Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations

In this paper, we extend to the time-harmonic Maxwell equations the p-version analysis technique developed in [R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version, SIAM J. Numer. Anal., 49 (2011), 264-284] for Trefftz-discontinuous Galerkin approximations of the Helmholtz problem. While error estimates in a mesh-skeleton norm are derived parallel to the Helmholtz case, the derivation of estimates in a mesh-independent norm requires new twists in the duality argument. The particular case where the local Trefftz approximation spaces are built of vector-valued plane wave functions is considered, and convergence rates are derived.

Bayesian estimation of the spatial Durbin error model with an application to voter turnout in the 2004 presidential election

The potential for spatial dependence in models of voter turnout, although plausible from a theoretical perspective, has not been adequately addressed in the literature. Using recent advances in Bayesian computation, we formulate and estimate the previously unutilized spatial Durbin error model and apply this model to the question of whether spillovers and unobserved spatial dependence in voter turnout matters from an empirical perspective. Formal Bayesian model comparison techniques are employed to compare the normal linear model, the spatially lagged X model (SLX), the spatial Durbin model, and the spatial Durbin error model. The results overwhelmingly support the spatial Durbin error model as the appropriate empirical model.

Sensitivity and out-of-sample error in continuous time data assimilation

Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically though, these two requirements cannot both be met at the same time–tracking the observations is not possible without the trajectory deviating from the proposed model equations, while adherence to the model requires deviations from the observations. Thus, data assimilation faces a trade-off. In this contribution, the sensitivity of the data assimilation with respect to perturbations in the observations is identified as the parameter which controls the trade-off. A relation between the sensitivity and the out-of-sample error is established, which allows the latter to be calculated under operational conditions. A minimum out-of-sample error is proposed as a criterion to set an appropriate sensitivity and to settle the discussed trade-off. Two approaches to data assimilation are considered, namely variational data assimilation and Newtonian nudging, also known as synchronization. Numerical examples demonstrate the feasibility of the approach.

Spatial coding of touch at the fingers: Insights from double simultaneous stimulation within and between hands

We studied the effect of tactile double simultaneous stimulation (DSS) within and between hands to examine spatial coding of touch at the fingers. Participants performed a go/no-go task to detect a tactile stimulus delivered to one target finger (e.g., right index), stimulated alone or with a concurrent non-target finger, either on the same hand (e.g., right middle finger) or on the other hand (e.g., left index finger=homologous; left middle finger=non-homologous). Across blocks we also changed the unseen hands posture (both hands palm down, or one hand rotated palm-up). When both hands were palm-down DSS interference effects emerged both within and between hands, but only when the non-homologous finger served as non-target. This suggests a clear segregation between the fingers of each hand, regardless of finger side. By contrast, when one hand was palm-up interference effects emerged only within hand, whereas between hands DSS interference was considerably reduced or absent. Thus, between hands interference was clearly affected by changes in hands posture. Taken together, these findings provide behavioral evidence in humans for multiple spatial coding of touch during tactile DSS at the fingers. In particular, they confirm the existence of representational stages of touch that distinguish between body-regions more than body-sides. Moreover, they show that the availability of tactile stimulation side becomes prominent when postural update is required.

Resolution of sharp fronts in the presence of model error in variational data assimilation

We show that the four-dimensional variational data assimilation method (4DVar) can be interpreted as a form of Tikhonov regularization, a very familiar method for solving ill-posed inverse problems. It is known from image restoration problems that L1-norm penalty regularization recovers sharp edges in the image more accurately than Tikhonov, or L2-norm, penalty regularization. We apply this idea from stationary inverse problems to 4DVar, a dynamical inverse problem, and give examples for an L1-norm penalty approach and a mixed total variation (TV) L1–L2-norm penalty approach. For problems with model error where sharp fronts are present and the background and observation error covariances are known, the mixed TV L1–L2-norm penalty performs better than either the L1-norm method or the strong constraint 4DVar (L2-norm)method. A strength of the mixed TV L1–L2-norm regularization is that in the case where a simplified form of the background error covariance matrix is used it produces a much more accurate analysis than 4DVar. The method thus has the potential in numerical weather prediction to overcome operational problems with poorly tuned background error covariance matrices.

