Dynamics and topographic organization of recursive self-organizing maps

Recently there has been an outburst of interest in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, there is no general consensus as to how best to process sequences using topographicmaps, and this topic remains an active focus of neurocomputational research. The representational capabilities and internal representations of the models are not well understood. Here, we rigorously analyze a generalization of the self-organizingmap (SOM) for processing sequential data, recursive SOM (RecSOM) (Voegtlin, 2002), as a nonautonomous dynamical system consisting of a set of fixed input maps. We argue that contractive fixed-input maps are likely to produce Markovian organizations of receptive fields on the RecSOM map. We derive bounds on parameter β (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed-input maps is guaranteed. Some generalizations of SOM contain a dynamic module responsible for processing temporal contexts as an integral part of the model. We show that Markovian topographic maps of sequential data can be produced using a simple fixed (nonadaptable) dynamic module externally feeding a standard topographic model designed to process static vectorial data of fixed dimensionality (e.g., SOM). However, by allowing trainable feedback connections, one can obtain Markovian maps with superior memory depth and topography preservation. We elaborate on the importance of non-Markovian organizations in topographic maps of sequential data. © 2006 Massachusetts Institute of Technology.

"Magic" dispersion maps with distributed Raman amplification

We analyze pulse propagation in an optical fiber with a periodic dispersion map and distributed amplification. Using an asymptotic theory and a momentum method, we identify a family of dispersion management schemes that are advantageous for massive multichannel soliton transmission. For the case of two-step dispersion maps with distributed Raman amplification to compensate for the fiber loss, we find special schemes that have optimal (chirp-free) launch point locations that are independent of the fiber dispersion. Despite the variation of dispersion with wavelength due to the fiber dispersion slope, the transmission in several different channels can be optimized simultaneously using the same optimal launch point. The theoretical predictions are verified by direct numerical simulations. The obtained results are applied to a practical multichannel transmission system.

Optimal dispersion maps for multichannel soliton transmission with distributed Raman amplification

Using an asymptotic theory and a momentum method, we identify a family of dispersion management schemes with distributed Raman amplification, which are advantageous for massive multichannel soliton transmission. For the case of two-step dispersion maps, special schemes are found that have optimal (chirp-free) launch point locations that are independent of the fibre dispersion. Despite the variation of dispersion with wavelength due to the fibre dispersion slope, the transmission in several different channels can be optimized simultaneously using the same optimal launch point. The theoretical results are verified by direct numerical simulations.

True chemical shift correlation maps:a TOCSY experiment with pure shifts in both dimensions

Signal resolution in H NMR is limited primarily by multiplet structure. Recent advances in pure shift NMR, in which the effects of homonuclear couplings are suppressed, have allowed this limitation to be circumvented in 1D NMR, gaining almost an order of magnitude in spectral resolution. Here for the first time an experiment is demonstrated that suppresses multiplet structure in both domains of a homonuclear two-dimensional spectrum. The principle is demonstrated for the TOCSY experiment, generating a chemical shift correlation map in which a single peak is seen for each coupled relationship, but the principle is general and readily extensible to other homonuclear correlation experiments. Such spectra greatly simplify manual spectral analysis and should be well-suited to automated methods for structure elucidation. © 2010 American Chemical Society.

Clustering epileptiform discharges in the interictal electroencephalogram with topography preserving maps

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Usability of VGI for validation of land cover maps

Volunteered Geographic Information (VGI) represents a growing source of potentially valuable data for many applications, including land cover map validation. It is still an emerging field and many different approaches can be used to take value from VGI, but also many pros and cons are related to its use. Therefore, since it is timely to get an overview of the subject, the aim of this article is to review the use of VGI as reference data for land cover map validation. The main platforms and types of VGI that are used and that are potentially useful are analysed. Since quality is a fundamental issue in map validation, the quality procedures used by the platforms that collect VGI to increase and control data quality are reviewed and a framework for addressing VGI quality assessment is proposed. A review of cases where VGI was used as an additional data source to assist in map validation is made, as well as cases where only VGI was used, indicating the procedures used to assess VGI quality and fitness for use. A discussion and some conclusions are drawn on best practices, future potential and the challenges of the use of VGI for land cover map validation.

Discovering knowledge structures in mind maps of mental health risks

This thesis addressed the problem of risk analysis in mental healthcare, with respect to the GRiST project at Aston University. That project provides a risk-screening tool based on the knowledge of 46 experts, captured as mind maps that describe relationships between risks and patterns of behavioural cues. Mind mapping, though, fails to impose control over content, and is not considered to formally represent knowledge. In contrast, this thesis treated GRiSTs mind maps as a rich knowledge base in need of refinement; that process drew on existing techniques for designing databases and knowledge bases. Identifying well-defined mind map concepts, though, was hindered by spelling mistakes, and by ambiguity and lack of coverage in the tools used for researching words. A novel use of the Edit Distance overcame those problems, by assessing similarities between mind map texts, and between spelling mistakes and suggested corrections. That algorithm further identified stems, the shortest text string found in related word-forms. As opposed to existing approaches’ reliance on built-in linguistic knowledge, this thesis devised a novel, more flexible text-based technique. An additional tool, Correspondence Analysis, found patterns in word usage that allowed machines to determine likely intended meanings for ambiguous words. Correspondence Analysis further produced clusters of related concepts, which in turn drove the automatic generation of novel mind maps. Such maps underpinned adjuncts to the mind mapping software used by GRiST; one such new facility generated novel mind maps, to reflect the collected expert knowledge on any specified concept. Mind maps from GRiST are stored as XML, which suggested storing them in an XML database. In fact, the entire approach here is ”XML-centric”, in that all stages rely on XML as far as possible. A XML-based query language allows user to retrieve information from the mind map knowledge base. The approach, it was concluded, will prove valuable to mind mapping in general, and to detecting patterns in any type of digital information.