Early type galaxies (ETGs) are known to possess a number of quite useful scaling relations among their photometric and/or kinematical quantities. We propose a unified picture reducing both the fundamental plane and the photometric plane to suitable projections of a single relation. Modelling the ETG as a two component system, made out of a luminous Sersic profile and a NFW dark halo, and applyi...

Suppose ∆ is a fully embeddable thick dual polar space of rank n ≥ 3. It is known that a hyperplane H of ∆ is classical if all its nontrivial intersections with quads are classical. In order to conclude that a hyperplane H is classical, it is perhaps not necessary to require in advance that all these intersections are classical. In fact, in this paper we show that for dual polar spaces admittin...

Above, w ∈ Rd is a vector of real-valued weights, which we call a weight vector, and θ ∈ R is a threshold value. The weight vector (assuming it is non-zero) is perpendicular to a hyperplane of dimension that passes through the point wθ/‖w‖2; this hyperplane separates the points x ∈ Rd that are classified as +1 from those that are classified as −1 by fw,θ. Homogeneous half-space functions are ha...

We study projective non-degenerate closed subschemes X ⊆ P having degenerate general hyperplane section, continuing our earlier work. We find inequalities involving three relevant integers, namely: the dimensions of the spans of Xred and of the general hyperplane section of X, and a measure of the “fatness” of X, which is introduced in this paper. We prove our results first for curves and then ...

Hyperplane hashing aims at rapidly searching nearest points to a hyperplane, and has shown practical impact in scaling up active learning with SVMs. Unfortunately, the existing randomized methods need long hash codes to achieve reasonable search accuracy and thus suffer from reduced search speed and large memory overhead. To this end, this paper proposes a novel hyperplane hashing technique whi...

AdaBoost produces a linear combination of weak hypotheses. It has been observed that the generalization error of the algorithm continues to improve even after all examples are classified correctly by the current linear combination, i.e. by a hyperplane in feature space spanned by the weak hypotheses. The improvement is attributed to the experimental observation that the distances (margins) of t...

This paper deals with sliding mode hyperplane design for a class of linear parameter-varying (LPV) plants, the state-space matrices of which are an affine function of timevarying physical parameters. The proposed hyperplane, involving a linear matrix inequality (LMI) approach, has continuous dynamics due to scheduling parameters and provides stability and robustness against parametric uncertain...

In large and continuous state-action spaces reinforcement learning heavily relies on function approximation techniques. Tile coding is a well-known function approximator that has been successfully applied to many reinforcement learning tasks. In this paper we introduce the hyperplane tile coding, in which the usual tiles are replaced by parameterized hyperplanes that approximate the action-valu...

Our context of interest is tree-structured exact search in metric spaces. We make the simple observation that, the deeper a data item is within the tree, the higher the probability of that item being excluded from a search. Assuming a fixed and independent probability p of any subtree being excluded at query time, the probability of an individual data item being accessed is (1− p) for a node at...