Smooth Regrading of Discretized Data

Methods for producing nonuniform transformations, or regradings, of discrete data are discussed. The transformations are useful in image processing, principally for enhancement and normalization of scenes. Regradings which “equidistribute” the histogram of the data, that is, which transform it into a constant function, are determined. Techniques for smoothing the regrading, dependent upon a continuously variable parameter, are presented. Generalized methods for constructing regradings such that the histogram of the data is transformed into any prescribed function are also discussed. Numerical algorithms for implementing the procedures and applications to specific examples are described.

Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the $p$-version

Plane wave discontinuous Galerkin (PWDG) methods are a class of Trefftz-type methods for the spatial discretization of boundary value problems for the Helmholtz operator $-\Delta-\omega^2$, $\omega>0$. They include the so-called ultra weak variational formulation from [O. Cessenat and B. Després, SIAM J. Numer. Anal., 35 (1998), pp. 255–299]. This paper is concerned with the a priori convergence analysis of PWDG in the case of $p$-refinement, that is, the study of the asymptotic behavior of relevant error norms as the number of plane wave directions in the local trial spaces is increased. For convex domains in two space dimensions, we derive convergence rates, employing mesh skeleton-based norms, duality techniques from [P. Monk and D. Wang, Comput. Methods Appl. Mech. Engrg., 175 (1999), pp. 121–136], and plane wave approximation theory.

A matrix iteration for dynamic network summaries

We propose a new algorithm for summarizing properties of large-scale time-evolving networks. This type of data, recording connections that come and go over time, is being generated in many modern applications, including telecommunications and on-line human social behavior. The algorithm computes a dynamic measure of how well pairs of nodes can communicate by taking account of routes through the network that respect the arrow of time. We take the conventional approach of downweighting for length (messages become corrupted as they are passed along) and add the novel feature of downweighting for age (messages go out of date). This allows us to generalize widely used Katz-style centrality measures that have proved popular in network science to the case of dynamic networks sampled at non-uniform points in time. We illustrate the new approach on synthetic and real data.

Inverse problems in neural field theory

We study inverse problems in neural field theory, i.e., the construction of synaptic weight kernels yielding a prescribed neural field dynamics. We address the issues of existence, uniqueness, and stability of solutions to the inverse problem for the Amari neural field equation as a special case, and prove that these problems are generally ill-posed. In order to construct solutions to the inverse problem, we first recast the Amari equation into a linear perceptron equation in an infinite-dimensional Banach or Hilbert space. In a second step, we construct sets of biorthogonal function systems allowing the approximation of synaptic weight kernels by a generalized Hebbian learning rule. Numerically, this construction is implemented by the Moore–Penrose pseudoinverse method. We demonstrate the instability of these solutions and use the Tikhonov regularization method for stabilization and to prevent numerical overfitting. We illustrate the stable construction of kernels by means of three instructive examples.

Diversity of strains of Salmonella enterica serotype Enteritidis from English poultry farms assessed by multiple genetic fingerprinting

Reliable and sufficiently discriminative methods are needed for differentiating individual strains of Salmonella enterica serotype Enteritidis beyond the phenotypic level; however, a consensus has not been reached as to which molecular method is best suited for this purpose. In addition, data are lacking on the molecular fingerprinting of serotype Enteritidis from poultry environments in the United Kingdom. This study evaluated the combined use of classical methods (phage typing) with three well-established molecular methods (ribotyping, macrorestriction analysis of genomic DNA, and plasmid profiling) in the assessment of diversity within 104 isolates of serotype Enteritidis from eight unaffiliated poultry farms in England. The most sensitive technique for identifying polymorphism was PstI-SphII ribotyping, distinguishing a total of 22 patterns, 10 of which were found among phage type 4 isolates. Pulsed-field gel electrophoresis of XhaI-digested genomic DNA segregated the isolates into only six types with minor differences between them. In addition, 14 plasmid profiles were found among this population. When all of the typing methods were combined, 54 types of strains were differentiated, and most of the poultry farms presented a variety of strains, which suggests that serotype Enteritidis organisms representing different genomic groups are circulating in England. In conclusion, geographical and animal origins of Salmonella serotype Enteritidis isolates may have a considerable influence on selecting the best typing strategy for individual programs, and a single method cannot be relied on for discriminating between strains.