Isolation of Actinomyces hyovaginalis from sheep and comparison with isolates obtained from pigs

Actinomyces hyovaginalis, an organism initially described from pigs, was recovered from nine sheep and a moufflon. Further strains of A. hyovaginalis were recovered from five samples from pigs over the same period. 16S rRNA sequencing and extensive phenotyping demonstrated high similarity between the ovine and porcine isolates; however differences with respect to erythritol, adonitol and l-arabitol fermentation were detected. Ovine isolates were made from various sample sites including abscesses and highlight the importance of the accurate identification of the various coryneform isolates which affect sheep. A. hyovaginalis can be added to the growing list of coryneforms which can cause disease in sheep including Corynebacterium pseudotuberculosis, Trueperella pyogenes and Arcanobacterium pluranimalium.

Detection of Chlamydia psittaci DNA in avian clinical samples by polymerase chain reaction

A polymerase chain reaction (PCR) assay was developed to detect Chlamydia psittaci DNA in faeces and tissue samples from avian species. Primers were designed to amplify a 264 bp product derived from part of the 5' non-translated region and part of the coding region of the ompA gene which encodes the major outer membrane protein. Amplified sequences were confirmed by Southern hybridization using an internal probe. The sensitivity of the combined assay was found to be between 60 to 600 fg of chlamydial DNA (approximately 6 to 60 genome copies). The specificity of the assay was confirmed since PCR product was not obtained from samples containing several serotypes of C. trachomatis, strains of C. pneumoniae, the type strain of C. pecorum, nor from samples containing microorganisms commonly found in the avian gut flora. In this study, 404 avian faeces and 141 avian tissue samples received by the Central Veterinary Laboratory over a 6 month period were analysed by PCR, antigen detection ELISA and where possible, cell culture isolation. PCR performed favourably compared with ELISA and cell culture, or with ELISA alone. The PCR assay was especially suited to the detection of C. psittaci DNA in avian faeces samples. The test was also useful when applied to tissue samples from small contact birds associated with a case of human psittacosis where ELISA results were negative and chlamydial isolation was a less favourable method due to the need for rapid diagnosis.

Isolation from a sheep of an attaching and effacing Escherichia coli O115:H- with a novel combination of virulence factors

Attaching and effacing (AE) lesions were observed in the caecum, proximal colon and rectum of one of four lambs experimentally inoculated at 6 weeks. of age with Escherichia coli O157:H7. However, the attached bacteria did not immunostain with O157-specific antiserum. Subsequent bacteriological analysis of samples from this animal yielded two E. coli O115:H- strains, one from the colon (CO) and one from the rectum (RC), and those bacteria forming the AE lesions were shown to be of the O115 serogroup by immunostaining. The O115:H(-)isolates formed microcolonies and attaching and effacing lesions, as demonstrated by the fluorescence actin staining test, on HEp-2 tissue culture cells. Both isolates were confirmed by PCR to encode the epsilon (epsilon) subtype of intimin. Supernates of both O115:H- isolates induced cytopathic effects on Vero cell monolayers, and PCR analysis verified that both isolates encoded EAST1, CNF1 and CNF2 toxins but not Shiga-like toxins. Both isolates harboured similar sized plasmids but-PCR analysis indicated that only one of the O115:H- isolates (CO) possessed the plasmid-associated virulence determinants ehxA and etpD. Neither strain possessed the espP, katP or bfpA plasmid-associated virulence determinants. These E. coli O115:H- strains exhibited a novel combination of virulence determinants and are the first isolates found to possess both CNF1 and CNF2.

