We examine spaces of connected tri-/univalent graphs subject to local relations which are motivated by the theory of Vassiliev invariants. It is shown that the behaviour of ladder-like subgraphs is strongly related to the parity of the number of rungs: there are similar relations for ladders of even and odd lengths, respectively. Moreover, we prove that under certain conditions an even number o...

Cubic forms in three variables are parametrised by points of a projec-tive space P 9. We study the subvarieties in this space defined by de-composable forms. Specifically, we calculate their equivariant minimal resolutions and describe their ideals invariant-theoretically.

We produce a complete descrption of the lattice of gauge-invariant ideals in C(Λ) for a finitely aligned k-graph Λ. We provide a condition on Λ under which every ideal is gauge-invariant. We give conditions on Λ under which C(Λ) satisfies the hypotheses of the Kirchberg-Phillips classification theorem.

RÉSUMÉ. Cet article présente une étude sur le diagnostic de noyaux de cellules sanguines provenant de patients atteints de Progéria. Les noyaux sont caractérisés à l’aide de différentes méthodes d’analyse de forme et de texture, puis classés par des techniques d’apprentissage. Les mesures extraites des noyaux servent aux calculs d’un ensemble de valeurs nommées des « indices ». Les indices sont...

In this paper, we propose a new approach for establishing the correspondence between local invariant features using Bayesian graph matching algorithm. First, we will discuss various local invariant feature detectors and descriptors for scale and affine transformation and illumination changes. Second, we propose an efficient features corresponding method using local invariant features and new gr...

This thesis explores approaches towards learning with kernel methods using prior knowledge. Invariant learning with kernel methods is considered in more details. In the first part of the thesis, kernels are developed which incorporate prior knowledge on invariant transformations. Next, algorithms which specifically include prior knowledge are considered. An algorithm which linearly classifies d...

We introduce the price of symmetrisation, a concept that aims to compare fundamental differences (gap and quotient) between values of a given graph invariant for digraphs and the values of the same invariant of the symmetric versions of these digraphs. Basically, given some invariant our goal is to characterise digraphs that maximise price of symmetrisation. In particular, we show that for some...

This paper is comprised of two related parts. First we discuss which k-graph algebras have faithful gauge invariant traces, where the gauge action of T k is the canonical one. We give a sufficient condition for the existence of such a trace, identify the C *-algebras of k-graphs satisfying this condition up to Morita equivalence, and compute their K-theory. For k-graphs with faithful gauge inva...

This paper presents a new feature matching algorithm for registering aerial images with large illumination distortion, similar patterns, affine transformation and low overlapping areas. In this algorithm, affine invariant regions are obtained by a K-NN graph and its corresponding adjacent graph. Then an illumination and affine invariant called Illumination Invariant MultiScale Autoconvolution (...

An isoradial graph is a planar graph in which each face is inscribable into a circle of common radius. We study the 2-dimensional perfect matchings on a bipartite isoradial graph, obtained from the union of an isoradial graph and its interior dual graph. Using the isoradial graph to approximate a simply-connected domain bounded by a simple closed curve, by letting the mesh size go to zero, we p...