Molecular typing of Salmonella serotypes prevalent in animals in England: assessment of methodology

Salmonella enterica serotypes Derby, Mbandaka, Montevideo, Livingstone, and Senftenberg were among the 10 most prevalent serotypes isolated from farm animals in England and Wales in 1999. These serotypes are of potential zoonotic relevance; however, there is currently no "gold standard" fingerprinting method for them. A collection of isolates representing the former serotypes and serotype Gold Coast were analyzed using plasmid profiling, pulsed-field gel electrophoresis (PFGE), and ribotyping. The success of the molecular methods in identifying DNA polymorphisms was different for each serotype. Plasmid profiling was particularly useful for serotype Derby isolates, and it also provided a good level of discrimination for serotype Senftenberg. For most serotypes, we observed a number of nontypeable plasmid-free strains, which represents a limitation of this technique. Fingerprinting of genomic DNA by ribotyping and PFGE produced a significant variation in results, depending on the serotype of the strain. Both PstI/SphI ribotyping and XbaI-PFGE provided a similar degree of strain differentiation for serotype Derby and serotype Senftenberg, only marginally lower than that achieved by plasmid profiling. Ribotyping was less sensitive than PFGE when applied to serotype Mbandaka or serotype Montevideo. Serotype Gold Coast isolates were found to be nontypeable by XbaI-PFGE, and a significant proportion of them were found to be plasmid free. A similar situation applies to a number of serotype Livingstone isolates which were nontypeable by plasmid profiling and/or PFGE. In summary, the serotype of the isolates has a considerable influence in deciding the best typing strategy; a single method cannot be relied upon for discriminating between strains, and a combination of typing methods allows further discrimination.

Use of a LightCycler gyrA mutation assay for rapid identification of mutations conferring decreased susceptibility to ciprofloxacin in multiresistant Salmonella enterica serotype typhimurium DT104 isolates

A LightCycler-based PCR-hybridization gyrA mutation assay (GAMA) was developed to rapidly detect gyrA point mutations in multiresistant (MR) Salmonella enterica serotype Typhimurium DT104 with decreased susceptibility to ciprofloxacin (MIC, 0.25 to 1.0 mg/liter). Ninety-two isolates (49 human, 43 animal) were tested with three individual oligonucleotide probes directed against an Asp-87-to-Asn (GAC --> AAC) mutation, an Asp-87-to-Gly (GAC --> GGC) mutation, and a Ser-83-to-Phe (TCC --> TTC) mutation. Strains homologous to the probes could be distinguished from strains that had different mutations by their probe-target melting temperatures. Thirty-seven human and 30 animal isolates had an Asp-87-to-Asn substitution, 6 human and 6 animal isolates had a Ser-83-to-Phe substitution, and 5 human and 2 animal isolates had an Asp-87-to-Gly substitution. The remaining six strains all had mismatches with the three probes and therefore different gyrA mutations. The sequencing of gyrA from these six isolates showed that one human strain and two animal strains had an Asp-87-to-Tyr (GAC --> TAC) substitution and two animal strains had a Ser-83-to-Tyr (TCC --> TAC) substitution. One animal strain had no gyrA mutation, suggesting that this isolate had a different mechanism of resistance. Fifty-eight of the strains tested were indistinguishable by several different typing methods including antibiograms, pulsed-field gel gel electrophoresis, and plasmid profiling, although they could be further subdivided according to gyrA mutation. This study confirmed that MR DT104 with decreased susceptibility to ciprofloxacin from humans and food animals in England and Wales may have arisen independently against a background of clonal spread of MR DT104.

Combined use of two genetic fingerprinting methods, pulsed-field gel electrophoresis and ribotyping, for characterization of Escherichia coli O157 isolates from food animals, retail meats, and cases of human disease

Two genetic fingerprinting techniques, pulsed-field gel electrophoresis (PFGE) and ribotyping, were used to characterize 207 Escherichia coli O157 isolates from food animals, foods of animal origin, and cases of human disease (206 of the isolates were from the United Kingdom). In addition, 164 of these isolates were also phage typed. The isolates were divided into two general groups: (i) unrelated isolates not known to be epidemiologically linked (n = 154) and originating from food animals, foods and the environment, or humans and (ii) epidemiologically related isolates (n = 53) comprised of four related groups (RGs) originating either from one farm plus the abattoir where cattle from that farm were slaughtered or from one of three different English abattoirs. PFGE was conducted with the restriction endonuclease XbaI. while for ribotyping, two restriction endonucleases (PstI and SphI) were combined to digest genomic DNAs simultaneously. The 207 E. coli O157 isolates produced 97 PFGE profiles and 51 ribotypes. The two genetic fingerprinting methods had similar powers to discriminate the 154 epidemiologically unrelated E. coli O157 isolates in the study (Simpson's index of diversity [D] = 0.98 and 0.94 for PFGE typing and ribotyping, respectively). There was no correlation between the source of an isolate (healthy meat or milk animals, retail meats, or cases of human infection) and either particular PFGE or ribotype profiles or clusters. Combination of the results of both genetic fingerprinting methods produced 146 types, significantly more than when either of the two methods was used individually. Consequently, the superior discriminatory performance of the PFGE-ribotyping combination was proven in two ways: (i) by demonstrating that the majority of the E. coli O157 isolates with unrelated histories were indeed distinguishable types and (ii) by identifying some clonal groups among two of the four RGs of E. coli O157 isolates (comprising PFGE types different by just one or two bands), the relatedness of which would have remained unconfirmed otherwise.

