Cluster analysis is a primary method for database mining. It is either used as a stand-alone tool to get insight into the distribution of a data set, e.g. to focus further analysis and data processing, or as a preprocessing step for other algorithms operating on the detected clusters. Almost all of the well-known clustering algorithms require input parameters which are hard to determine but have a significant influence on the clustering result. Furthermore, for many real-data sets there does not even exist a global parameter setting for which the result of the clustering algorithm describes the intrinsic clustering structure accurately. We introduce a new algorithm for the purpose of cluster analysis which does not produce a clustering of a data set explicitly; but instead creates an augmented ordering of the database representing its density-based clustering structure. This cluster-ordering contains information which is equivalent to the density-based clusterings corresponding to a broad range of parameter settings. It is a versatile basis for both automatic and interactive cluster analysis. We show how to automatically and efficiently extract not only ‘traditional ’ clustering information (e.g. representative points, arbitrary shaped clusters), but also the intrinsic clustering structure. For medium sized data sets, the cluster-ordering can be represented graphically and for very large data sets, we introduce an appropriate visualization technique. Both are suitable for interactive exploration of the intrinsic clustering structure offering additional insights into the distribution and correlation of the data.

This minicourse is an introduction to basic concepts and tools in group representation theory, both commutative and noncommutative, that are fundamental for the analysis of radar and sonar imaging. Several symmetry groups of physical interest will be studied (circle, line, rotation, ax + b, Heisenberg, etc.) together with their associated transforms and representation theories (DFT, Fourier transform, expansions in spherical harmonics, wavelets, etc.). Through the unifying concepts of group representation theory, familiar tools for commutative groups, such as the Fourier transform on the line, extend to transforms for the noncommutative groups which arise in radar-sonar. The insight and results obtained will be related directly to objects of interest in radar-sonar, such as the ambiguity function. The material will be presented with many examples and should be easily comprehensible by engineers and physicists, as well as mathematicians. *School of Mathematics and IMA, University of Minnesota. The research contribution of this paper was supported in part by the National Science Foundation under grant DMS 88--23054 Typeset by A M S-T E X 1 2 WILLARD MILLER JR.* TABLE OF CONTENTS 1.

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping “pictures”.

Medial prefrontal theta bursts precede rapid motor responses during visual selective attention Abbreviated Title: Medial prefrontal theta EEG preceding rapid responses.

In recent years, subdivision surfaces have come to the forefront of geometric modeling and design. They are currently in use in many production houses, and are slowly becoming commonplace in the computer gaming industry. Furthermore, subdivision surfaces are used extensively in the solution of partial di#erential equations using the finite element method. However, practitioners wishing to use subdivision surfaces are faced with choosing a scheme to suit their needs from the relatively small set of existing subdivision schemes. In this thesis,

Two methods for the identification of coherent structures in fluid flows are studied for possible combination in a hybrid method providing deeper insight and greater efficiency. One method uses wavelet transforms to partition the field into coherent and incoherent portions using a thresholding of the wavelet coefficients. The other method is based on the stability analysis of trajectories through the fluid, defining two type of Lagrangian coherent structures based on the degree hyperbolicity or ellipticity of the flow. It is hoped that computational efficiency of the wavelet method can be combined with the level of detail of the stability analysis to give a fast and insightful method for analyzing and identify coherent structures in a flow. Two types of tests are done to determine the feasibility of combining the two methods. The first test is used to determine the degree to which the coherent partition from the wavelet method agrees with the Lagrangian coherent structures of the stability analysis method. The second test is used to determine how

Abstract- This paper deals with the study of the spectral components of Lamb waves generated in thin aluminium plate using pulsed Nd-YAG laser and detected using a He-Ne Laser Heterodyne interferometer. Laser generation of Lamb waves leads to simultaneous generation of various frequency component as well as multiple Lamb wave modes. The Lamb wave signals are successfully and comprehensively analyzed using Wavelet transform technique. The velocities of various frequencies present in the Lamb wave signal are calculated and the experimental dispersion curve is plotted. The behavior of various frequency components with respect to reflection from plate ends is explained satisfactorily.

Abstract-This paper deals with the analysis of the pressure wave signals generated in an aluminium-stepped sample. The ultrasonic signals are generated using pulsed Nd-YAG laser and detected using a He-Ne Heterodyne interferometer. The pressure wave signals at constant laser power are recorded at various directions with respect to source laser direction and the intensity of various frequency components present in these pressure wave signals are estimated with the help of coefficient lines in theirs wavelet transforms. The variation of the intensity of individual frequency components with detection direction and the intensity variation with signal frequency at a given detection direction are studied and the results are presented. Key words: Laser generation, pressure waves, frequency spectrum. 1

1 On the use of continuous wavelet analysis for modal identification