Stability of Filters for the Navier-Stokes Equation

Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation algorithms designed to update the estimation of the state in a on-line fashion, as data is acquired sequentially. For linear problems subject to Gaussian noise filtering can be performed exactly using the Kalman filter. For nonlinear systems it can be approximated in a systematic way by particle filters. However in high dimensions these particle filtering methods can break down. Hence, for the large nonlinear systems arising in applications such as weather forecasting, various ad hoc filters are used, mostly based on making Gaussian approximations. The purpose of this work is to study the properties of these ad hoc filters, working in the context of the 2D incompressible Navier-Stokes equation. By working in this infinite dimensional setting we provide an analysis which is useful for understanding high dimensional filtering, and is robust to mesh-refinement. We describe theoretical results showing that, in the small observational noise limit, the filters can be tuned to accurately track the signal itself (filter stability), provided the system is observed in a sufficiently large low dimensional space; roughly speaking this space should be large enough to contain the unstable modes of the linearized dynamics. Numerical results are given which illustrate the theory. In a simplified scenario we also derive, and study numerically, a stochastic PDE which determines filter stability in the limit of frequent observations, subject to large observational noise. The positive results herein concerning filter stability complement recent numerical studies which demonstrate that the ad hoc filters perform poorly in reproducing statistical variation about the true signal

Medication Therapy Management Services Provided by Student Pharmacists

Objectives. To evaluate the impact of student pharmacists delivering medication therapy management (MTM) services during an elective advanced pharmacy practice experience (APPE). Methods. Student pharmacists provided MTM services at community pharmacy APPE sites, documented their recommendations, and then made follow-up telephone calls to patients to determine the impact of the MTM provided. Students were surveyed about the MTM experience. Results. Forty-seven students provided MTM services to 509 patients over 2 years and identified 704 drug-related problems (average of 1.4 problems per patient). About 53% of patients relayed the recommendations to their physician and 205 (75%) physicians accepted the recommendations. Eighty-eight percent of patients reported feeling better about their medications after receiving MTM services. A majority of the students perceived their provision of MTM services as valuable to their patients. Conclusions. Providing MTM services to patients in a pharmacy practice setting allowed student pharmacists to apply skills learned in the doctor of pharmacy (PharmD) curriculum

Accuracy and stability of filters for dissipative PDEs

Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation algorithms designed to update the estimation of the state in an on-line fashion, as data is acquired sequentially. For linear problems subject to Gaussian noise, filtering can be performed exactly using the Kalman filter. For nonlinear systems filtering can be approximated in a systematic way by particle filters. However in high dimensions these particle filtering methods can break down. Hence, for the large nonlinear systems arising in applications such as oceanography and weather forecasting, various ad hoc filters are used, mostly based on making Gaussian approximations. The purpose of this work is to study the accuracy and stability properties of these ad hoc filters. We work in the context of the 2D incompressible Navier-Stokes equation, although the ideas readily generalize to a range of dissipative partial differential equations (PDEs). By working in this infinite dimensional setting we provide an analysis which is useful for the understanding of high dimensional filtering, and is robust to mesh-refinement. We describe theoretical results showing that, in the small observational noise limit, the filters can be tuned to perform accurately in tracking the signal itself (filter accuracy), provided the system is observed in a sufficiently large low dimensional space; roughly speaking this space should be large enough to contain the unstable modes of the linearized dynamics. The tuning corresponds to what is known as variance inflation in the applied literature. Numerical results are given which illustrate the theory. The positive results herein concerning filter stability complement recent numerical studies which demonstrate that the ad hoc filters can perform poorly in reproducing statistical variation about the true signal

Emission-Line Galaxy Surveys as Probes of the Spatial Distribution of Dwarf Galaxies. I. The University of Michigan Survey

