, both in theory and in practice. The goal of this note is to give Hirschberg’s idea the visibility it deserves by developing a linear-space version of Gotoh’s algorithm, which accommodates affine gap penalties. A portable C-software package implementing this algorithm is available on the BIONET free

this paper. For simplicity, we follow the rules: x is a set, a, b are real numbers, V is a real linear space, W 1 , W 2 , W 3 are subspaces of V , v, v 1 , v 2 are vectors of V , A, B are subsets of the carrier of V , L, L 1 , L 2 are linear combinations of V , l is a linear combination of A, F , G

We define tropical analogues of the notions of linear space and Plücker coordinate and study their combinatorics. We introduce tropical analogues of intersection and dualization and define a tropical linear space built by repeated dualization and transverse intersection to be constructible. Our

wide variety of lighting conditions can be approximated accurately by a low-dimensional linear subspace, explaining prior empirical results. We also provide a simple analytic characterization of this linear space. We obtain these results by representing lighting using spherical harmonics and describing

We call a finite linear space regular, if all pencils of lines are similar. This means

of an undirect graph are presented. The space and time requirements of both algorithms are bounded by k 1V + k2E d- k for some constants kl, k2, and k a, where Vis the number of vertices and E is the number of edges of the graph being examined.

We present a new polynomial-time algorithm for linear programming. In the worst case, the algorithm requires O(tf'SL) arithmetic operations on O(L) bit numbers, where n is the number of variables and L is the number of bits in the input. The running,time of this algorithm is better than

bias, strict linear feature-space transformations are inappropriate in this case. Hence, only model-based linear transforms are considered. The paper compares the two possible forms of model-based transforms: (i) unconstrained, where any combination of mean and variance transform may be used, and (ii

of the space–time block code and gives a maximum-likelihood decoding algorithm which is based only on linear processing at the receiver. Space–time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple

of a particular face, under varying illumination but fixed pose, lie in a 3-D linear subspace of the high dimensional image space -- if the face is a Lambertian surface without shadowing. However, since faces are not truly Lambertian surfaces and do indeed produce self-shadowing, images will deviate