Narrow Results

We study the $k$-error linear complexity of subsequences of the $d$-ary Sidel’nikov sequences over the prime field ${𝔽}_d$. A general lower bound for the $k$-error linear complexity is given. For several special periods, we show that these sequences have large $k$-error linear complexity.

The splitting of Quasi-Monte Carlo (QMC) point sequences into interleaved substreams has been suggested to raise the speed of distributed numerical integration and to lower the traffic on the network. The usefulness of this approach in GRID environments is discussed. After specifying requirements for using QMC techniques in GRID environments in general we review and evaluate the proposals made in literature so far. In numerical integration experiments we investigate the quality of single leaped QMC point sequence substreams, comparing the respective properties of Sobol', Halton, Faure, Niederreiter-Xing, and Zinterhof sequences in detail. Numerical integration results obtained on a distributed system show that leaping sensitivity varies tremendously among the different sequences and we provide examples of deteriorated results caused by leaping effects, especially in heterogeneous settings which would be expected in GRID environments.

One of the results of the surge in interest in the internet is the great increase in availability of pictorial and video data. Web browsers such as Netscape give access to an enormous range of such data. In order to make use of large amounts of pictorial and video data, it is necessary to develop indexing and retrieval methods.Pictorial databases have made great progress recently, to theextent that there are now a number of commercially available products. Video databases are now being researched and developed from a number ofdifferent viewpoints.Given a general indexing scheme for video, the next step is to reuse clipsin further applications.

In this paper we present an initial application for the reuse of video clips. The aim of the system is to resequence video clips for a particularapplication. We have chosen a well-constrained application for this purpose,the aim being to produce a video tour of a campus between designatedstart and destination points from a set of indexed videoclips. We use clips of a guide entering and leaving buildings on ourcampus, and when visitors select a start location and a destination, the systemwill retrieve clips suitable for guiding the visitor along the correct path.The system uses an index of spatial relationships of key objects for thevideo clips to decide which clips provide the correct sequence of motionaround the campus.

Although the full power of the indexing notation is unnecessary for this simple problem, the results from this initial implementation indicate that the concept could be applicable to more complex problems.

For a rotation by an irrational $\alpha$ on the circle and a BV function $\phi$, we study the variance of the ergodic sums $S_L\phi (x):={\sum }_{j=0}^{L-1}\phi (x+j\alpha )$. When $\alpha$ is not of constant type, we construct sequences $(L_N)$ such that, at some scale, the ergodic sums $S_{L_N}\phi$ satisfy an ASIP. Explicit non-degenerate examples are given with an application to the rectangular periodic billiard in the plane.

One of the results of the surge in interest in the internet is the great increase in availability of pictorial and video data. Web browsers such as Netscape give access to an enormous range of such data. In order to make use of large amounts of pictorial and video data, it is necessary to develop indexing and retrieval methods. Pictorial databases have made great progress recently, to the extent that there are now a number of commercially available products. Video databases are now being researched and developed from a number of different viewpoints. Given a general indexing scheme for video, the next step is to reuse clips in further applications.

In this paper we present an initial application for the reuse of video clips. The aim of the system is to resequence video clips for a particular application. We have chosen a well-constrained application for this purpose, the aim being to produce a video tour of a campus between designated start and destination points from a set of indexed video clips. We use clips of a guide entering and leaving buildings on our campus, and when visitors select a start location and a destination, the system will retrieve clips suitable for guiding the visitor along the correct path. The system uses an index of spatial relationships of key objects for the video clips to decide which clips provide the correct sequence of motion around the campus.

Although the full power of the indexing notation is unnecessary for this simple problem, the results from this initial implementation indicate that the concept could be applicable to more complex problems.