We prove that the first complex homology of the Johnson subgroup of the Torelli group Tg is a non-trivial, unipotent Tg-module for all g ≥ 4 and give an explicit presentation of it as a Sym • H1(Tg,C)-module when g ≥ 6. We do this by proving that, for a finitely generated group G satisfying an assumption close to formality, the triviality of the restricted characteristic variety implies that th...

The classical Airy function has been generalised by Kontsevich to a function of a matrix argument, which is an integral over the space of (skew) hermitian matrices of a unitary-invariant exponential kernel. In this paper, the Kontsevich integral is generalised to integrals over the Lie algebra of an arbitrary connected compact Lie group, using exponential kernels invariant under the group. The ...

We describe an approach to kernel selection in Support Vector Machines (SVMs) driven by the Gram matrix. Our study extracts properties from this matrix (e.g., Fisher’s discriminant, Bregman’s divergence) using different kernel functions (linear, polynomial, Gaussian, Laplacian, Bessel and ANOVARBF), and incorporates such properties as meta-features within a meta-learning framework. The goal is ...

In this paper we study strictly positive definite functions on the unit sphere of the m-dimensional Euclidean space. Such functions can be used for solving a scattered data interpolation problem on spheres. Since positive definite functions on the sphere were already characterized by Schoenberg some fifty years ago, the issue here is to determine what kind of positive definite functions are act...

The classical Airy function has been generalised by Kontsevich to a function of a matrix argument, which is an integral over the space of (skew) hermitian matrices of a unitary-invariant exponential kernel. In this paper, the Kontsevich integral is generalised to integrals over the Lie algebra of an arbitrary connected compact Lie group, using exponential kernels invariant under the group. The ...

We introduce a new kernel for Support Vector Machine learning in a natural language setting. As a case study to incorporate domain knowledge into a kernel, we consider the problem of resolving Prepositional Phrase attachment ambiguities. The new kernel is derived from a distance function that proved to be succesful in memory-based learning. We start with the Simple Overlap Metric from which we ...

This article deals with the equivalence of representations of behaviors of linear differential systems. In general, the behavior of a given linear differential system has many different representations. In this paper we restrict ourselves to kernel representations and image representations. Two kernel representations or image representations are called equivalent if they represent one and the s...

In this paper, we are mainly concerned with consistency-based diagnoses for systems represented in a propositional framework. Several characterizations of such diagnoses (mainly minimal diagnoses, kernel diagnoses, MT-diagnoses) have been proposed so far. Unfortunately, minimal diagnoses, and MT-diagnoses characterize only some consistency-based diagnoses and the set of kernel diagnoses for a s...

An approach to obtaining a parsimonious polynomial model from time series is proposed. An optimal minimal nonuniform time series embedding schema is used to obtain a time delay kernel. This scheme recursively optimizes an objective functional that eliminates a maximum number of false nearest neighbors between successive state space reconstruction cycles. A polynomial basis is then constructed f...

Exact results for the density of states and the ac conductivity of the spinless Holstein model at finite carrier density are obtained combining Lanczos and kernel polynomial methods.