Efficient and automatic methods for flexible regression on spatiotemporal data, with applications to groundwater monitoring

Fitting statistical models to spatiotemporal data requires finding the right balance between imposing smoothness and following the data. In the context of P-splines, we propose a Bayesian framework for choosing the smoothing parameter which allows the construction of fully-automatic data-driven methods for fitting flexible models to spatiotemporal data. An implementation, which is highly computationally efficient and which exploits the sparsity of the design and penalty matrices, is proposed. The findings are illustrated using a simulation study and two examples, all concerned with the modelling of contaminants in groundwater. This suggests that the proposed strategy is more stable that competing methods based on the use of criteria such as GCV and AIC

Hydrogen Bond Energies in Carboxylic Acids

A question of interest to the study of the chemisorption of carbon monoxide on iron is whether the carbon is desorbed with the same oxygen to which it was bonded prior to the adsorption. A mixture of C13O and CO18 in the desorbed gas in amounts greater than expected from normal abundance ratios shows that an intermolecular oxygen exchange occurs

Statistical modelling of groundwater contamination monitoring data: a comparison of spatial and spatiotemporal methods

Field monitoring of groundwater contamination plumes is an important component of managing risks for downgradient receptors and remedial strategies that rely on monitored natural attenuation. Collection of groundwater quality data can however take a considerable effort and be associated with high cost. Here, we investigated the relative merits of analyzing groundwater quality data using spatial compared to spatiotemporal statistical modelling and assessed the accuracy of both methods and implications for data collection requirements. The aim of this was to determine whether the quantity of data collected can be reduced, while retaining the same level of estimation accuracy, by analyzing groundwater contamination data using a spatiotemporal model which “borrows strength” across time, rather than a spatial model for individual sampling events. To capture the variability encountered under field conditions, we used three hypothetical groundwater contamination plumes with increasing complexity, and site data for a large groundwater gasoline additive plume. The results show that spatiotemporal methods can increase efficiency markedly so that, in comparison with repeated spatial analysis, spatiotemporal methods can achieve the same level of performance but with smaller sample sizes

The fading of two transient ultraluminous x-ray sources to below the stellar mass Eddington limit

We report new detections of the two transient ultraluminous X-ray sources (ULXs) in NGC 5128 from an ongoing series of Chandra observations. Both sources have previously been observed L (2-3) × ∼10 erg s, at the lower end of the ULX luminosity range. The new observations allow us to study these sources in the luminosity regime frequented by the Galactic black hole X-ray binaries (BH XBs). We present the recent lightcurves of both ULXs. 1RXH J132519.8-430312 (ULX1) was observed at L 1 × 10 erg s, while CXOU J132518.2-430304 (ULX2) declined to L 2 × 10 erg s and then lingered at this luminosity for hundreds of days. We show that a reasonable upper limit for both duty cycles is 0.2, with a lower limit of 0.12 for ULX2. This duty cycle is larger than anticipated for transient ULXs in old stellar populations. By fitting simple spectral models in an observation with ∼50 counts we recover properties consistent with Galactic BH XBs, but inconclusive as to the spectral state. We utilize quantile analyses to demonstrate that the spectra are generally soft, and that in one observation the spectrum of ULX2 is inconsistent with a canonical hard state at >95% confidence. This is contrary to what would be expected of an accreting intermediate mass black hole primary, which we would expect to be in the hard state at these luminosities. We discuss the paucity of transient ULXs discovered in early-type galaxies and excogitate explanations. We suggest that the number of transient ULXs scales with the giant and sub-giant populations, rather than the total number of XBs.Peer reviewe

Determination of pi-N scattering lengths from pionic hydrogen and pionic deuterium data

The pi-N s-wave scattering lengths have been inferred from a joint analysis of the pionic hydrogen and the pionic deuterium x-ray data using a non-relativistic approach in which the pi-N interaction is simulated by a short-ranged potential. The pi-d scattering length has been calculated exactly by solving the Faddeev equations and also by using a static approximation. It has been shown that the same very accurate static formula for pi-d scattering length can be derived (i) from a set of boundary conditions; (ii) by a reduction of Faddeev equations; and (iii) through a summation of Feynman diagrams. By imposing the requirement that the pi-d scattering length, resulting from Faddeev-type calculation, be in agreement with pionic deuterium data, we obtain bounds on the pi-N scattering lengths. The dominant source of uncertainty on the deduced values of the pi-N scattering lengths are the experimental errors in the pionic hydrogen data.Comment: RevTeX, 20 pages,4 PostScript figure

Force-Extension Relations for Polymers with Sliding Links

Topological entanglements in polymers are mimicked by sliding rings (slip-links) which enforce pair contacts between monomers. We study the force-extension curve for linear polymers in which slip-links create additional loops of variable size. For a single loop in a phantom chain, we obtain exact expressions for the average end-to-end separation: The linear response to a small force is related to the properties of the unstressed chain, while for a large force the polymer backbone can be treated as a sequence of Pincus--de Gennes blobs, the constraint effecting only a single blob. Generalizing this picture, scaling arguments are used to include self-avoiding effects.Comment: 4 pages, 5 figures; accepted to Phys. Rev. E (Brief Report

