The finite-temperature thermodynamics of a trapped unitary Fermi gas within fractional exclusion statistics

We utilize a fractional exclusion statistics of Haldane and Wu hypothesis to study the thermodynamics of a unitary Fermi gas trapped in a harmonic oscillator potential at ultra-low finite temperature. The entropy per particle as a function of the energy per particle and energy per particle versus rescaled temperature are numerically compared with the experimental data. The study shows that, except the chemical potential behavior, there exists a reasonable consistency between the experimental measurement and theoretical attempt for the entropy and energy per particle. In the fractional exclusion statistics formalism, the behavior of the isochore heat capacity for a trapped unitary Fermi gas is also analyzed.Comment: 6 pages, 6 figure

Ground state energy of unitary fermion gas with the Thomson Problem approach

The dimensionless universal coefficient $\xi$ defines the ratio of the unitary fermions energy density to that for the ideal non-interacting ones in the non-relativistic limit with T=0. The classical Thomson Problem is taken as a nonperturbative quantum many-body arm to address the ground state energy including the low energy nonlinear quantum fluctuation/correlation effects. With the relativistic Dirac continuum field theory formalism, the concise expression for the energy density functional of the strongly interacting limit fermions at both finite temperature and density is obtained. Analytically, the universal factor is calculated to be $\xi={4/9}$. The energy gap is \Delta=\frac{{5}{18}{k_f^2}/(2m).Comment: Identical to published version with revisions according to comment

Searching for radiative pumping lines of OH masers: II. The 53.3um absorption line towards 1612MHz OH maser sources

This paper analyzes the 53.3um line in the ISO LWS spectra towards a similar sample of OH/IR sources. We find 137 LWS spectra covering 53.3um and associated with 47 galactic OH/IR sources. Ten of these galactic OH/IR sources are found to show and another 5 ones tentatively show the 53.3um absorption while another 7 sources highly probably do not show this line. The source class is found to be correlated with the type of spectral profile: red supergiants (RSGs) and AGB stars tend to show strong blue-shifted filling emission in their 53.3um absorption line profiles while HII regions tend to show a weak red-shifted filling emission in the line profile. GC sources and megamasers do not show filling emission feature. It is argued that the filling emission might be the manifestation of an unresolved half emission half absorption profile of the 53.3um doublet. The 53.3 to 34.6um equivalent width (EW) ratio is close to unity for RSGs but much larger than unity for GC sources and megamasers while H II regions only show the 53.3um line. The pump rate defined as maser to IR photon flux ratio is approximately 5% for RSGs. The pump rates of GC sources are three order of magnitude smaller. Both the large 53.3 to 34.6um EW ratio and the small pump rate of the GC OH masers reflect that the two detected `pumping lines' in these sources are actually of interstellar origin. The pump rate of Arp 220 is 32%--much larger than that of RSGs, which indicates that the contribution of other pumping mechanisms to this megamaser is important.Comment: 34 pages, 12 figures, 4 table

A quality adjusted wage index

In this paper, a new method of estimating a wage index is proposed and implemented. We construct a wage index by controlling for quantity, as well as quality of labor. Our approach uses a set of year dummies as the basis for calculation of a wage index. The March Current Population Survey Supplement (1983-2000) is employed, and empirical wage equation models are estimated in this paper. The estimation results of the proposed wage index suggest that the existing Employment Cost Index perhaps overestimates the increases in wages adjusted for quality.quality of labor

Multiband effects on the conductivity for a multiband Hubbard model

The newly discovered iron-based superconductors have attracted lots of interests, and the corresponding theoretical studies suggest that the system should have six bands. In this paper, we study the multiband effects on the conductivity based on the exact solutions of one-dimensional two-band Hubbard model. We find that the orbital degree of freedom might enhance the critical value $U_c$ of on-site interaction of the transition from a metal to an insulator. This observation is helpful to understand why undoped High-$T_c$ superconductors are usually insulators, while recently discovered iron-based superconductors are metal. Our results imply that the orbital degree of freedom in the latter cases might play an essential role.Comment: 4 pages, 5 figure

Semantics-Space-Time Cube. A Conceptual Framework for Systematic Analysis of Texts in Space and Time

