Pattern formation inside bacteria: fluctuations due to low copy number of proteins

We examine fluctuation effects due to the low copy number of proteins involved in pattern-forming dynamics within a bacterium. We focus on a stochastic model of the oscillating MinCDE protein system regulating accurate cell division in E. coli. We find that, for some parameter regions, the protein concentrations are low enough that fluctuations are essential for the generation of patterns. We also examine the role of fluctuations in constraining protein concentration levels.Comment: 4 pages, 3 figures, accepted for publication in Phys. Rev. Let

Fractional Quantum Hall Physics in Jaynes-Cummings-Hubbard Lattices

Jaynes-Cummings-Hubbard arrays provide unique opportunities for quantum emulation as they exhibit convenient state preparation and measurement, and in-situ tuning of parameters. We show how to realise strongly correlated states of light in Jaynes-Cummings-Hubbard arrays under the introduction of an effective magnetic field. The effective field is realised by dynamic tuning of the cavity resonances. We demonstrate the existence of Fractional Quantum Hall states by com- puting topological invariants, phase transitions between topologically distinct states, and Laughlin wavefunction overlap.Comment: 5 pages, 3 figure

Bayesian Analysis of Continuous Time Models of the Australian Short Rate

This paper provides an empirical analysis of a range of alternative single-factor continuous time models for the Australian short-term interest rate. The models are indexed by the level effect parameter for the volatility in the short rate process. The inferential approach adopted is Bayesian, with estimation of the models proceeding via a Markov Chain Monte Carlo simulation scheme. Discrimination between the alternative models is based on Bayes factors, estimated from the simulation output using the Savage-Dickey density ratio. A data augmentation approach is used to improve the accuracy of the discrete time approximation of the continuous time models. An empirical investigation is conducted using weekly observations on the Australian 90 day interest rate from January 1990 to July 2000. The Bayes factors indicate that the square root diffusion model has the highest posterior probability of all the nested models.Interest Rate Models, Markov Chain Monte Carlo, Data Augmentation

Implications of very rapid TeV variability in blazars

We discuss the implications of rapid (few-minute) variability in the TeV flux of blazars, which has been observed recently with the HESS and MAGIC telescopes. The variability timescales seen in PKS 2155-304 and Mrk 501 are much shorter than inferred light-crossing times at the black hole horizon, suggesting that the variability involves enhanced emission in a small region within an outflowing jet. The enhancement could be triggered by dissipation in part of the black hole's magnetosphere at the base of the outflow, or else by instabilities in the jet itself. By considering the energetics of the observed flares, along with the requirement that TeV photons escape without producing pairs, we deduce that the bulk Lorentz factors in the jets must be >50. The distance of the emission region from the central black hole is less well-constrained. We discuss possible consequences for multi-wavelength observations.Comment: 5 pages, no figures, accepted for publication in Monthly Notices of the Royal Astronomical Society Letter

Simulation-Based Bayesian Estimation of Affine Term Structure Models

This paper demonstrates the application of Bayesian simulation-based estimation to a class of interest rate models known as Affine Term Structure (ATS) models. The technique used is based on a Markov Chain Monte Carlo algorithm, with the discrete observations on yields augmented by additional higher frequency latent data. The introduction of augmented yield data reduces the bias associated with estimating a continuous time model using discretely observed data. The technique is demon-strated using a one-factor ATS model, with the latent factor process that underlies the yields sampled via a single-move algorithm. Numerical application of the method is demonstrated using both simulated and empirical data. Extension of the method to a three-factor ATS model is also discussed, as well as the application of a multi-move sampler based on a Kalman Filtering and Smoothing algorithm.Interest Rate Models, Markov Chain Monte Carlo, Data Augmentation, Nonlinear State Space Models, Kalman Filtering.

Many-body Quantum Chaos and Entanglement in a Quantum Ratchet

We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.Comment: 6 pages, 3 figures. 1 tabl

The Scythe Statistical Library: An Open Source C++ Library for Statistical Computation

The Scythe Statistical Library is an open source C++ library for statistical computation. It includes a suite of matrix manipulation functions, a suite of pseudo-random number generators, and a suite of numerical optimization routines. Programs written using Scythe are generally much faster than those written in commonly used interpreted languages, such as R and \proglang{MATLAB}; and can be compiled on any system with the GNU GCC compiler (and perhaps with other C++ compilers). One of the primary design goals of the Scythe developers has been ease of use for non-expert C++ programmers. Ease of use is provided through three primary mechanisms: (1) operator and function over-loading, (2) numerous pre-fabricated utility functions, and (3) clear documentation and example programs. Additionally, Scythe is quite flexible and entirely extensible because the source code is available to all users under the GNU General Public License.

MCMCpack: Markov Chain Monte Carlo in R

We introduce MCMCpack, an R package that contains functions to perform Bayesian inference using posterior simulation for a number of statistical models. In addition to code that can be used to fit commonly used models, MCMCpack also contains some useful utility functions, including some additional density functions and pseudo-random number generators for statistical distributions, a general purpose Metropolis sampling algorithm, and tools for visualization.

Narrow Line Cooling: Finite Photon Recoil Dynamics

We present an extensive study of the unique thermal and mechanical dynamics for narrow-line cooling on the 1S0 - 3P1 88Sr transition. For negative detuning, trap dynamics reveal a transition from the semiclassical regime to the photon-recoil-dominated quantum regime, yielding an absolute minima in the equilibrium temperature below the single-photon recoil limit. For positive detuning, the cloud divides into discrete momentum packets whose alignment mimics lattice points on a face-centered-cubic crystal. This novel behavior arises from velocity selection and "positive feedback" acceleration due to a finite number of photon recoils. Cooling is achieved with blue-detuned light around a velocity where gravity balances the radiative force.Comment: 4 pages, 3 figures, Phys. Rev. Lett., in pres

Precision spectroscopy and density-dependent frequency shifts in ultracold Sr

By varying the density of an ultracold $^{88}$Sr sample from $10^9$ cm$^{-3}$ to $> 10^{12}$ cm$^{-3}$, we make the first definitive measurement of the density-related frequency shift and linewidth broadening of the $^1S_0$ - $^3P_1$ optical clock transition in an alkaline earth system. In addition, we report the most accurate measurement to date of the $^{88}$Sr $^1S_0 - ^3P_1$ optical clock transition frequency. Including a detailed analysis of systematic errors, the frequency is ($434 829 121 312 334 \pm 20_{stat} \pm 33_{sys}$) Hz.Comment: 4 pages, 4 figures, 1 table. submitte