On The Inverse Geostatistical Problem of Inference on Missing Locations

The standard geostatistical problem is to predict the values of a spatially continuous phenomenon, $S(x)$ say, at locations $x$ using data $(y_i,x_i):i=1,..,n$ where $y_i$ is the realization at location $x_i$ of $S(x_i)$, or of a random variable $Y_i$ that is stochastically related to $S(x_i)$. In this paper we address the inverse problem of predicting the locations of observed measurements $y$. We discuss how knowledge of the sampling mechanism can and should inform a prior specification, $\pi(x)$ say, for the joint distribution of the measurement locations $X = \{x_i: i=1,...,n\}$, and propose an efficient Metropolis-Hastings algorithm for drawing samples from the resulting predictive distribution of the missing elements of $X$. An important feature in many applied settings is that this predictive distribution is multi-modal, which severely limits the usefulness of simple summary measures such as the mean or median. We present two simulated examples to demonstrate the importance of the specification for $\pi(x)$, and analyze rainfall data from Paran\'a State, Brazil to show how, under additional assumptions, an empirical of estimate of $\pi(x)$ can be used when no prior information on the sampling design is available.Comment: Under revie

Model-Based Geostatistics for Prevalence Mapping in Low-Resource Settings

In low-resource settings, prevalence mapping relies on empirical prevalence data from a finite, often spatially sparse, set of surveys of communities within the region of interest, possibly supplemented by remotely sensed images that can act as proxies for environmental risk factors. A standard geostatistical model for data of this kind is a generalized linear mixed model with binomial error distribution, logistic link and a combination of explanatory variables and a Gaussian spatial stochastic process in the linear predictor. In this paper, we first review statistical methods and software associated with this standard model, then consider several methodological extensions whose development has been motivated by the requirements of specific applications. These include: methods for combining randomised survey data with data from non-randomised, and therefore potentially biased, surveys; spatio-temporal extensions; spatially structured zero-inflation. Throughout, we illustrate the methods with disease mapping applications that have arisen through our involvement with a range of African public health programmes.Comment: Submitte

Kohn-Sham calculations combined with an average pair-density functional theory

A recently developed formalism in which Kohn-Sham calculations are combined with an ``average pair density functional theory'' is reviewed, and some new properties of the effective electron-electron interaction entering in this formalism are derived. A preliminary construction of a fully self-consitent scheme is also presented in this framework.Comment: submitted to Int. J. Mod. Phys. B (proceedings of the 30th International Workshop on Condensed Matter Theories

Functional Derivative of the Zero Point Energy Functional from the Strong Interaction Limit of Density Functional Theory

We derive an explicit expression for the functional derivative of the subleading term in the strong interaction limit expansion of the generalized Levy--Lieb functional for the special case of two electrons in one dimension. The expression is derived from the zero point energy (ZPE) functional, which is valid if the quantum state reduces to strongly correlated electrons in the strong coupling limit. The explicit expression is confirmed numerically and respects the relevant sum-rule. We also show that the ZPE potential is able to generate a bond mid-point peak for homo-nuclear dissociation and is properly of purely kinetic origin. Unfortunately, the ZPE diverges for Coulomb systems, whereas the exact peaks should be finite.Comment: 12 pages, 7 figure

Power calculation for gravitational radiation: oversimplification and the importance of time scale

A simplified formula for gravitational-radiation power is examined. It is shown to give completely erroneous answers in three situations, making it useless even for rough estimates. It is emphasized that short timescales, as well as fast speeds, make classical approximations to relativistic calculations untenable.Comment: Three pages, no figures, accepted for publication in Astronomische Nachrichte

Routing quantum information in spin chains

Two different models for performing efficiently routing of a quantum state are presented. Both cases involve an XX spin chain working as data bus and additional spins that play the role of sender and receivers, one of which is selected to be the target of the quantum state transmission protocol via a coherent quantum coupling mechanism making use of local/global magnetic fields. Quantum routing is achieved, in the first of the models considered, by weakly coupling the sender and the receiver to the data bus. In the second model, strong magnetic fields acting on additional spins located between the sender/receiver and the data bus allow us to perform high fidelity routing.Comment: added references in v

Strictly correlated uniform electron droplets

We study the energetic properties of finite but internally homogeneous D-dimensional electron droplets in the strict-correlation limit. The indirect Coulomb interaction is found to increase as a function of the electron number, approaching the tighter forms of the Lieb-Oxford bound recently proposed by Rasanen et al. [Phys. Rev. Lett. 102, 206406 (2009)]. The bound is satisfied in three-, two-, and one-dimensional droplets, and in the latter case it is reached exactly - regardless of the type of interaction considered. Our results provide useful reference data for delocalized strongly correlated systems, and they can be used in the development and testing of exchange-correlation density functionals in the framework of density-functional theory