On the problems of object restoration and image extrapolation in optics

In this paper we consider the problems of object restoration and image extrapolation, according to the regularization theory of improperly posed problems. In order to take into account the stochastic nature of the noise and to introduce the main concepts of information theory, great attention is devoted to the probabilistic methods of regularization. The kind of the restored continuity is investigated in detail; in particular we prove that, while the image extrapolation presents a Hölder type stability, the object restoration has only a logarithmic continuity. © 1979 American Institute of Physics.

Sorting under partial information (without the ellipsoid algorithm)

We revisit the well-known problem of sorting under partial information: sort a finite set given the outcomes of comparisons between some pairs of elements. The input is a partially ordered set P, and solving the problem amounts to discovering an unknown linear extension of P, using pairwise comparisons. The information-theoretic lower bound on the number of comparisons needed in the worst case is log e(P), the binary logarithm of the number of linear extensions of P. In a breakthrough paper, Jeff Kahn and Jeong Han Kim (STOC 1992) showed that there exists a polynomial-time algorithm for the problem achieving this bound up to a constant factor. Their algorithm invokes the ellipsoid algorithm at each iteration for determining the next comparison, making it impractical. We develop efficient algorithms for sorting under partial information. Like Kahn and Kim, our approach relies on graph entropy. However, our algorithms differ in essential ways from theirs. Rather than resorting to convex programming for computing the entropy, we approximate the entropy, or make sure it is computed only once in a restricted class of graphs, permitting the use of a simpler algorithm. Specifically, we present: an O(n2) algorithm performing O(log n·log e(P)) comparisons; an O(n2.5) algorithm performing at most (1+ε) log e(P) + Oε(n) comparisons; an O(n2.5) algorithm performing O(log e(P)) comparisons. All our algorithms are simple to implement. © 2010 ACM.

Exploring the benefits of using multi-touch devices in performing information search tasks: An analysis in terms of performance, cognitive load and task engagement

Over the last decade, multi-touch devices (MTD) have spread in a range of contexts. In the learning context, MTD accessibility leads more and more teachers to use them in their classroom, assuming that it will improve the learning activities. Despite a growing interest, only few studies have focused on the impacts of MTD use in terms of performance and suitability in a learning context.However, even if the use of touch-sensitive screens rather than a mouse and keyboard seems to be the easiest and fastest way to realize common learning tasks (as for instance web surfing), we notice that the use of MTD may lead to a less favorable outcome. More precisely, tasks that require users to generate complex and/or less common gestures may increase extrinsic cognitive load and impair performance, especially for intrinsically complex tasks. It is hypothesized that task and gesture complexity will affect users’ cognitive resources and decrease task efficacy and efficiency. Because MTD are supposed to be more appealing, it is assumed that it will also impact cognitive absorption. The present study also takes into account user’s prior knowledge concerning MTD use and gestures by using experience with MTD as a moderator. Sixty university students were asked to perform information search tasks on an online encyclopedia. Tasks were set up so that users had to generate the most commonly used mouse actions (e.g. left/right click, scrolling, zooming, text encoding…). Two conditions were created: MTD use and laptop use (with mouse and keyboard) in order to make a comparison between the two devices. An eye tracking device was used to measure user’s attention and cognitive load. Our study sheds light on some important aspects towards the use of MTD and the added value compared to a laptop in a student learning context.