Cup and cap products in intersection (co)homology

We construct cup and cap products in intersection (co)homology with field coefficients. The existence of the cap product allows us to give a new proof of Poincaré duality in intersection (co)homology which is similar in spirit to the usual proof for ordinary (co)homology of manifolds.     

Improving motion estimation by accounting for local image distortion

Cardiac elastography is a useful diagnostic technique for detection of heart function abnormalities, based on analysis of echocardiograms. The analysis of the regional heart motion allows assessing the extent of myocardial ischemia and infarction. In this paper, a new two-stage algorithm for cardiac motion estimation is proposed, where the data is taken from a sequence of 2D echocardiograms. The method combines the advantages of block-matching and optical flow techniques. The first stage employs a standard block-matching algorithm (sum of absolute differences) to provide a displacement estimate with accuracy of up to one pixel. At the second stage, this estimate is corrected by estimating the parameters of a local image transform within a test window. The parameters of the image transform are estimated in the least-square sense. In order to account for typical heart motions, like contraction/expansion, translation and rotation, a local affine model is assumed within the test window. The accuracy of the new algorithm is evaluated using a sequence of 500 grayscale B-mode images, which are generated as distorted, but known copies of an original ROI, taken from a real echocardiogram. The accuracy of the motion estimation is expressed in terms of errors: maximum absolute error, root-mean-square error, average error and standard deviation. The errors of the proposed algorithm are compared with these of the known block-matching technique with cross-correlation and interpolation in the sub-pixel space. Statistical analysis of the errors shows that the proposed algorithm provides more accurate estimates of the heart motion than the cross-correlation technique with interpolation in the sub-pixel space.     

Some graphs with small second eigenvalue

For any prime,p, we construct a Cayley graph on the group,G, of affine linear transformations ofℤ/pℤ of degree 2(p−1) and second eigenvalue with the following special property: the adjacency matrix of the graph is supported on the “blocks” associated to the trivial representation and the irreducible representation of sizep−1. SinceG is of orderp(p−1), the correspondingt-uniform Cayley hypergraph has essentially optimal second eigenvalue for this degree and size of the graph (see [2] for definitions). En route we give, for any integerk>1, a simple Cayley graph onp ^k nodes of degreep of second eigenvalue . The author wishes to acknowledge the National Science Foundation for supporting this research in part under Grant CCR-8858788, and the Office of Naval Research under Grant N00014-87-K-0467.     

Thermal multifragmentation in p + Au interactions at 2.16, 3.6 and 8.1 GeV incident energies

Multiple emission of intermediate-mass fragments has been studied for the collisions p + Au at 2.16, 3.6 and 8.1 GeV with the FASA setup. The mean IMF multiplicities for events with at least one IMF are equal to 1.7, 1.9 and 2.1 (±0.2) respectively. The multiplicity, charge distributions and kinetic energy spectra of IMF are described in the framework of a intranuclear cascade model followed by the statistical multifragmentation model. However, between the two parts of the calculation the excitation energies and the residual masses and charges are modified to take into account the losses during expansion. The results support a scenario of true thermal multifragmentation of a hot and expanded target spectator. Received: 15 December 1997 / Revised version: 24 April 1998     

Rank one lightly mixing

A rank one transformationT was constructed by Chacón that is weakly mixing but not mixing. We will show thatT is lightly mixing, not partially mixing, and not lightly 2-mixing. Partially supported by an NSF Postdoctoral Research Fellowship.