of gene and protein interaction databases and to lie at
the core of several computer-generated genetic networks. Here, we propose and
mathematically study a model of the MFL and show that, by itself, it can serve
both as a bistable switch and as a clock (an oscillator) depending on kinetic
parameters. The MFL phase diagram as well as a detailed description of the
nonlinear oscillation regime are presented and some biological examples are
discussed. The results emphasize the role of protein interactions in the
function of genetic modules and the usefulness of modelling RNA dynamics
explicitly.Comment: To be published in Physical Review
Non-invertible transformations and spatiotemporal randomness
We generalize the exact solution to the Bernoulli shift map. Under certain
conditions, the generalized functions can produce unpredictable dynamics. We
use the properties of the generalized functions to show that certain dynamical
systems can generate random dynamics. For instance, the chaotic Chua's circuit
coupled to a circuit with a non-invertible I-V characteristic can generate
unpredictable dynamics. In general, a nonperiodic time-series with truncated
exponential behavior can be converted into unpredictable dynamics using
non-invertible transformations. Using a new theoretical framework for chaos and
randomness, we investigate some classes of coupled map lattices. We show that,
in some cases, these systems can produce completely unpredictable dynamics. In
a similar fashion, we explain why some wellknown spatiotemporal systems have
been found to produce very complex dynamics in numerical simulations. We
discuss real physical systems that can generate random dynamics.Comment: Accepted in International Journal of Bifurcation and Chao
Robustness and Enhancement of Neural Synchronization by Activity-Dependent Coupling
We study the synchronization of two model neurons coupled through a synapse
having an activity-dependent strength. Our synapse follows the rules of
Spike-Timing Dependent Plasticity (STDP). We show that this plasticity of the
coupling between neurons produces enlarged frequency locking zones and results
in synchronization that is more rapid and much more robust against noise than
classical synchronization arising from connections with constant strength. We
also present a simple discrete map model that demonstrates the generality of
the phenomenon.Comment: 4 pages, accepted for publication in PR
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