Objective-prism surveys which select galaxies on the basis of line-emission are extremely effective at detecting low-luminosity galaxies and constitute some of the deepest available samples of dwarfs. In this study, we confirm that emission-line galaxies (ELGs) in the University of Michigan (UM) objective-prism survey (MacAlpine et al. 1977-1981) are reliable tracers of large-scale structure, and utilize the depth of the samples to examine the spatial distribution of low-luminosity (M$_{B} >$ -18.0) dwarfs relative to higher luminosity giant galaxies (M$_{B} \leq$ -18.0) in the Updated Zwicky Catalogue (Falco et al. 1999). New spectroscopic data are presented for 26 UM survey objects. We analyze the relative clustering properties of the overall starbursting ELG and normal galaxy populations, using nearest neighbor and correlation function statistics. This allows us to determine whether the activity in ELGs is primarily caused by gravitational interactions. We conclude that galaxy-galaxy encounters are not the sole cause of activity in ELGs since ELGs tend to be more isolated and are more often found in the voids when compared to their normal galaxy counterparts. Furthermore, statistical analyses performed on low-luminosity dwarf ELGs show that the dwarfs are less clustered when compared to their non-active giant neighbors. The UM dwarf samples have greater percentages of nearest neighbor separations at large values and lower correlation function amplitudes relative to the UZC giant galaxy samples. These results are consistent with the expectations of galaxy biasing.Comment: 17 pages, 4 tables, 10 figures. Accepted for publication in the Ap

The Host Galaxy and Redshift of the Repeating Fast Radio Burst FRB 121102

The precise localization of the repeating fast radio burst (FRB 121102) has provided the first unambiguous association (chance coincidence probability $p\lesssim3\times10^{-4}$) of an FRB with an optical and persistent radio counterpart. We report on optical imaging and spectroscopy of the counterpart and find that it is an extended ($0.6^{\prime\prime}-0.8^{\prime\prime}$) object displaying prominent Balmer and [OIII] emission lines. Based on the spectrum and emission line ratios, we classify the counterpart as a low-metallicity, star-forming, $m_{r^\prime} = 25.1$ AB mag dwarf galaxy at a redshift of $z=0.19273(8)$, corresponding to a luminosity distance of 972 Mpc. From the angular size, the redshift, and luminosity, we estimate the host galaxy to have a diameter $\lesssim4$ kpc and a stellar mass of $M_*\sim4-7\times 10^{7}\,M_\odot$, assuming a mass-to-light ratio between 2 to 3$\,M_\odot\,L_\odot^{-1}$. Based on the H$\alpha$ flux, we estimate the star formation rate of the host to be $0.4\,M_\odot\,\mathrm{yr^{-1}}$ and a substantial host dispersion measure depth $\lesssim 324\,\mathrm{pc\,cm^{-3}}$. The net dispersion measure contribution of the host galaxy to FRB 121102 is likely to be lower than this value depending on geometrical factors. We show that the persistent radio source at FRB 121102's location reported by Marcote et al (2017) is offset from the galaxy's center of light by $\sim$200 mas and the host galaxy does not show optical signatures for AGN activity. If FRB 121102 is typical of the wider FRB population and if future interferometric localizations preferentially find them in dwarf galaxies with low metallicities and prominent emission lines, they would share such a preference with long gamma ray bursts and superluminous supernovae.Comment: 12 pages, 3 figures, Published in ApJ Letters. V2: Corrected mistake in author lis

The XMM-Newton serendipitous survey. VII. The third XMM-Newton serendipitous source catalogue

