1,108 research outputs found
Statistical mechanics of transcription-factor binding site discovery using Hidden Markov Models
Hidden Markov Models (HMMs) are a commonly used tool for inference of
transcription factor (TF) binding sites from DNA sequence data. We exploit the
mathematical equivalence between HMMs for TF binding and the "inverse"
statistical mechanics of hard rods in a one-dimensional disordered potential to
investigate learning in HMMs. We derive analytic expressions for the Fisher
information, a commonly employed measure of confidence in learned parameters,
in the biologically relevant limit where the density of binding sites is low.
We then use techniques from statistical mechanics to derive a scaling principle
relating the specificity (binding energy) of a TF to the minimum amount of
training data necessary to learn it.Comment: 25 pages, 2 figures, 1 table V2 - typos fixed and new references
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Photon blockade and quantum dynamics in intracavity coherent photoassociation of Bose-Einstein condensates
We demonstrate that a photon blockade effect exists in the intracavity coherent photoassociation of an atomic Bose-Einstein condensate and that the dynamics of the coupled atomic and molecular condensates can only be successfully described by a quantum treatment of all the interacting fields. We show that the usual mean-field calculational approaches give answers that are qualitatively wrong, even for the mean fields. The quantization of the fields gives a degree of freedom that is not present in analogous nonlinear optical processes. The difference between the semiclassical and quantum predictions can actually increase as the three fields increase in size so that there is no obvious classical limit for this process
Landscape equivalent of the shoving model
It is shown that the shoving model expression for the average relaxation time
of viscous liquids follows largely from a classical "landscape" estimation of
barrier heights from curvature at energy minima. The activation energy involves
both instantaneous bulk and shear moduli, but the bulk modulus contributes less
than 8% to the temperature dependence of the activation energy. This reflects
the fact that the physics of the two models are closely related.Comment: 4 page
Precision Requirements for Space-based XCO2 Data
Precision requirements have been determined for the column-averaged CO2 dry air mole fraction (X(sub CO2)) data products to be delivered by the Orbiting Carbon Observatory (OCO). These requirements result from an assessment of the amplitude and spatial gradients in X(sub CO2), the relationship between X(sub CO2) precision and surface CO2 flux uncertainties calculated from inversions of the X(sub CO2) data, and the effects of X,,Z biases on CO2 flux inversions. Observing system simulation experiments and synthesis inversion modeling demonstrate that the OCO mission design and sampling strategy provide the means to achieve the X(sub CO2) precision requirements. The impact of X(sub CO2) biases on CO2 flux uncertainties depend on their spatial and temporal extent since CO2 sources and sinks are inferred from regional-scale X(sub CO2) gradients. Simulated OCO sampling of the TRACE-P CO2 fields shows the ability of X(sub CO2) data to constrain CO2 flux inversions over Asia and distinguish regional fluxes from India and China
Nonclassical statistics of intracavity coupled waveguides: the quantum optical dimer
A model is proposed where two nonlinear waveguides are contained
in a cavity suited for second-harmonic generation. The evanescent wave coupling
between the waveguides is considered as weak, and the interplay between this
coupling and the nonlinear interaction within the waveguides gives rise to
quantum violations of the classical limit. These violations are particularly
strong when two instabilities are competing, where twin-beam behavior is found
as almost complete noise suppression in the difference of the fundamental
intensities. Moreover, close to bistable transitions perfect twin-beam
correlations are seen in the sum of the fundamental intensities, and also the
self-pulsing instability as well as the transition from symmetric to asymmetric
states display nonclassical twin-beam correlations of both fundamental and
second-harmonic intensities. The results are based on the full quantum Langevin
equations derived from the Hamiltonian and including cavity damping effects.
The intensity correlations of the output fields are calculated
semi-analytically using a linearized version of the Langevin equations derived
through the positive-P representation. Confirmation of the analytical results
are obtained by numerical simulations of the nonlinear Langevin equations
derived using the truncated Wigner representation.Comment: 15 pages, 8 figures, submitted to Phys. Rev.
Lyapunov spectrum of asymptotically sub-additive potentials
For general asymptotically sub-additive potentials (resp. asymptotically
additive potentials) on general topological dynamical systems, we establish
some variational relations between the topological entropy of the level sets of
Lyapunov exponents, measure-theoretic entropies and topological pressures in
this general situation. Most of our results are obtained without the assumption
of the existence of unique equilibrium measures or the differentiability of
pressure functions. Some examples are constructed to illustrate the
irregularity and the complexity of multifractal behaviors in the sub-additive
case and in the case that the entropy map that is not upper-semi continuous.Comment: 44 page
Multifractal Analysis of inhomogeneous Bernoulli products
We are interested to the multifractal analysis of inhomogeneous Bernoulli
products which are also known as coin tossing measures. We give conditions
ensuring the validity of the multifractal formalism for such measures. On
another hand, we show that these measures can have a dense set of phase
transitions
Quantum superchemistry: Role of trapping profile and quantum statistics
The process of Raman photoassociation of a trapped atomic condensate to form condensed molecules has been labeled superchemistry because it can occur at 0 K and experiences coherent bosonic stimulation. We show here that the differences from ordinary chemical processes go even deeper, with the conversion rates depending on the quantum state of the reactants, as expressed by the Wigner function. We consider different initial quantum states of the trapped atomic condensate and different forms of the confining potentials, demonstrating the importance of the quantum statistics and the extra degrees of freedom which massive particles and trapping potentials make available over the analogous optical process of second-harmonic generation. We show that both mean-field analyses and quantum calculations using an inappropriate initial condition can make inaccurate predictions for a given system. This is possible whether using a spatially dependent analysis or a zero-dimensional approach as commonly used in quantum optics
Role of quantum statistics in the photoassociation of Bose-Einstein condensates
We show that the photoassociation of an atomic Bose-Einstein condensate to form condensed molecules is a chemical process which not only does not obey the Arrhenius rules for chemical reactions, but that it can also depend on the quantum statistics of the reactants. Comparing the predictions of a truncated Wigner representation for different initial quantum states, we find that, even when the quantum prediction for an initial coherent state is close to the Gross-Pitaevskii prediction, other quantum states may result in very different dynamics
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