Estimators in capture–recapture studies with two sources

This paper investigates the applications of capture–recapture methods to human populations. Capture–recapture methods are commonly used in estimating the size of wildlife populations but can also be used in epidemiology and social sciences, for estimating prevalence of a particular disease or the size of the homeless population in a certain area. Here we focus on estimating the prevalence of infectious diseases. Several estimators of population size are considered: the Lincoln–Petersen estimator and its modified version, the Chapman estimator, Chao’s lower bound estimator, the Zelterman’s estimator, McKendrick’s moment estimator and the maximum likelihood estimator. In order to evaluate these estimators, they are applied to real, three-source, capture-recapture data. By conditioning on each of the sources of three source data, we have been able to compare the estimators with the true value that they are estimating. The Chapman and Chao estimators were compared in terms of their relative bias. A variance formula derived through conditioning is suggested for Chao’s estimator, and normal 95% confidence intervals are calculated for this and the Chapman estimator. We then compare the coverage of the respective confidence intervals. Furthermore, a simulation study is included to compare Chao’s and Chapman’s estimator. Results indicate that Chao’s estimator is less biased than Chapman’s estimator unless both sources are independent. Chao’s estimator has also the smaller mean squared error. Finally, the implications and limitations of the above methods are discussed, with suggestions for further development.

Estimators in capture-recapture studies with two sources

This paper investigates the applications of capture-recapture methods to human populations. Capture-recapture methods are commonly used in estimating the size of wildlife populations but can also be used in epidemiology and social sciences, for estimating prevalence of a particular disease or the size of the homeless population in a certain area. Here we focus on estimating the prevalence of infectious diseases. Several estimators of population size are considered: the Lincoln-Petersen estimator and its modified version, the Chapman estimator, Chao's lower bound estimator, the Zelterman's estimator, McKendrick's moment estimator and the maximum likelihood estimator. In order to evaluate these estimators, they are applied to real, three-source, capture-recapture data. By conditioning on each of the sources of three source data, we have been able to compare the estimators with the true value that they are estimating. The Chapman and Chao estimators were compared in terms of their relative bias. A variance formula derived through conditioning is suggested for Chao's estimator, and normal 95% confidence intervals are calculated for this and the Chapman estimator. We then compare the coverage of the respective confidence intervals. Furthermore, a simulation study is included to compare Chao's and Chapman's estimator. Results indicate that Chao's estimator is less biased than Chapman's estimator unless both sources are independent. Chao's estimator has also the smaller mean squared error. Finally, the implications and limitations of the above methods are discussed, with suggestions for further development.

New dioxadiaza- and trioxadiaza-macrocycles containing one dibenzofuran unit with two amino pendant arms: synthesis, protonation and complexation studies

New dioxadiaza- and trioxadiaza-macrocycles containing one rigid dibenzofuran unit (DBF) and N-(2-aminoethyl) pendant arms were synthesized, N,N'-bis(2-aminoethyl)-[17]( DBF) N2O2 (L-1) and N,N'-bis(2-aminoethyl)-[22](DBF)N2O3 (L-2), respectively. The binding properties of both macrocycles to metal ions and structural studies of their metal complexes were carried out. The protonation constants of both compounds and the stability constants of their complexes with Co2+, Ni2+, Cu2+, Zn2+, Cd2+, and Pb2+ were determined at 298.2 K, in aqueous solutions, and at ionic strength 0.10 mol dm(-3) in KNO3. Mononuclear complexes with both ligands were formed, and dinuclear complexes were only found for L-2. The thermodynamic binding affinities of the metal complexes of L-2 are lower than those of L-1 as expected, but the Pb2+ complexes of both macrocycles exhibit close stability constant values. On the other hand, the binding affinities of Cd2+ and Pb2+ for L-1 are very high, when compared to those of Co2+, Ni2+ and Zn2+. These interesting properties were explained by the presence of the rigid DBF moiety in the backbone of the macrocycle and to the special match between the macrocyclic cavity size and the studied larger metal ions. To elucidate the adopted structures of complexes in solution, the nickel(II) and copper( II) complexes with both ligands were further studied by UV-vis-MR spectroscopy in DMSO-H2O 1 : 1 (v/v) solution. The copper(II) complexes were also studied by EPR spectroscopy in the same mixture of solvents. The crystal structure of the copper complex of L-1 was also determined. The copper(II) displays an octahedral geometry, the four nitrogen atoms forming the equatorial plane and two oxygen atoms, one from the DBF unit and the other one from the ether oxygen, in axial positions. One of the ether oxygens of the macrocycle is out of the coordination sphere. Our results led us to suggest that this geometry is also adopted by the Co2+ to Zn2+ complexes, and only the larger Cd2+ and Pb2+ manage to form complexes with the involvement of all the oxygen atoms of the macrocyclic backbone.