THE AMUNDSEN SEA LOW Variability, Change, and Impact on Antarctic Climate

The Amundsen Sea low (ASL) is a climatological low pressure center that exerts considerable influence on the climate of West Antarctica. Its potential to explain important recent changes in Antarctic climate, for example, in temperature and sea ice extent, means that it has become the focus of an increasing number of studies. Here, the authors summarize the current understanding of the ASL, using reanalysis datasets to analyze recent variability and trends, as well as ice-core chemistry and climate model projections, to examine past and future changes in the ASL, respectively. The ASL has deepened in recent decades, affecting the climate through its influence on the regional meridional wind field, which controls the advection of moisture and heat into the continent. Deepening of the ASL in spring is consistent with observed West Antarctic warming and greater sea ice extent in the Ross Sea. Climate model simulations for recent decades indicate that this deepening is mediated by tropical variability while climate model projections through the twenty-first century suggest that the ASL will deepen in some seasons in response to greenhouse gas concentration increases

On spherical averages of radial basis functions

A radial basis function (RBF) has the general form $$s(x)=\sum_{k=1}^{n}a_{k}\phi(x-b_{k}),\quad x\in\mathbb{R}^{d},$$ where the coefficients a 1,…,a n are real numbers, the points, or centres, b 1,…,b n lie in ℝ d , and φ:ℝ d →ℝ is a radially symmetric function. Such approximants are highly useful and enjoy rich theoretical properties; see, for instance (Buhmann, Radial Basis Functions: Theory and Implementations, [2003]; Fasshauer, Meshfree Approximation Methods with Matlab, [2007]; Light and Cheney, A Course in Approximation Theory, [2000]; or Wendland, Scattered Data Approximation, [2004]). The important special case of polyharmonic splines results when φ is the fundamental solution of the iterated Laplacian operator, and this class includes the Euclidean norm φ(x)=‖x‖ when d is an odd positive integer, the thin plate spline φ(x)=‖x‖2log  ‖x‖ when d is an even positive integer, and univariate splines. Now B-splines generate a compactly supported basis for univariate spline spaces, but an analyticity argument implies that a nontrivial polyharmonic spline generated by (1.1) cannot be compactly supported when d>1. However, a pioneering paper of Jackson (Constr. Approx. 4:243–264, [1988]) established that the spherical average of a radial basis function generated by the Euclidean norm can be compactly supported when the centres and coefficients satisfy certain moment conditions; Jackson then used this compactly supported spherical average to construct approximate identities, with which he was then able to derive some of the earliest uniform convergence results for a class of radial basis functions. Our work extends this earlier analysis, but our technique is entirely novel, and applies to all polyharmonic splines. Furthermore, we observe that the technique provides yet another way to generate compactly supported, radially symmetric, positive definite functions. Specifically, we find that the spherical averaging operator commutes with the Fourier transform operator, and we are then able to identify Fourier transforms of compactly supported functions using the Paley–Wiener theorem. Furthermore, the use of Haar measure on compact Lie groups would not have occurred without frequent exposure to Iserles’s study of geometric integration

The effect of the COVID-19 pandemic on domestic violence and child abuse

In response to the COVID-19 pandemic, many governments around the world have implemented lockdown or mass quarantine measures. While the purpose of these measures is to prevent the spread of the virus, they have had important social consequences. To determine the effect that pandemic-related isolation and quarantine measures have had on domestic violence and child abuse, we analyzed Canadian police calls for service data from 2015 to 2020. Our findings indicate that calls for service related to both domestic violence and child abuse have significantly increased during the pandemic. In light of these findings, we make recommendations for both government officials responsible for pandemic management and policing organizations on how to prevent increases in domestic violence and child abuse during future lockdowns

Spectral functions of isoscalar scalar and isovector electromagnetic form factors of the nucleon at two-loop order

We calculate the imaginary parts of the isoscalar scalar and isovector electromagnetic form factors of the nucleon up to two-loop order in chiral perturbation theory. Particular attention is paid on the correct behavior of Im $\sigma_N(t)$ and Im $G_{E,M}^V(t)$ at the two-pion threshold $t_0=4 m_\pi^2$ in connection with the non-relativistic 1/M-expansion. We recover the well-known strong enhancement near threshold originating from the nearby anomalous singularity at $t_c = 4m_\pi^2-m_\pi^4/M^2 = 3.98 m_\pi^2$. In the case of the scalar spectral function Im $\sigma_N(t)$ one finds a significant improvement in comparison to the lowest order one-loop result. Higher order $\pi\pi$-rescattering effects are however still necessary to close a remaining 20%-gap to the empirical scalar spectral function. The isovector electric and magnetic spectral functions Im $G_{E,M}^V(t)$ get additionally enhanced near threshold by the two-pion-loop contributions. After supplementing their two-loop results by a phenomenological $\rho$-meson exchange term one can reproduce the empirical isovector electric and magnetic spectral functions fairly well.Comment: 10 pages, 6 figures, submitted to Physical Review