Kernel Spectral Curvature Clustering (KSCC)

Multi-manifold modeling is increasingly used in segmentation and data representation tasks in computer vision and related fields. While the general problem, modeling data by mixtures of manifolds, is very challenging, several approaches exist for modeling data by mixtures of affine subspaces (which is often referred to as hybrid linear modeling). We translate some important instances of multi-manifold modeling to hybrid linear modeling in embedded spaces, without explicitly performing the embedding but applying the kernel trick. The resulting algorithm, Kernel Spectral Curvature Clustering, uses kernels at two levels - both as an implicit embedding method to linearize nonflat manifolds and as a principled method to convert a multiway affinity problem into a spectral clustering one. We demonstrate the effectiveness of the method by comparing it with other state-of-the-art methods on both synthetic data and a real-world problem of segmenting multiple motions from two perspective camera views.Comment: accepted to 2009 ICCV Workshop on Dynamical Visio

Wrapper Maintenance: A Machine Learning Approach

The proliferation of online information sources has led to an increased use of wrappers for extracting data from Web sources. While most of the previous research has focused on quick and efficient generation of wrappers, the development of tools for wrapper maintenance has received less attention. This is an important research problem because Web sources often change in ways that prevent the wrappers from extracting data correctly. We present an efficient algorithm that learns structural information about data from positive examples alone. We describe how this information can be used for two wrapper maintenance applications: wrapper verification and reinduction. The wrapper verification system detects when a wrapper is not extracting correct data, usually because the Web source has changed its format. The reinduction algorithm automatically recovers from changes in the Web source by identifying data on Web pages so that a new wrapper may be generated for this source. To validate our approach, we monitored 27 wrappers over a period of a year. The verification algorithm correctly discovered 35 of the 37 wrapper changes, and made 16 mistakes, resulting in precision of 0.73 and recall of 0.95. We validated the reinduction algorithm on ten Web sources. We were able to successfully reinduce the wrappers, obtaining precision and recall values of 0.90 and 0.80 on the data extraction task

Mathematical thinking: studying the notion of 'transfer'.

These analyses form part of a three-year project* looking at mathematical thinking as a socially organised activity. We revisit data from a University Calculus class using tools from two theoretical perspectives, used increasingly in mathematics education research: (1) semiotic mediation and (2) discursive practices. We highlight how different theory-driven analyses taking a sociocultural view of thinking and learning can offer insights into the conceptualisation of the 'transfer' of learning

Uniqueness and examples of compact toric Sasaki-Einstein metrics

In [11] it was proved that, given a compact toric Sasaki manifold of positive basic first Chern class and trivial first Chern class of the contact bundle, one can find a deformed Sasaki structure on which a Sasaki-Einstein metric exists. In the present paper we first prove the uniqueness of such Einstein metrics on compact toric Sasaki manifolds modulo the action of the identity component of the automorphism group for the transverse holomorphic structure, and secondly remark that the result of [11] implies the existence of compatible Einstein metrics on all compact Sasaki manifolds obtained from the toric diagrams with any height, or equivalently on all compact toric Sasaki manifolds whose cones have flat canonical bundle. We further show that there exists an infinite family of inequivalent toric Sasaki-Einstein metrics on $S^5 \sharp k(S^2 \times S^3)$ for each positive integer $k$.Comment: Statements of the results are modifie

Minimal H\"older regularity implying finiteness of integral Menger curvature

We study two families of integral functionals indexed by a real number $p > 0$. One family is defined for 1-dimensional curves in $\R^3$ and the other one is defined for $m$-dimensional manifolds in $\R^n$. These functionals are described as integrals of appropriate integrands (strongly related to the Menger curvature) raised to power $p$. Given $p > m(m+1)$ we prove that $C^{1,\alpha}$ regularity of the set (a curve or a manifold), with $\alpha > \alpha_0 = 1 - \frac{m(m+1)}p$ implies finiteness of both curvature functionals ($m=1$ in the case of curves). We also show that $\alpha_0$ is optimal by constructing examples of $C^{1,\alpha_0}$ functions with graphs of infinite integral curvature

Coronary artery endothelial dysfunction is positively correlated with low density lipoprotein and inversely correlated with high density lipoprotein subclass particles measured by nuclear magnetic resonance spectroscopy.

OBJECTIVE: The association between cholesterol and endothelial dysfunction remains controversial. We tested the hypothesis that lipoprotein subclasses are associated with coronary endothelial dysfunction. METHODS AND RESULTS: Coronary endothelial function was assessed in 490 patients between November 1993 and February 2007. Fasting lipids and nuclear magnetic resonance (NMR) lipoprotein particle subclasses were measured. There were 325 females and 165 males with a mean age of 49.8+/-11.6 years. Coronary endothelial dysfunction (epicardial constriction>20% or increase in coronary blood flow<50% in response to intracoronary acetylcholine) was diagnosed in 273 patients, the majority of whom (64.5%) had microvascular dysfunction. Total cholesterol and LDL-C (low density lipoprotein cholesterol) were not associated with endothelial dysfunction. One-way analysis and multivariate methods adjusting for age, gender, diabetes, hypertension and lipid-lowering agent use were used to determine the correlation between lipoprotein subclasses and coronary endothelial dysfunction. Epicardial endothelial dysfunction was significantly correlated with total (p=0.03) and small LDLp (LDL particles) (p<0.01) and inversely correlated with total and large HDLp (high density lipoprotein particles) (p<0.01). CONCLUSIONS: Epicardial, but not microvascular, coronary endothelial dysfunction was associated directly with LDL particles and inversely with HDL particles, suggesting location-dependent impact of lipoprotein particles on the coronary circulation

First year engineering mathematics: the London South Bank University experience

This short article describes an innovative approach to teaching mathematics to first year undergraduates on a variety of B. Eng. courses offered in the Faculty of Engineering, Science and Built Environment (FESBE) of London South Bank University (LSBU)

On Non-Abelian Symplectic Cutting

We discuss symplectic cutting for Hamiltonian actions of non-Abelian compact groups. By using a degeneration based on the Vinberg monoid we give, in good cases, a global quotient description of a surgery construction introduced by Woodward and Meinrenken, and show it can be interpreted in algebro-geometric terms. A key ingredient is the `universal cut' of the cotangent bundle of the group itself, which is identified with a moduli space of framed bundles on chains of projective lines recently introduced by the authors.Comment: Various edits made, to appear in Transformation Groups. 28 pages, 8 figure

Intelligent Self-Repairable Web Wrappers

The amount of information available on the Web grows at an incredible high rate. Systems and procedures devised to extract these data from Web sources already exist, and different approaches and techniques have been investigated during the last years. On the one hand, reliable solutions should provide robust algorithms of Web data mining which could automatically face possible malfunctioning or failures. On the other, in literature there is a lack of solutions about the maintenance of these systems. Procedures that extract Web data may be strictly interconnected with the structure of the data source itself; thus, malfunctioning or acquisition of corrupted data could be caused, for example, by structural modifications of data sources brought by their owners. Nowadays, verification of data integrity and maintenance are mostly manually managed, in order to ensure that these systems work correctly and reliably. In this paper we propose a novel approach to create procedures able to extract data from Web sources -- the so called Web wrappers -- which can face possible malfunctioning caused by modifications of the structure of the data source, and can automatically repair themselves.\u