Detection of gyrA mutations in quinolone-resistant Salmonella enterica by denaturing high-performance liquid chromatography

Denaturing high-performance liquid chromatography (DHPLC) was evaluated as a rapid screening and identification method for DNA sequence variation detection in the quinolone resistance-determining region of gyrA from Salmonella serovars. A total of 203 isolates of Salmonella were screened using this method. DHPLC analysis of 14 isolates representing each type of novel or multiple mutations and the wild type were compared with LightCycler-based PCR-gyrA hybridization mutation assay (GAMA) and single-strand conformational polymorphism (SSCP) analyses. The 14 isolates gave seven different SSCP patterns, and LightCycler detected four different mutations. DHPLC detected 11 DNA sequence variants at eight different codons, including those detected by LightCycler or SSCP. One of these mutations was silent. Five isolates contained multiple mutations, and four of these could be distinguished from the composite sequence variants by their DHPLC profile. Seven novel mutations were identified at five different loci not previously described in quinolone-resistant salmonella. DHPLC analysis proved advantageous for the detection of novel and multiple mutations. DHPLC also provides a rapid, high-throughput alternative to LightCycler and SSCP for screening frequently occurring mutations.

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.

(Non-)ergodicity of a degenerate diffusion modeling the fiber lay down process

We analyze the large time behavior of a stochastic model for the lay down of fibers on a moving conveyor belt in the production process of nonwovens. It is shown that under weak conditions this degenerate diffusion process has a unique invariant distribution and is even geometrically ergodic. This generalizes results from previous works [M. Grothaus and A. Klar, SIAM J. Math. Anal., 40 (2008), pp. 968–983; J. Dolbeault et al., arXiv:1201.2156] concerning the case of a stationary conveyor belt, in which the situation of a moving conveyor belt has been left open.

Scattering of electromagnetic waves by rough interfaces and inhomogeneous layers

We consider a two-dimensional problem of scattering of a time-harmonic electromagnetic plane wave by an infinite inhomogeneous conducting or dielectric layer at the interface between semi-infinite homogeneous dielectric half-spaces. The magnetic permeability is assumed to be a fixed positive constant. The material properties of the media are characterized completely by an index of refraction, which is a bounded measurable function in the layer and takes positive constant values above and below the layer, corresponding to the homogeneous dielectric media. In this paper, we examine only the transverse magnetic (TM) polarization case. A radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as an equivalent mixed system of boundary and domain integral equations, consisting of second-kind integral equations over the layer and interfaces within the layer. Assumptions on the variation of the index of refraction in the layer are then imposed which prove to be sufficient, together with the radiation condition, to prove uniqueness of solution and nonexistence of guided wave modes. Recent, general results on the solvability of systems of second kind integral equations on unbounded domains establish existence of solution and continuous dependence in a weighted norm of the solution on the given data. The results obtained apply to the case of scattering by a rough interface between two dielectric media and to many other practical configurations.

A uniqueness result for scattering by infinite rough surfaces

Consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane with an unbounded, piecewise Lyapunov boundary. This problem models time-harmonic electromagnetic scattering in transverse magnetic polarization by one-dimensional rough, perfectly conducting surfaces. A radiation condition is introduced for the problem, which is a generalization of the usual one used in the study of diffraction by gratings when the solution is quasi-periodic, and allows a variety of incident fields including an incident plane wave to be included in the results obtained. We show in this paper that the boundary value problem for the scattered field has at most one solution. For the case when the whole boundary is Lyapunov and is a small perturbation of a flat boundary we also prove existence of solution and show a limiting absorption principle.

Acoustic scattering by an inhomogeneous layer on a rigid plate

The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data.

Approximate solution of second kind integral equations on infinite cylindrical surfaces

The paper considers second kind integral equations of the form $\phi (x) = g(x) + \int_S {k(x,y)} \phi (y)ds(y)$ (abbreviated $\phi = g + K\phi $), in which S is an infinite cylindrical surface of arbitrary smooth cross section. The “truncated equation” (abbreviated $\phi _a = E_a g + K_a \phi _a $), obtained by replacing S by $S_a $, a closed bounded surface of class $C^2 $, the boundary of a section of the interior of S of length $2a$, is also discussed. Conditions on k are obtained (in particular, implying that K commutes with the operation of translation in the direction of the cylinder axis) which ensure that $I - K$ is invertible, that $I - K_a $ is invertible and $(I - K_a )^{ - 1} $ is uniformly bounded for all sufficiently large a, and that $\phi _a $ converges to $\phi $ in an appropriate sense as $a \to \infty $. Uniform stability and convergence results for a piecewise constant boundary element collocation method for the truncated equations are also obtained. A boundary integral equation, which models three-dimensional acoustic scattering from an infinite rigid cylinder, illustrates the application of the above results to prove existence of solution (of the integral equation and the corresponding boundary value problem) and convergence of a particular collocation method.