Rapid heuristic projection on simplicial cones

A very fast heuristic iterative method of projection on simplicial cones is presented. It consists in solving two linear systems at each step of the iteration. The extensive experiments indicate that the method furnishes the exact solution in more then 99.7 percent of the cases. The average number of steps is 5.67 (we have not found any examples which required more than 13 steps) and the relative number of steps with respect to the dimension decreases dramatically. Roughly speaking, for high enough dimensions the absolute number of steps is independent of the dimension.

Alzheimer's disease: Are cellular neurofibrillary tangles linked to beta/A4 formation at the projection sites?

The density of senile plaques (SP) and cellular neurofibrillary tabgles (NFT) revealed by the Glees and Gallyas stains; and beta/A4 deposits revealed by immunocytochemical staining, was estimated in the hippocampus and adjacent gyri in Alzheimer's disease (AD). Stepwise multiple regression was used to detemine whether the density of cellular NFT was related to the density of SP or beta/A4 deposits totalled over the projection sites. Cellular NFT density was only weakly correlated with the density of Glees SP and beta/A4 deposits at some of the projection sites. However, beta/A4 deposit density in a tissue was strongly correlated with the density of beta/A4 deposits at the projection sites suggesting that the lesions could spread through the brain. Hence, although there is a strong correlation between the density of beta/A4 deposits in different parts of the hippocampal formation there is little association between SP or beta/A4 and cellular NFT. These results do not provide strong evidence that beta/A4 protein is the cause of the neuritc changes in AD.

Projection and interpolation based techniques for structured and impulsive noise filtering

In this chapter we present the relevant mathematical background to address two well defined signal and image processing problems. Namely, the problem of structured noise filtering and the problem of interpolation of missing data. The former is addressed by recourse to oblique projection based techniques whilst the latter, which can be considered equivalent to impulsive noise filtering, is tackled by appropriate interpolation methods.

Peer mentoring in higher education:a multidimensional approach to conceptualising the role of peer mentoring programmes in enhancing the first year undergraduate experience

Across the literature researchers agree that the concept of mentoring results in positive outcomes for both mentors and mentees alike (Enrich et al, 2004). From a pedagogical perspective, student focused mentoring activities in Higher Education are generally perceived to comprise dyadic or triadic relationships that encapsulate a diverse range of learning strategies and/or support mechanisms. Whilst there exists a significant amount of literature regarding the wider value of Peer Mentoring in Higher Education, there remains a notable gap in knowledge about the value of such programmes in enhancing the first year undergraduate experience and thus promoting a smooth transition to University. Using the emergent study findings of a large international project, a multidimensional conceptual framework bringing together the theoretical, conceptual and contextual determinants of Peer Mentoring is proposed. This framework makes a distinctive contribution to current pedagogical theory and practice – particularly in relation to the first year experience.

Visual data mining using principled projection algorithms and information visualization techniques

We introduce a flexible visual data mining framework which combines advanced projection algorithms from the machine learning domain and visual techniques developed in the information visualization domain. The advantage of such an interface is that the user is directly involved in the data mining process. We integrate principled projection algorithms, such as generative topographic mapping (GTM) and hierarchical GTM (HGTM), with powerful visual techniques, such as magnification factors, directional curvatures, parallel coordinates and billboarding, to provide a visual data mining framework. Results on a real-life chemoinformatics dataset using GTM are promising and have been analytically compared with the results from the traditional projection methods. It is also shown that the HGTM algorithm provides additional value for large datasets. The computational complexity of these algorithms is discussed to demonstrate their suitability for the visual data mining framework. Copyright 2006 ACM.

Symbolic use of export information:a multidimensional conceptualisation, its' effect on performance and key antecedents

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

Feed-forward neural networks and topographic mappings for exploratory data analysis

A recent novel approach to the visualisation and analysis of datasets, and one which is particularly applicable to those of a high dimension, is discussed in the context of real applications. A feed-forward neural network is utilised to effect a topographic, structure-preserving, dimension-reducing transformation of the data, with an additional facility to incorporate different degrees of associated subjective information. The properties of this transformation are illustrated on synthetic and real datasets, including the 1992 UK Research Assessment Exercise for funding in higher education. The method is compared and contrasted to established techniques for feature extraction, and related to topographic mappings, the Sammon projection and the statistical field of multidimensional scaling.

Quantifying the complexity of chaos in multibasin multidimensional dynamics of molecular systems

The simulated classical dynamics of a small molecule exhibiting self-organizing behavior via a fast transition between two states is analyzed by calculation of the statistical complexity of the system. It is shown that the complexity of molecular descriptors such as atom coordinates and dihedral angles have different values before and after the transition. This provides a new tool to identify metastable states during molecular self-organization. The highly concerted collective motion of the molecule is revealed. Low-dimensional subspaces dynamics is found sensitive to the processes in the whole, high-dimensional phase space of the system. © 2004 Wiley Periodicals, Inc.

Bridging the gap between stylistic and cognitive approaches to authorship analysis using systemic functional linguistics and multidimensional analysis

In the present state of the art of authorship attribution there seems to be an opposition between two approaches: cognitive and stylistic methodologies. It is proposed in this article that these two approaches are complementary and that the apparent gap between them can be bridged using Systemic Functional Linguistics (SFL) and in particular some of its theoretical constructions, such as codal variation. This article deals with the theoretical explanation of why such a theory would solve the debate between the two approaches and shows how these two views of authorship attribution are indeed complementary. Although the article is fundamentally theoretical, two example experimental trials are reported to show how this theory can be developed into a workable methodology of doing authorship attribution. In Trial 1, a SFL analysis was carried out on a small dataset consisting of three 300-word texts collected from three different authors whose socio-demographic background matched across a number of parameters. This trial led to some conclusions about developing a methodology based on SFL and suggested the development of another trial, which might hint at a more accurate and useful methodology. In Trial 2, Biber's (1988) multidimensional framework is employed, and a final methodology of authorship analysis based on this kind of analysis is proposed for future research. © 2013, EQUINOX PUBLISHING.

Extreme Situations Prediction by MultidimenSional Heterogeneous Time Series Using Logical Decision Functions

* The work is supported by RFBR, grant 04-01-00858-a

Multidimensional Heterogeneous Variable Prediction Based on Experts’ Statements

* The work was supported by the RFBR under Grant N07-01-00331a.

On Multidimensional Analogue of Marchaud Formula for Fractional Riesz-Type Derivatives in Domains in R^n

2000 Mathematics Subject Classification: 26A33, 42B20

2D-3D registration of CT vertebra volume to fluoroscopy projection:a calibration model assessment

This study extends a previous research concerning intervertebral motion registration by means of 2D dynamic fluoroscopy to obtain a more comprehensive 3D description of vertebral kinematics. The problem of estimating the 3D rigid pose of a CT volume of a vertebra from its 2D X-ray fluoroscopy projection is addressed. 2D-3D registration is obtained maximising a measure of similarity between Digitally Reconstructed Radiographs (obtained from the CT volume) and real fluoroscopic projection. X-ray energy correction was performed. To assess the method a calibration model was realised a sheep dry vertebra was rigidly fixed to a frame of reference including metallic markers. Accurate measurement of 3D orientation was obtained via single-camera calibration of the markers and held as true 3D vertebra position; then, vertebra 3D pose was estimated and results compared. Error analysis revealed accuracy of the order of 0.1 degree for the rotation angles of about 1mm for displacements parallel to the fluoroscopic plane, and of order of 10mm for the orthogonal displacement. © 2010 P. Bifulco et al.