A new solution of the rendering equation with stratified Monte Carlo approach

This paper is turned to the advanced Monte Carlo methods for realistic image creation. It offers a new stratified approach for solving the rendering equation. We consider the numerical solution of the rendering equation by separation of integration domain. The hemispherical integration domain is symmetrically separated into 16 parts. First 9 sub-domains are equal size of orthogonal spherical triangles. They are symmetric each to other and grouped with a common vertex around the normal vector to the surface. The hemispherical integration domain is completed with more 8 sub-domains of equal size spherical quadrangles, also symmetric each to other. All sub-domains have fixed vertices and computable parameters. The bijections of unit square into an orthogonal spherical triangle and into a spherical quadrangle are derived and used to generate sampling points. Then, the symmetric sampling scheme is applied to generate the sampling points distributed over the hemispherical integration domain. The necessary transformations are made and the stratified Monte Carlo estimator is presented. The rate of convergence is obtained and one can see that the algorithm is of super-convergent type.

Dimetallic complexes of macrocycles with two rigid dibenzofuran units as receptors for detection of anionic substrates

The hexaazamacrocycles [28](DBF)2N6 {cyclo[bis(4,6-dimethyldibenzo[b,d]furaniminoethyleneiminoethylene]} and [32](DBF)2N6 {cyclo[bis(4,6-dimethyldibenzo[b,d]furaniminopropyleneiminopropylene]} form stable dinuclear copper(II) complexes suitable to behave as receptors for several anionic substrates. These two receptors were used to study the binding interactions with several substrates, such as imidazole (Him) and some carboxylates [benzoate (bz−), oxalate (ox2−), malonate (mal2−), phthalate (ph2−), isophthalate (iph2−), and terephthalate (tph2−)] by spectrophotometric titrations and EPR spectroscopy in MeOH (or H2O):DMSO (1:1 v/v) solution. The largest association constant was found for ox2− with Cu2[32](DBF)2N64+, whereas for the aromatic dicarboxylate anions the binding constants follow the trend ph2− > iph2− > tph2−, i.e. decrease with the increase of the distance of the two binding sites of the substrate. On the other hand, the large blue shift of 68 nm observed by addition of Him to Cu2[32](DBF)2N64+ points out for the formation of the bridged CuimCu cascade complex, indicating this receptor as a potential sensor for the detection and determination of imidazole in solution. The X-band EPR spectra of the Cu2[28](DBF)2N64+ and Cu2[32](DBF)2N6]4+ complexes and the cascade complexes with the substrates, performed in H2O:DMSO (1:1 v/v) at 5 to 15 K, showed that the CuCu distance is slightly larger than the one found in crystal state and that this distance increases when the substrate is accommodated between the two copper centres. The crystal structure of [Cu2[28](DBF)2N6(ph)2]·CH3OH was determined by X-ray diffraction and revealed the two copper centres bridged by two ph2− anions at a Cu···Cu distance of 5.419(1) Å. Each copper centre is surrounded by three carboxylate oxygen atoms from two phthalate anions and three contiguous nitrogen atoms of the macrocycle in a pseudo octahedral coordination environment.

