Abstract For each central essential hyperplane arrangement $\mathcal{A}$ over an algebraically closed field, let $Z_\mathcal{A}^{\hat\mu}(T)$ denote the Denef–Loeser motivic zeta function of . We prove a formula expressing in terms Milnor fibers related arrangements. This shows that, precise sense, degree to which $Z_{\mathcal{A}}^{\hat\mu}(T)$ fails be combinatorial invariant is completely con...

We develop the rst nontrivial lower bounds on the complexity of online hyperplane and halfspace emptiness queries. Our lower bounds apply to a general class of geometric range query data structures called partition graphs. Informally, a partition graph is a directed acyclic graph that describes a recursive decomposition of space. We show that any partition graph that supports hyperplane emptine...

Audio event detection has become a hot research due to its wide applications in many fields, such as multimedia retrieval etc., the detection needs large amounts of labeled samples to train the audio event models, but in real life, the labeled samples are expensive to obtain, the shortage of such labeled samples is a big obstacle. Active learning is an efficient way to deal with the problem of ...

The homotopy Lie algebra of a complex hyperplane arrangement is not necessarily finitely presented. Abstract. We present a theory that produces several examples where the homotopy Lie algebra of a complex hyperplane arrangement is not finitely presented. This answers a question of Denham and Suciu.

A new evolutionary technique for multicriteria optimization called Target Hyperplane Evolutionary Algorithm (THEA) is proposed. The originality of the approach consists in the fact that the fitness assignment is realized by using a guiding hyperplane and a new non Pareto optimality concept. THEA has been tested on consecrated benchmarks.

Generalizing a result of Yoshinaga in dimension 3, we show that a central hyperplane arrangement in 4-space is free exactly if its restriction with multiplicities to a fixed hyperplane of the arrangement is free and its reduced characteristic polynomial equals the characteristic polynomial of this restriction. We show that the same statement holds true in any dimension when imposing certain tam...

In this survey we deal with the location of hyperplanes in n{ dimensional normed spaces, i.e., we present all known results and a unifying approach to the so-called median hyperplane problem in Minkowski spaces. We describe how to nd a hyperplane H minimizing the weighted sum f(H) of distances to a given, nite set of demand points. In robust statistics and operations research such an optimal hy...

In this report we show some simple properties of SVM for regression. In particular we show that for close to zero, minimizing the norm of w is equivalent to maximizing the distance between the optimal approximating hyperplane solution of SVMR and the closest points in the data set. So, in this case, there exists a complete analogy between SVM for regression and classiication, and the-tube plays...