Asymptotic behavior of the Poisson--Dirichlet distribution for large mutation rate

The large deviation principle is established for the Poisson--Dirichlet distribution when the parameter $\theta$ approaches infinity. The result is then used to study the asymptotic behavior of the homozygosity and the Poisson--Dirichlet distribution with selection. A phase transition occurs depending on the growth rate of the selection intensity. If the selection intensity grows sublinearly in $\theta$, then the large deviation rate function is the same as the neutral model; if the selection intensity grows at a linear or greater rate in $\theta$, then the large deviation rate function includes an additional term coming from selection. The application of these results to the heterozygote advantage model provides an alternate proof of one of Gillespie's conjectures in [Theoret. Popul. Biol. 55 145--156].Comment: Published at http://dx.doi.org/10.1214/105051605000000818 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Quasiperiodic Dynamics in Bose-Einstein Condensates in Periodic Lattices and Superlattices

We employ KAM theory to rigorously investigate quasiperiodic dynamics in cigar-shaped Bose-Einstein condensates (BEC) in periodic lattices and superlattices. Toward this end, we apply a coherent structure ansatz to the Gross-Pitaevskii equation to obtain a parametrically forced Duffing equation describing the spatial dynamics of the condensate. For shallow-well, intermediate-well, and deep-well potentials, we find KAM tori and Aubry-Mather sets to prove that one obtains mostly quasiperiodic dynamics for condensate wave functions of sufficiently large amplitude, where the minimal amplitude depends on the experimentally adjustable BEC parameters. We show that this threshold scales with the square root of the inverse of the two-body scattering length, whereas the rotation number of tori above this threshold is proportional to the amplitude. As a consequence, one obtains the same dynamical picture for lattices of all depths, as an increase in depth essentially only affects scaling in phase space. Our approach is applicable to periodic superlattices with an arbitrary number of rationally dependent wave numbers.Comment: 29 pages, 6 figures (several with multiple parts; higher-quality versions of some of them available at http://www.its.caltech.edu/~mason/papers), to appear very soon in Journal of Nonlinear Scienc

High-throughput on-chip DNA fragmentation

free microfluidic deoxyribonucleic acid (DNA) fragmentation chip that is based on hydrodynamic shearing. Genomic DNA has been reproducibly fragmented with 2-10 kbp fragment lengths by applying hydraulic pressure ΔP across micromachined constrictions in the microfluidic channels. The utilization of a series of constrictions reduces the variance of the fragmented DNA length distribution; and parallel microfluidic channels design eliminates the device clogging

Existence Criterion of Genuine Tripartite Entanglement

In this paper, an intuitive mathematical formulation is provided to generalize the residual entanglement for tripartite systems of qubits [Phys. Rev. A 61, 052306 (2000)] to the tripartite systems in higher dimension. The spirit lies in the tensor treatment of tripartite pure states [Phys. Rev. A 72, 022333 (2005)]. A distinct characteristic of the present generalization is that the formulation for higher dimensional systems is invariant under permutation of the subsystems, hence is employed as a criterion to test the existence of genuine tripartite entanglement. Furthermore, the formulation for pure states can be conveniently extended to the case of mixed states by utilizing the Kronecker product approximate technique. As applications, we give the analytic approximation of the criterion for weakly mixed tripartite quantum states and consider the existence of genuine tripartite entanglement of some weakly mixed states.Comment: 6 pages, 2 figure

Lattice Boltzmann Approach to High-Speed Compressible Flows

We present an improved lattice Boltzmann model for high-speed compressible flows. The model is composed of a discrete-velocity model by Kataoka and Tsutahara [Phys. Rev. E \textbf{69}, 056702 (2004)] and an appropriate finite-difference scheme combined with an additional dissipation term. With the dissipation term parameters in the model can be flexibly chosen so that the von Neumann stability condition is satisfied. The influence of the various model parameters on the numerical stability is analyzed and some reference values of parameter are suggested. The new scheme works for both subsonic and supersonic flows with a Mach number up to 30 (or higher), which is validated by well-known benchmark tests. Simulations on Riemann problems with very high ratios ($1000:1$) of pressure and density also show good accuracy and stability. Successful recovering of regular and double Mach shock reflections shows the potential application of the lattice Boltzmann model to fluid systems where non-equilibrium processes are intrinsic. The new scheme for stability can be easily extended to other lattice Boltzmann models.Comment: Figs.11 and 12 in JPEG format. Int. J. Mod. Phys. C (to appear

Spatially resolved pump-probe study of single-layer graphene produced by chemical vapor deposition

Carrier dynamics in single-layer graphene grown by chemical vapor deposition (CVD) is studied using spatially and temporally resolved pump-probe spectroscopy by measuring both differential transmission and differential reflection. By studying the expansion of a Gaussian spatial profile of carriers excited by a 1500-nm pump pulse with a 1761-nm probe pulse, we observe a diffusion of hot carriers of 5500 square centimeter per second. We also observe that the expansion of the carrier density profile decreases to a slow rate within 1 ps, which is unexpected. Furthermore, by using an 810-nm probe pulse we observe that both the differential transmission and reflection change signs, but also that this sign change can be permanently removed by exposure of the graphene to femtosecond laser pulses of relatively high fluence. This indicates that the differential transmission and reflection at later times may not be directly caused by carriers, but may be from some residue material from the sample fabrication or transfer process.Comment: 9 pages, 3 figure

Concurrence of superposition

The bounds on concurrence of the superposition state in terms of those of the states being superposed are studied in this paper. The bounds on concurrence are quite different from those on the entanglement measure based on von Neumann entropy (Phys. Rev. Lett. 97, 100502 (2006)). In particular, a nonzero lower bound can be provided if the states being superposed are properly constrained.Comment: 4 page

In vitro identification and in silico utilization of interspecies sequence similarities using GeneChip(® )technology

BACKGROUND: Genomic approaches in large animal models (canine, ovine etc) are challenging due to insufficient genomic information for these species and the lack of availability of corresponding microarray platforms. To address this problem, we speculated that conserved interspecies genetic sequences can be experimentally detected by cross-species hybridization. The Affymetrix platform probe redundancy offers flexibility in selecting individual probes with high sequence similarities between related species for gene expression analysis. RESULTS: Gene expression profiles of 40 canine samples were generated using the human HG-U133A GeneChip (U133A). Due to interspecies genetic differences, only 14 ± 2% of canine transcripts were detected by U133A probe sets whereas profiling of 40 human samples detected 49 ± 6% of human transcripts. However, when these probe sets were deconstructed into individual probes and examined performance of each probe, we found that 47% of human probes were able to find their targets in canine tissues and generate a detectable hybridization signal. Therefore, we restricted gene expression analysis to these probes and observed the 60% increase in the number of identified canine transcripts. These results were validated by comparison of transcripts identified by our restricted analysis of cross-species hybridization with transcripts identified by hybridization of total lung canine mRNA to new Affymetrix Canine GeneChip(®). CONCLUSION: The experimental identification and restriction of gene expression analysis to probes with detectable hybridization signal drastically increases transcript detection of canine-human hybridization suggesting the possibility of broad utilization of cross-hybridizations of related species using GeneChip technology