An adaptive linear equalizer with optimum filter length and decision delay

The power of an adaptive equalizer is maximized when the structural parameters including the tap-length and decision delay can be optimally chosen. Although the method for adjusting either the tap-length or decision delay has been proposed, adjusting both simultaneously becomes much more involved as they interact with each other. In this paper, this problem is solved by putting a linear prewhitener before the equalizer, with which the equivalent channel becomes maximum-phase. This implies that the optimum decision delay can be simply ¯xed at the tap-length minus one, while the tap-length can then be chosen using a similar approach as that proposed in our previous work.

Emotion processing in infancy: specificity in risk for social anxiety and associations with two year outcomes

The current study examined the specificity of patterns of responding to high and low intensity negative emotional expressions of infants of mothers with social phobia, and their association with child outcomes at two years of age. Infants of mothers with social phobia, generalised anxiety disorder (GAD) or no history of anxiety were shown pairs of angry and fearful emotional expressions at 10 weeks of age. Symptoms of social withdrawal, anxiety and sleep problems were assessed at two years of age. Only infants of mothers with social phobia showed a tendency to look away from high intensity fear faces; however infants of mothers with both social phobia and GAD showed a bias towards high intensity angry faces. Among the offspring of mothers with social phobia, anxiety symptoms at two years of age were associated with a preference for high intensity fear faces in infancy. The reverse pattern was found amongst the offspring of non-anxious mothers. These findings suggest a possible specific response to emotional expressions among the children of mothers with social phobia.

Knowledge of A/A'-dependencies on subject extraction with two types of infinitives in non-native Portuguese adult bilingualism

Within generative L2 acquisition research there is a longstanding debate as to what underlies observable differences in L1/L2 knowledge/ performance. On the one hand, Full Accessibility approaches maintain that target L2 syntactic representations (new functional categories and features) are acquirable (e.g., Schwartz & Sprouse, 1996). Conversely, Partial Accessibility approaches claim that L2 variability and/or optionality, even at advanced levels, obtains as a result of inevitable deficits in L2 narrow syntax and is conditioned upon a maturational failure in adulthood to acquire (some) new functional features (e.g., Beck, 1998; Hawkins & Chan, 1997; Hawkins & Hattori, 2006; Tsimpli & Dimitrakopoulou, 2007). The present study tests the predictions of these two sets of approaches with advanced English learners of L2 Brazilian Portuguese (n = 21) in the domain of inflected infinitives. These advanced L2 learners reliably differentiate syntactically between finite verbs, uninflected and inflected infinitives, which, as argued, only supports Full Accessibility approaches. Moreover, we will discuss how testing the domain of inflected infinitives is especially interesting in light of recent proposals that Brazilian Portuguese colloquial dialects no longer actively instantiate them (Lightfoot, 1991; Pires, 2002, 2006; Pires & Rothman, 2009; Rothman, 2007).

A comparison of tests of non-linear cointegration with an application to the predictability of US interest rates using the term structure

We test whether there are nonlinearities in the response of short- and long-term interest rates to the spread in interest rates, and assess the out-of-sample predictability of interest rates using linear and nonlinear models. We find strong evidence of nonlinearities in the response of interest rates to the spread. Nonlinearities are shown to result in more accurate short-horizon forecasts, especially of the spread.

[C7H10N][In3Se5]: a layered selenide with two indium coordination environments

A new layered indium selenide, [C7H10N][In3Se5], was prepared under solvothermal conditions using 3,5-dimethylpyridine as a structure-directing agent. The crystal structure contains anionic layers of stoichiometry [In3Se5]− in which indium atoms with octahedral and tetrahedral coordination coexist. This material represents the first occurrence of octahedrally coordinated indium in a solvothermally-prepared indium selenide.