We propose an approach to analyzing data in which texts are associated with spatial and temporal references with the aim to understand how the text semantics vary over space and time. To represent the semantics, we apply probabilistic topic modeling. After extracting a set of topics and representing the texts by vectors of topic weights, we aggregate the data into a data cube with the dimensions corresponding to the set of topics, the set of spatial locations (e.g., regions), and the time divided into suitable intervals according to the scale of the planned analysis. Each cube cell corresponds to a combination (topic, location, time interval) and contains aggregate measures characterizing the subset of the texts concerning this topic and having the spatial and temporal references within these location and interval. Based on this structure, we systematically describe the space of analysis tasks on exploring the interrelationships among the three heterogeneous information facets, semantics, space, and time. We introduce the operations of projecting and slicing the cube, which are used to decompose complex tasks into simpler subtasks. We then present a design of a visual analytics system intended to support these subtasks. To reduce the complexity of the user interface, we apply the principles of structural, visual, and operational uniformity while respecting the specific properties of each facet. The aggregated data are represented in three parallel views corresponding to the three facets and providing different complementary perspectives on the data. The views have similar look-and-feel to the extent allowed by the facet specifics. Uniform interactive operations applicable to any view support establishing links between the facets. The uniformity principle is also applied in supporting the projecting and slicing operations on the data cube. We evaluate the feasibility and utility of the approach by applying it in two analysis scenarios using geolocated social media data for studying people's reactions to social and natural events of different spatial and temporal scales

Sparse kernel density estimation technique based on zero-norm constraint

A sparse kernel density estimator is derived based on the zero-norm constraint, in which the zero-norm of the kernel weights is incorporated to enhance model sparsity. The classical Parzen window estimate is adopted as the desired response for density estimation, and an approximate function of the zero-norm is used for achieving mathemtical tractability and algorithmic efficiency. Under the mild condition of the positive definite design matrix, the kernel weights of the proposed density estimator based on the zero-norm approximation can be obtained using the multiplicative nonnegative quadratic programming algorithm. Using the -optimality based selection algorithm as the preprocessing to select a small significant subset design matrix, the proposed zero-norm based approach offers an effective means for constructing very sparse kernel density estimates with excellent generalisation performance

Distance-two labelings of digraphs

For positive integers $j\ge k$, an $L(j,k)$-labeling of a digraph $D$ is a function $f$ from $V(D)$ into the set of nonnegative integers such that $|f(x)-f(y)|\ge j$ if $x$ is adjacent to $y$ in $D$ and $|f(x)-f(y)|\ge k$ if $x$ is of distant two to $y$ in $D$. Elements of the image of $f$ are called labels. The $L(j,k)$-labeling problem is to determine the $\vec{\lambda}_{j,k}$-number $\vec{\lambda}_{j,k}(D)$ of a digraph $D$, which is the minimum of the maximum label used in an $L(j,k)$-labeling of $D$. This paper studies $\vec{\lambda}_{j,k}$- numbers of digraphs. In particular, we determine $\vec{\lambda}_{j,k}$- numbers of digraphs whose longest dipath is of length at most 2, and $\vec{\lambda}_{j,k}$-numbers of ditrees having dipaths of length 4. We also give bounds for $\vec{\lambda}_{j,k}$-numbers of bipartite digraphs whose longest dipath is of length 3. Finally, we present a linear-time algorithm for determining $\vec{\lambda}_{j,1}$-numbers of ditrees whose longest dipath is of length 3.Comment: 12 pages; presented in SIAM Coference on Discrete Mathematics, June 13-16, 2004, Loews Vanderbilt Plaza Hotel, Nashville, TN, US

Consistency of Markov chain quasi-Monte Carlo on continuous state spaces

The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0,1) random variables. Tribble [Markov chain Monte Carlo algorithms using completely uniformly distributed driving sequences (2007) Stanford Univ.] reports substantial improvements when those random numbers are replaced by carefully balanced inputs from completely uniformly distributed sequences. The previous theoretical justification for using anything other than i.i.d. U(0,1) points shows consistency for estimated means, but only applies for discrete stationary distributions. We extend those results to some MCMC algorithms for continuous stationary distributions. The main motivation is the search for quasi-Monte Carlo versions of MCMC. As a side benefit, the results also establish consistency for the usual method of using pseudo-random numbers in place of random ones.Comment: Published in at http://dx.doi.org/10.1214/10-AOS831 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org