Efficient processing of spatial joins is very important due to their high cost and frequent application in spatial databases and other areas involving multidimensional data. This paper proposes slot index spatial join (SISJ), an algorithm that joins a nonindexed data set with one indexed by an R-tree. We explore two optimization techniques that reduce the space requirements and the computationa...

The product of experts learning procedure [1] can discover a set of stochastic binary features that constitute a non-linear generative model of handwritten images of digits. The quality of generative models learned in this way can be assessed by learning a separate model for each class of digit and then comparing the unnormalized probabilities of test images under the 10 different class-specifi...

We examine implications of semi-local invariance in Ising models with multispin interaction. In ergodic models all spin-spin correlation functions vanish and the local symmetry is the same as in locally gauge-invariant models. The d = 3 model with four-spin interaction is nonergodic at low temperature but the magnetic symmetry remains unbroken. The d = 3 model with eight-spin interaction is erg...

Several techniques that compute the join between two spatial datasets have been proposed during the last decade. Among these methods, some consider existing indices for the joined inputs, while others treat datasets with no index, thus providing solutions for the case where at least one input comes as an intermediate result of another database operator. In this paper we analyze previous work on...

Groups defined by presentations of the form 〈s1, . . . , sn | si = 1, (sisj)i,j = 1 (i, j = 1, . . . , n)〉 are called Coxeter groups. The exponents mi,j ∈ N ∪ {∞} form the Coxeter matrix, which characterizes the group up to isomorphism. The Coxeter groups that are most important for applications are the Weyl groups and affine Weyl groups. For example, the symmetric group Sn is isomorphic to the...

The goal of this paper is to define new deformations of group algebras of Coxeter groups. Recall that a Coxeter group W is generated by elements si, i ∈ I modulo two kinds of relations – the involutivity relations si = 1 and the relations (sisj) mij = 1, where 2 ≤ mij = mji ≤ ∞; in presence of the involutivity relations these are equivalent to the braid relations sisjsi... = sjsisj... (mij fact...

A finite complete rewriting system for a group is a finite presentation which gives a solution to the word problem and a regular language of normal forms for the group. In this paper it is shown that the fundamental group of an orientable closed surface of genus g has a finite complete rewriting system, using the usual generators a1, .., ag, b1, .., bg along with generators representing their i...

We show that the kernel I of the ring homomorphism R[yij | i, j ∈ N, i > j]→ R[si, ti | i ∈ N] determined by yij 7→ sisj +titj is generated by two types of polynomials: off-diagonal 3 × 3-minors and pentads. This confirms a conjecture by Drton, Sturmfels, and Sullivant on the Gaussian two-factor model. Our proof is computational: inspired by work of Aschenbrenner and Hillar we introduce the con...