Two-point boundary value problems for linear evolution equations

We study boundary value problems for a linear evolution equation with spatial derivatives of arbitrary order, on the domain 0 < x < L, 0 < t < T, with L and T positive nite constants. We present a general method for identifying well-posed problems, as well as for constructing an explicit representation of the solution of such problems. This representation has explicit x and t dependence, and it consists of an integral in the k-complex plane and of a discrete sum. As illustrative examples we solve some two-point boundary value problems for the equations iqt + qxx = 0 and qt + qxxx = 0.

Understanding mixing efficiency in the oceans. Do the nonlinearities of the equation of state matter?

There exist two central measures of turbulent mixing in turbulent stratified fluids that are both caused by molecular diffusion: 1) the dissipation rate D(APE) of available potential energy APE; 2) the turbulent rate of change Wr, turbulent of background gravitational potential energy GPEr. So far, these two quantities have often been regarded as the same energy conversion, namely the irreversible conversion of APE into GPEr, owing to the well known exact equality D(APE)=Wr, turbulent for a Boussinesq fluid with a linear equation of state. Recently, however, Tailleux (2009) pointed out that the above equality no longer holds for a thermally-stratified compressible, with the ratio ξ=Wr, turbulent/D(APE) being generally lower than unity and sometimes even negative for water or seawater, and argued that D(APE) and Wr, turbulent actually represent two distinct types of energy conversion, respectively the dissipation of APE into one particular subcomponent of internal energy called the "dead" internal energy IE0, and the conversion between GPEr and a different subcomponent of internal energy called "exergy" IEexergy. In this paper, the behaviour of the ratio ξ is examined for different stratifications having all the same buoyancy frequency N vertical profile, but different vertical profiles of the parameter Υ=α P/(ρCp), where α is the thermal expansion coefficient, P the hydrostatic pressure, ρ the density, and Cp the specific heat capacity at constant pressure, the equation of state being that for seawater for different particular constant values of salinity. It is found that ξ and Wr, turbulent depend critically on the sign and magnitude of dΥ/dz, in contrast with D(APE), which appears largely unaffected by the latter. These results have important consequences for how the mixing efficiency should be defined and measured in practice, which are discussed.

On integral equation and least squares methods for scattering by diffraction gratings

In this paper we consider the scattering of a plane acoustic or electromagnetic wave by a one-dimensional, periodic rough surface. We restrict the discussion to the case when the boundary is sound soft in the acoustic case, perfectly reflecting with TE polarization in the EM case, so that the total field vanishes on the boundary. We propose a uniquely solvable first kind integral equation formulation of the problem, which amounts to a requirement that the normal derivative of the Green's representation formula for the total field vanish on a horizontal line below the scattering surface. We then discuss the numerical solution by Galerkin's method of this (ill-posed) integral equation. We point out that, with two particular choices of the trial and test spaces, we recover the so-called SC (spectral-coordinate) and SS (spectral-spectral) numerical schemes of DeSanto et al., Waves Random Media, 8, 315-414 1998. We next propose a new Galerkin scheme, a modification of the SS method that we term the SS* method, which is an instance of the well-known dual least squares Galerkin method. We show that the SS* method is always well-defined and is optimally convergent as the size of the approximation space increases. Moreover, we make a connection with the classical least squares method, in which the coefficients in the Rayleigh expansion of the solution are determined by enforcing the boundary condition in a least squares sense, pointing out that the linear system to be solved in the SS* method is identical to that in the least squares method. Using this connection we show that (reflecting the ill-posed nature of the integral equation solved) the condition number of the linear system in the SS* and least squares methods approaches infinity as the approximation space increases in size. We also provide theoretical error bounds on the condition number and on the errors induced in the numerical solution computed as a result of ill-conditioning. Numerical results confirm the convergence of the SS* method and illustrate the ill-conditioning that arises.