The inverse electromagnetic scattering problem in a piecewise homogeneous medium

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation method. Inspired by a novel idea developed by Hahner [11], we prove that the penetrable interface between layers can be uniquely determined from a knowledge of the electric far field pattern for incident plane waves. Then, using the idea developed by Liu and Zhang [21], a new mixed reciprocity relation is obtained and used to show that the impenetrable obstacle with its physical property can also be recovered. Note that the wave numbers in the corresponding medium may be different and therefore this work can be considered as a generalization of the uniqueness result of [20].Comment: 19 pages, 2 figures, submitted for publicatio

"Oxide-free" tip for scanning tunneling microscopy

We report a new tip for scanning tunneling microscopy and a tip repair procedure that allows one to reproducibly obtain atomic images of highly oriented pyrolytic graphite with previously inoperable tips. The tips are shown to be relatively oxide-free and highly resistant to oxidation. The tips are fabricated with graphite by two distinct methods

On the Convergence of the Born Series in Optical Tomography with Diffuse Light

We provide a simple sufficient condition for convergence of Born series in the forward problem of optical diffusion tomography. The condition does not depend on the shape or spatial extent of the inhomogeneity but only on its amplitude.Comment: 23 pages, 7 figures, submitted to Inverse Problem

Convergence and Stability of the Inverse Scattering Series for Diffuse Waves

We analyze the inverse scattering series for diffuse waves in random media. In previous work the inverse series was used to develop fast, direct image reconstruction algorithms in optical tomography. Here we characterize the convergence, stability and approximation error of the serie

Plasticity of face processing in infancy

Experience plays a crucial role for the normal development of many perceptual and cognitive functions, such as speech perception. For example, between 6 and 10 months of age, the infant's ability to discriminate among native speech sounds improves, whereas the ability to discriminate among foreign speech sounds declines. However, a recent investigation suggests that some experience with nonnative languages from 9 months of age facilitates the maintenance of this ability at 12 months. Nelson has suggested that the systems underlying face processing may be similarly sculpted by experience with different kinds of faces. In the current investigation, we demonstrate that, in human infants between 6 and 9 months of age, exposure to nonnative faces, in this case, faces of Barbary macaques (Macaca sylvanus), facilitates the discrimination of monkey faces, an ability that is otherwise lost around 9 months of age. These data support, and further elucidate, the role of early experience in the development of face processing

Some Empirical Criteria for Attributing Creativity to a Computer Program

Peer reviewedPostprin

Faster Approximate String Matching for Short Patterns

We study the classical approximate string matching problem, that is, given strings $P$ and $Q$ and an error threshold $k$, find all ending positions of substrings of $Q$ whose edit distance to $P$ is at most $k$. Let $P$ and $Q$ have lengths $m$ and $n$, respectively. On a standard unit-cost word RAM with word size $w \geq \log n$ we present an algorithm using time $$O(nk \cdot \min(\frac{\log^2 m}{\log n},\frac{\log^2 m\log w}{w}) + n)$$ When $P$ is short, namely, $m = 2^{o(\sqrt{\log n})}$ or $m = 2^{o(\sqrt{w/\log w})}$ this improves the previously best known time bounds for the problem. The result is achieved using a novel implementation of the Landau-Vishkin algorithm based on tabulation and word-level parallelism.Comment: To appear in Theory of Computing System

Confidentiality and public protection: ethical dilemmas in qualitative research with adult male sex offenders

This paper considers the ethical tensions present when engaging in in-depth interviews with convicted sex offenders. Many of the issues described below are similar to those found in other sensitive areas of research. However, confidentiality and public protection are matters that require detailed consideration when the desire to know more about men who have committed serious and harmful offences is set against the possibility of a researcher not disclosing previously unknown sensitive information that relates to the risk of someone being harmed.</p

Inverting the Sachs-Wolfe Formula: an Inverse Problem Arising in Early-Universe Cosmology

The (ordinary) Sachs-Wolfe effect relates primordial matter perturbations to the temperature variations $\delta T/T$ in the cosmic microwave background radiation; $\delta T/T$ can be observed in all directions around us. A standard but idealised model of this effect leads to an infinite set of moment-like equations: the integral of $P(k) j_\ell^2(ky)$ with respect to k ($0<k<\infty$) is equal to a given constant, $C_\ell$, for $\ell=0,1,2,...$. Here, P is the power spectrum of the primordial density variations, $j_\ell$ is a spherical Bessel function and y is a positive constant. It is shown how to solve these equations exactly for ~$P(k)$. The same solution can be recovered, in principle, if the first ~m equations are discarded. Comparisons with classical moment problems (where $j_\ell^2(ky)$ is replaced by $k^\ell$) are made.Comment: In Press Inverse Problems 1999, 15 pages, 0 figures, Late