A Bayesian Collocation Integral Method for Parameter Estimation in Ordinary Differential Equations

Inferring the parameters of ordinary differential equations (ODEs) from noisy observations is an important problem in many scientific fields. Currently, most parameter estimation methods that bypass numerical integration tend to rely on basis functions or Gaussian processes to approximate the ODE solution and its derivatives. Due to the sensitivity of the ODE solution to its derivatives, these methods can be hindered by estimation error, especially when only sparse time-course observations are available. We present a Bayesian collocation framework that operates on the integrated form of the ODEs and also avoids the expensive use of numerical solvers. Our methodology has the capability to handle general nonlinear ODE systems. We demonstrate the accuracy of the proposed method through a simulation study, where the estimated parameters and recovered system trajectories are compared with other recent methods. A real data example is also provided

Aeroacoustic Data for a High Reynolds Number Axisymmetric Subsonic Jet

The near field fluctuating pressure and aerodynamic mean flow characteristics of a cold subsonic jet issuing from a contoured convergent nozzle are presented. The data are presented for nozzle exit Mach numbers of 0.30, 0.60, and 0.85 at a constant jet stagnation temperature of 104 F. The fluctuating pressure measurements were acquired via linear and semi-circular microphone arrays and the presented results include plots of narrowband spectra, contour maps, streamwise/azimuthal spatial correlations for zero time delay, and cross-spectra of the azimuthal correlations. A pitot probe was used to characterize the mean flow velocity by assuming the subsonic flow to be pressure-balanced with the ambient field into which it exhausts. Presented are mean flow profiles and the momentum thickness of the free shear layer as a function of streamwise position

The Star Formation History of LGS 3

We have determined the distance and star formation history of the Local Group dwarf galaxy LGS 3 from deep Hubble Space Telescope WFPC2 observations. LGS 3 is intriguing because ground-based observations showed that, while its stellar population is dominated by old, metal-poor stars, there is a handful of young, blue stars. Also, the presence of HI gas makes this a possible ``transition object'' between dwarf spheroidal and dwarf irregular galaxies. The HST data are deep enough to detect the horizontal branch and young main sequence for the first time. A new distance of D=620+/-20 kpc has been measured from the positions of the TRGB, the red clump, and the horizontal branch. The mean metallicity of the stars older than 8 Gyr is Fe/H = -1.5 +/- 0.3. The most recent generation of stars has Fe/H ~ -1. For the first few Gyr the global star formation rate was several times higher than the historical average and has been fairly constant since then. However, we do see significant changes in stellar populations and star formation history with radial position in the galaxy. Most of the young stars are found in the central 63 pc (21''), where the star formation rate has been relatively constant, while the outer parts have had a declining star formation rate.Comment: To appear in The Astrophysical Journal, 26 pages, 14 figures, uses AASTe

Composite-fermion crystallites in quantum dots

The correlations in the ground state of interacting electrons in a two-dimensional quantum dot in a high magnetic field are known to undergo a qualitative change from liquid-like to crystal-like as the total angular momentum becomes large. We show that the composite-fermion theory provides an excellent account of the states in both regimes. The quantum mechanical formation of composite fermions with a large number of attached vortices automatically generates omposite fermion crystallites in finite quantum dots.Comment: 5 pages, 3 figure

EM Decay of X(3872) as the 11D2(2−+)1{^1D_2}(2^{-+}) charmonium

The recently BaBar results raise the possibility that X(3872) has negative parity. This makes people reconsider assigning X(3872) to the $1{^1D_2}(c\bar c)$ state. In this paper we give a general form of the wave function of $2^{-+}$ mesons. By solving the instantaneous Bethe-Salpeter equation, we get the mass spectrum and corresponding wave functions. We calculate electromagnetic decay widths of the first $2^{-+}$ state which we assume to be the X(3872) particle. The results are $\Gamma(2^{-+}(3872)\rightarrow J/\psi\gamma) = 1.59^{+0.53}_{-0.42}$ keV, $\Gamma(2^{-+}(3872)\rightarrow \psi(2S)\gamma) = 2.87^{+1.46}_{-0.97}$ eV and $\Gamma(2^{-+}(3872)\rightarrow \psi(3770)\gamma) = 0.135^{+0.066}_{-0.047}$ keV. The ratio of branch fractions of the second and first channel is about 0.002, which is inconsistent with the experimental value $3.4\pm 1.4$. So X(3872) is unlikely to be a $2^{-+}$ charmonium state. In addition, we obtain a relatively large decay width for $2^{-+}(3872)\rightarrow h_c\gamma$ channel which is $392^{+62}_{-111}$ keV.Comment: Revised versio

Multidrug-resistant enteroaggregative Escherichia coli associated with persistent diarrhea in Kenyan children.

To study the association of multidrug-resistant enteroaggregative Escherichia coli with persistent diarrhea in Kenyan children, stool specimens were obtained from 862 outpatients under 5 years of age from July 1991 to June 1993. E. coli O44 was identified as the sole bacterial pathogen in four patients experiencing at least 14 days of fever, vomiting, and diarrhea. Disk diffusion testing showed E. coli O44 resistance to tetracycline, ampicillin, erythromycin, trimethoprim-sulphamethoxazole, and amoxicillin/clavulanate and sensitivity to chloramphenicol, nalidixic acid, azithromycin, and cefuroxime. Further studies are needed to clarify the epidemiology, clinical spectrum, and pathogenesis of enteroaggregative E. coli infection

A Variational Expansion for the Free Energy of a Bosonic System

In this paper, a variational perturbation scheme for nonrelativistic many-Fermion systems is generalized to a Bosonic system. By calculating the free energy of an anharmonic oscillator model, we investigated this variational expansion scheme for its efficiency. Using the modified Feynman rules for the diagrams, we obtained the analytical expression of the free energy up to the fourth order. Our numerical results at various orders are compared with the exact and other relevant results.Comment: 9 pages, 3 EPS figures. With a few typo errors corrected. to appear in J. Phys.

A New Method of Synthesizing Black Birnessite Nanoparticles: From Brown to Black Birnessite with Nanostructures

A new method for preparing black birnessite nanoparticles is introduced. The initial synthesis process resembles the classical McKenzie method of preparing brown birnessite except for slower cooling and closing the system from the ambient air. Subsequent process, including wet-aging at 7◦C for 48 hours, overnight freezing, and lyophilization, is shown to convert the brown birnessite into black birnessite with complex nanomorphology with folded sheets and spirals. Characterization of the product is performed by X-ray diffraction (XRD), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM), thermogravimetric analysis (TGA), and N2 adsorption (BET) techniques. Wet-aging and lyophilization times are shown to affect the architecture of the product. XRD patterns show a single phase corresponding to a semicrystalline birnessite-based manganese oxide. TEM studies suggest its fibrous and petal-like structures. The HRTEM images at 5 and 10 nm length scales reveal the fibrils in folding sheets and also show filamentary breaks. The BET surface area of this nanomaterial was found to be 10.6m2/g. The TGA measurement demonstrated that it possessed an excellent thermal stability up to 400◦C. Layerstructured black birnessite nanomaterial containing sheets, spirals, and filamentary breaks can be produced at low temperature (−49◦C) from brown birnessite without the use of cross-linking reagents