Occupation numbers of the harmonically trapped few-boson system

We consider a harmonically trapped dilute $N$-boson system described by a low-energy Hamiltonian with pairwise interactions. We determine the condensate fraction, defined in terms of the largest occupation number, of the weakly-interacting $N$-boson system ($N \ge 2$) by employing a perturbative treatment within the framework of second quantization. The one-body density matrix and the corresponding occupation numbers are compared with those obtained by solving the two-body problem with zero-range interactions exactly. Our expressions are also compared with high precision {\em{ab initio}} calculations for Bose gases with $N=2-4$ that interact through finite-range two-body model potentials. Non-universal corrections are identified to enter at subleading order, confirming that different low-energy Hamiltonians, constructed to yield the same energy, may yield different occupation numbers. Lastly, we consider the strongly-interacting three-boson system under spherically symmetric harmonic confinement and determine its occupation numbers as a function of the three-body "Efimov parameter".Comment: 16 pages, 7 figure

Calculating Biological Behaviors of Epigenetic States in Phage lambda Life Cycle

Gene regulatory network of lambda phage is one the best studied model systems in molecular biology. More 50 years of experimental study has provided a tremendous amount of data at all levels: physics, chemistry, DNA, protein, and function. However, its stability and robustness for both wild type and mutants has been a notorious theoretical/mathematical problem. In this paper we report our successful calculation on the properties of this gene regulatory network. We believe it is of its first kind. Our success is of course built upon numerous previous theoretical attempts, but following 3 features make our modeling uniqu: 1) A new modeling method particular suitable for stability and robustness study; 2) Paying a close attention to the well-known difference of in vivo and in vitro; 3) Allowing more important role for noise and stochastic effect to play. The last two points have been discussed by two of us (Ao and Yin, cond-mat/0307747), which we believe would be enough to make some of previous theoretical attempts successful, too. We hope the present work would stimulate a further interest in the emerging field of gene regulatory network.Comment: 16 pages, 3 figures, 1 tabl

The correlations between the twin kHz QPO frequencies of LMXBs

We analyzed the recently published kHz QPO data in the neutron star low-mass X-ray binaries (LMXBs), in order to investigate the different correlations of the twin peak kilohertz quasi-eriodic oscillations (kHz QPOs) in bright Z sources and in the less luminous Atoll sources. We find that a power-law relation \no\sim\nt^{b} between the upper and the lower kHz QPOs with different indices: $b\simeq$1.5 for the Atoll source 4U 1728-34 and $b\simeq$1.9 for the Z source Sco X-1. The implications of our results for the theoretical models for kHz QPOs are discussed.Comment: 6 pages, accepted by MNRA

Wilson ratio of Fermi gases in one dimension

We calculate the Wilson ratio of the one-dimensional Fermi gas with spin imbalance. The Wilson ratio of attractively interacting fermions is solely determined by the density stiffness and sound velocity of pairs and of excess fermions for the two-component Tomonaga-Luttinger liquid (TLL) phase. The ratio exhibits anomalous enhancement at the two critical points due to the sudden change in the density of states. Despite a breakdown of the quasiparticle description in one dimension, two important features of the Fermi liquid are retained, namely the specific heat is linearly proportional to temperature whereas the susceptibility is independent of temperature. In contrast to the phenomenological TLL parameter, the Wilson ratio provides a powerful parameter for testing universal quantum liquids of interacting fermions in one, two and three dimensions.Comment: 5+2 pages, 4+1 figures, Eq. (4) is proved, figures were refine

Scanning Tunneling Spectroscopy and Vortex Imaging in the Iron-Pnictide Superconductor BaFe1.8_{1.8}Co0.2_{0.2}As2_2

We present an atomic resolution scanning tunneling spectroscopy study of superconducting BaFe$_{1.8}$Co$_{0.2}$As$_2$ single crystals in magnetic fields up to $9 \text{Tesla}$. At zero field, a single gap with coherence peaks at $\overline{\Delta}=6.25 \text{meV}$ is observed in the density of states. At $9 \text{T}$ and $6 \text{T}$, we image a disordered vortex lattice, consistent with isotropic, single flux quantum vortices. Vortex locations are uncorrelated with strong scattering surface impurities, demonstrating bulk pinning. The vortex-induced sub-gap density of states fits an exponential decay from the vortex center, from which we extract a coherence length $\xi=27.6\pm 2.9 \text{\AA}$, corresponding to an upper critical field $H_{c2}=43 \text{T}$.Comment: 4 pages, 4 figure

Schema Independent Relational Learning

Learning novel concepts and relations from relational databases is an important problem with many applications in database systems and machine learning. Relational learning algorithms learn the definition of a new relation in terms of existing relations in the database. Nevertheless, the same data set may be represented under different schemas for various reasons, such as efficiency, data quality, and usability. Unfortunately, the output of current relational learning algorithms tends to vary quite substantially over the choice of schema, both in terms of learning accuracy and efficiency. This variation complicates their off-the-shelf application. In this paper, we introduce and formalize the property of schema independence of relational learning algorithms, and study both the theoretical and empirical dependence of existing algorithms on the common class of (de) composition schema transformations. We study both sample-based learning algorithms, which learn from sets of labeled examples, and query-based algorithms, which learn by asking queries to an oracle. We prove that current relational learning algorithms are generally not schema independent. For query-based learning algorithms we show that the (de) composition transformations influence their query complexity. We propose Castor, a sample-based relational learning algorithm that achieves schema independence by leveraging data dependencies. We support the theoretical results with an empirical study that demonstrates the schema dependence/independence of several algorithms on existing benchmark and real-world datasets under (de) compositions

Dinitrosyl formation as an intermediate stage of the reduction of NO in the presence of MoO_3

We present first-principles calculations in the framework of density-functional theory and the pseudopotential approach, aiming to model the intermediate stages of the reduction of NO in the presence of MoO$_3$(010). In particular, we study the formation of dinitrosyl, which proves to be an important intermediate stage in the catalytic reduction. We find that the replacement of an oxygen of MoO$_3$ by NO is energetically favorable, and that the system lowers further its energy by the formation of (NO)$_2$. Moreover, the geometry and charge distribution for the adsorbed dinitrosyl indicates a metal-oxide mediated coupling between the two nitrogen and the two oxygen atoms. We discuss the mechanisms for the dinitrosyl formation and the role of the oxide in the reaction.Comment: 6 pages, 4 figs, RevTeX. To be published in J. Chem. Phy