Thanks to the large collecting area (3 x ~1500 cm$^2$ at 1.5 keV) and wide field of view (30' across in full field mode) of the X-ray cameras on board the European Space Agency X-ray observatory XMM-Newton, each individual pointing can result in the detection of hundreds of X-ray sources, most of which are newly discovered. Recently, many improvements in the XMM-Newton data reduction algorithms have been made. These include enhanced source characterisation and reduced spurious source detections, refined astrometric precision, greater net sensitivity and the extraction of spectra and time series for fainter sources, with better signal-to-noise. Further, almost 50\% more observations are in the public domain compared to 2XMMi-DR3, allowing the XMM-Newton Survey Science Centre (XMM-SSC) to produce a much larger and better quality X-ray source catalogue. The XMM-SSC has developed a pipeline to reduce the XMM-Newton data automatically and using improved calibration a new catalogue version has been produced from XMM-Newton data made public by 2013 Dec. 31 (13 years of data). Manual screening ensures the highest data quality. This catalogue is known as 3XMM. In the latest release, 3XMM-DR5, there are 565962 X-ray detections comprising 396910 unique X-ray sources. For the 133000 brightest sources, spectra and lightcurves are provided. For all detections, the positions on the sky, a measure of the quality of the detection, and an evaluation of the X-ray variability is provided, along with the fluxes and count rates in 7 X-ray energy bands, the total 0.2-12 keV band counts, and four hardness ratios. To identify the detections, a cross correlation with 228 catalogues is also provided for each X-ray detection. 3XMM-DR5 is the largest X-ray source catalogue ever produced. Thanks to the large array of data products, it is an excellent resource in which to find new and extreme objects.Comment: 23 pages, version accepted for publication in A&

A Multi-telescope Campaign on FRB 121102: Implications for the FRB Population

We present results of the coordinated observing campaign that made the first subarcsecond localization of a Fast Radio Burst, FRB 121102. During this campaign, we made the first simultaneous detection of an FRB burst by multiple telescopes: the VLA at 3 GHz and the Arecibo Observatory at 1.4 GHz. Of the nine bursts detected by the Very Large Array at 3 GHz, four had simultaneous observing coverage at other observatories. We use multi-observatory constraints and modeling of bursts seen only at 3 GHz to confirm earlier results showing that burst spectra are not well modeled by a power law. We find that burst spectra are characterized by a ~500 MHz envelope and apparent radio energy as high as $10^{40}$ erg. We measure significant changes in the apparent dispersion between bursts that can be attributed to frequency-dependent profiles or some other intrinsic burst structure that adds a systematic error to the estimate of DM by up to 1%. We use FRB 121102 as a prototype of the FRB class to estimate a volumetric birth rate of FRB sources $R_{FRB} \approx 5x10^{-5}/N_r$ Mpc$^{-3}$ yr$^{-1}$, where $N_r$ is the number of bursts per source over its lifetime. This rate is broadly consistent with models of FRBs from young pulsars or magnetars born in superluminous supernovae or long gamma-ray bursts, if the typical FRB repeats on the order of thousands of times during its lifetime.Comment: 17 pages, 7 figures. Submitted to AAS Journal

The effect of slow-wave sleep and rapid eye-movement sleep interventions on glycaemic control: a systematic review and meta-analysis of randomised controlled trials

Poor glycaemic control is found in diabetes, one of the most common, serious, non- communicable diseases worldwide. Trials suggest a relationship between glycaemic control and measures of sleep including duration and quality of sleep. Currently, the relationship between specific sleep stages (including slow-wave sleep (SWS), a sleep stage mainly found early in the night and linked to restorative functioning) and glycaemic control remains unclear. This systematic review aimed to synthesise the evidence of the effectiveness of specific sleep stage manipulation on measures of glycaemic control (insulin resistance, fasting and post-prandial glucose and insulin). Public databases (e.g. psychINFO, MEDLINE, Academic Search Complete, psychARTICLES, OpenDissertations, Scopus and Cochrane library) were searched for randomised controlled trials. Trials were included if they involved direct manipulation of SWS and/or rapid eye-movement sleep to explore the impact on measures of glycaemic control (insulin resistance, fasting and post-prandial glucose and insulin). Eight trials met the eligibility criteria, with four providing data for inclusion in one of the three meta-analyses. Insulin resistance was significantly higher in the SWS disruption when compared to the normal sleep condition, (p = 0.02). No significant differences were found for measures of fasting or post-prandial glucose or insulin. Risk of bias was considered low for performance bias, detection bias and incomplete outcome data, with unclear selection bias. This is an emerging area of research and this review provides preliminary findings and recommendations for future research around optimising sleep stage disruption (to further explore mechanisms) and sleep stage enhancement techniques (to explore potential interventions)