Through the study of Morse theory on the associated Milnor fiber, we show that complex hyperplane arrangement complements are minimal. That is, the complement of any complex hyperplane arrangement has the homotopy type of a CW-complex in which the number of p-cells equals the p-th betti number. Combining this result with recent work of Papadima and Suciu, one obtains a characterization of when ...

We introduce a scheme for optimally allocating a variable number of bits per LSH hyperplane. Previous approaches assign a constant number of bits per hyperplane. This neglects the fact that a subset of hyperplanes may be more informative than others. Our method, dubbed Variable Bit Quantisation (VBQ), provides a datadriven non-uniform bit allocation across hyperplanes. Despite only using a frac...

The conventional decision feedback equalizer (DFE) separates the different signal classes using a single hyperplane. It is well known that the popular minimum mean square error (MMSE) design is generally not the optimal minimum bit error rate (MBER) solution. We propose a method of designing the separating hyperplane for the conventional DFE based on support vector machines (SVMs). The SVM desi...

ÐHager and Belhumeur [6] recently proposed a general framework for object tracking in video images. It consists of low-order parametric models for the image motion of a target region. These models are used to predict movement and to track the target. The difference in intensity between the pixels belonging to the current region and the pixels of the selected target (learned during an offline st...

We give a generalization of the theorem of Bondal and Orlov about the derived categories of coherent sheaves on intersections of quadrics revealing its relation to projective duality. As an application we describe the derived categories of coherent sheaves on Fano 3-folds of index 1 and degrees 12, 16 and 18.

We explore a novel approach to upper bound the misclassification error for problems with data comprising a small number of positive samples and a large number of negative samples. We assign the hinge-loss to upper bound the misclassification error of the positive examples and use the minimax risk to upper bound the misclassification error with respect to the worst case distribution that generat...

In this article there are two main results. The first result gives a formula, in terms of a log resolution, for the graded pieces of the Hodge filtration on the cohomology of a unitary local system of rank one on the complement of an arbitrary divisor in a smooth projective complex variety. The second result is an application of the first. We give a combinatorial formula for the spectrum of a h...

Let C be the set of chambers of a real hyperplane arrangement. We study a random walk on C introduced by Bidigare, Hanlon, and Rockmore. This includes various shuuing schemes used in computer science, biology, and card games. It also includes random walks on zonotopes and zonotopal tilings. We nd the stationary distributions of these Markov chains, give good bounds on the rate of convergence to...

Let Sd be a d-dimensional simplex in Rd , and let H be an affine hyperplane of Rd . We say that H is a medial hyperplane of Sd if the distance between H and any vertex of Sd is the same constant. The intersection of Sd and a medial hyperplane is called a medial section of Sd . In this paper we give a simple formula for the (d − 1)-volume of any medial section of Sd in terms of the lengths of th...

We investigate some topological and geometric properties of the set R of all refinable functions in L(R), and of the set of all MRA affine frames. We prove that R is nowhere dense in L(R); the unit sphere of R is path-connected in the L-norm; and for any M -dimensional hyperplane generated by L-functions f0, . . . , fM , either almost all the functions in the hyperplane are refinable or almost ...