Curves on threefolds and a conjecture of Griffiths-Harris

We prove that any arithmetically Gorenstein curve on a smooth, general hypersurface of degree at least 6, is a complete intersection. This gives a characterisation of complete intersection curves on general type hypersurfaces in . We also verify that certain 1-cycles on a general quintic hypersurface are non-trivial elements of the Griffiths group.

Document page layout analysis using Harris corner points

Extraction of text areas from the document images with complex content and layout is one of the challenging tasks. Few texture based techniques have already been proposed for extraction of such text blocks. Most of such techniques are greedy for computation time and hence are far from being realizable for real time implementation. In this work, we propose a modification to two of the existing texture based techniques to reduce the computation. This is accomplished with Harris corner detectors. The efficiency of these two textures based algorithms, one based on Gabor filters and other on log-polar wavelet signature, are compared. A combination of Gabor feature based texture classification performed on a smaller set of Harris corner detected points is observed to deliver the accuracy and efficiency.

T. E. Harris and branching processes

T. E. Harris was a pioneer par excellence in many fields of probability theory. In this paper, we give a brief survey of the many fundamental contributions of Harris to the theory of branching processes, starting with his doctoral work at Princeton in the late forties and culminating in his fundamental book ``The Theory of Branching Processes,'' published in 1963.