Isolation of recombinant antibodies against EspA and intimin of Escherichia coli O157:H7

Intimin, Tir, and EspA proteins are expressed by attaching-effacing Escherichia coli, which include enteropathogenic and enterohemorrhagic E. coli pathotypes. EspA proteins are part of the type three secretion system needle complex that delivers Tir to the host epithelial cell, while surface arrayed intimin docks the bacterium to the translocated Tir. This intimate attachment leads to attaching and effacing lesions. Recombinant forms of these effector proteins from enterohemorrhagic E. coli O157:H7 were produced by using E. coli expression vectors. Binding of intimin and Tir fragments in enzyme-linked immunosorbent assay (ELISAs) demonstrated the interaction of intimin fragments containing the C-terminal 282 or 188 amino acids to a Tir fragment containing amino acid residues 258 to 361. Recombinant intimin and EspA proteins were used to elicit immune responses in rabbits and immune phage-display antibody libraries were produced. Screening of these immune libraries by conventional phage-antibody panning and colony filter screening produced a panel of antibodies with specificity for EspA or intimin. Antibodies recognizing different C-terminal epitopes on intimin bound specifically to the gamma intimin of O157:H7 and not to other classes of intimin. Antibodies recognizing EspA from E. coli O157 also recognized the protein from the eae-deficient O157 mutant DM3 and from E. coli O111. Anti-intimin antibodies were also produced as fusion proteins coupled to the reporter molecule alkaline phosphatase, allowing the one-step detection of gamma intimin. The isolated recombinant monoclonal antibodies were functional in a range of assay formats, including ELISA, Western blotting, and dot blots, thus demonstrating their diagnostic potential.

Hetero-metallic trinuclear nickel(II)–cadmium(II) complexes of a salicylaldimine ligand with thiocyanate, cyanate and azide ions: isolation of a pair of polymorphs with thiocyanate ion

Four new trinuclear hetero-metallic nickel(II)-cadmium(II) complexes [(NiL)(2)Cd(NCS)(2)] (1A and 1B), [(NiL)(2)Cd(NCO)(2)] (2) and [(NiL)(2)Cd(N-3)(2)] (3) have been synthesized using [NiL] as a so-called "ligand complex" (where H2L = N,N'-bis(salicylidene)-1,3-propanediamine) and structurally characterized. Crystal structure analyses reveal that all four complexes contain a trinuclear moiety in which two square planar [NiL] units are bonded to a central cadmium(II) ion through double phenoxido bridges. The Cd(II) is in a six-coordinate distorted octahedral environment being bonded additionally to two mutually cis nitrogen atoms of terminal thiocyanate (in 1A and 1B), cyanate (in 2) and azide (in 3). Complexes 1A and 1B have the same molecular formula but crystallize in very different monoclinic unit cells and can be considered as polymorphs. On the other hand, the two isoelectronic complexes 2 and 3 are indeed isomorphous and crystallize only in one form. Their conformation is similar to that observed in 1A.

Nonlinear error dynamics for cycled data assimilation methods

We investigate the error dynamics for cycled data assimilation systems, such that the inverse problem of state determination is solved at tk, k = 1, 2, 3, ..., with a first guess given by the state propagated via a dynamical system model from time tk − 1 to time tk. In particular, for nonlinear dynamical systems that are Lipschitz continuous with respect to their initial states, we provide deterministic estimates for the development of the error ||ek|| := ||x(a)k − x(t)k|| between the estimated state x(a) and the true state x(t) over time. Clearly, observation error of size δ > 0 leads to an estimation error in every assimilation step. These errors can accumulate, if they are not (a) controlled in the reconstruction and (b) damped by the dynamical system under consideration. A data assimilation method is called stable, if the error in the estimate is bounded in time by some constant C. The key task of this work is to provide estimates for the error ||ek||, depending on the size δ of the observation error, the reconstruction operator Rα, the observation operator H and the Lipschitz constants K(1) and K(2) on the lower and higher modes of controlling the damping behaviour of the dynamics. We show that systems can be stabilized by choosing α sufficiently small, but the bound C will then depend on the data error δ in the form c||Rα||δ with some constant c. Since ||Rα|| → ∞ for α → 0, the constant might be large. Numerical examples for this behaviour in the nonlinear case are provided using a (low-dimensional) Lorenz '63 system.