Reflection anisotropy spectroscopy (RAS) is a non-destructive optical probe of surfaces that is capable of operation within a wide range of environments. In this review we trace the development of RAS from its origins in the 1980s as a probe of semiconductor surfaces and semiconductor growth through to the present where it is emerging as a powerful addition to the wide range of existing ultra-high vacuum (UHV) surface science techniques. The principles, instrumentation and theoretical considerations of RAS are discussed. The recent progress in the application of RAS to investigate phenomena at metal surfaces is reviewed, and applications in fields including electrochemistry, molecular assembly, liquid crystal device fabrication and remote stress sensing are discussed. We show that the experimental study of relatively simple surfaces combined with continuing progress in the theoretical description of surface optics promises to unlock the full potential of RAS. This provides a firm foundation for the application of the technique to the challenging fields of ambient, high pressure and liquid environments. It is in these environments that RAS has a clear advantage over UHVbased probes for investigating surface phenomena, and its surface sensitivity, ability to monitor macroscopic areas and rapidity of response make it an ideal complement to scanning probe techniques which can also operate in such environments.

No abstract

In the design and analysis of revenue-maximizing auctions, auction performance is typically measured with respect to a prior distribution over inputs. The most obvious source for such a distribution is past data. The goal of this paper is to understand how much data is necessary and sufficient to guarantee near-optimal expected revenue.Our basic model is a single-item auction in which bidders' valuations are drawn independently from unknown and nonidentical distributions. The seller is given m samples from each of these distributions "for free" and chooses an auction to run on a fresh sample. How large does m need to be, as a function of the number k of bidders and > 0, so that a (1 − )-approximation of the optimal revenue is achievable?We prove that, under standard tail conditions on the underlying distributions, m = poly(k, 1 ) samples are necessary and sufficient. Our lower bound stands in contrast to many recent results on simple and prior-independent auctions and fundamentally involves the interplay between bidder competition, non-identical distributions, and a very close (but still constant) approximation of the optimal revenue. It effectively shows that the only way to achieve a sufficiently good constant approximation of the optimal revenue is through a detailed understanding of bidders' valuation distributions. Our upper bound is constructive and applies in particular to a variant of the empirical Myerson auction, the natural auction that runs the revenue-maximizing auction with respect to the empirical distributions of the samples. To capture how our sample complexity upper bound depends on the set of allowable distributions, we introduce α-strongly regular distributions, which interpolate between the well-studied classes of regular (α = 0) and MHR (α = 1) distributions. We give evidence that this definition is of independent interest.

This paper considers various flavors of the following online problem: preprocess a text or collection of strings, so that given a query string p, all matches of p with the text can be reported quickly.In this paper we consider matches in which a bounded number of mismatches are allowed, or in which a bounded number of "don't care" characters are allowed.The specific problems we look at are: indexing, in which there is a single text t, and we seek locations where p matches a substring of t; dictionary queries, in which a collection of strings is given upfront, and we seek those strings which match p in their entirety; and dictionary matching, in which a collection of strings is given upfront, and we seek those substrings of a (long) p which match an original string in its entirety. These are all instances of an all-to-all matching problem, for which we provide a single solution.The performance bounds all have a similar character. For example, for the indexing problem with n = |t| and m = |p|, the query time for k substitutions is O(m + (c 1 log n) k k! + # matches), with a data structure of size O(n (c 2 log n) k k! ) and a preprocessing time of O(n (c 2 log n) k k!), where c1, c2 > 1 are constants. The deterministic preprocessing assumes a weakly nonuniform RAM model; this assumption is not needed if randomization is used in the preprocessing.