Open-source mapping and services for Web-based land-cover validation

Monitoring land-cover changes on sites of conservation importance allows environmental problems to be detected, solutions to be developed and the effectiveness of actions to be assessed. However, the remoteness of many sites or a lack of resources means these data are frequently not available. Remote sensing may provide a solution, but large-scale mapping and change detection may not be appropriate, necessitating site-level assessments. These need to be easy to undertake, rapid and cheap. We present an example of a Web-based solution based on free and open-source software and standards (including PostGIS, OpenLayers, Web Map Services, Web Feature Services and GeoServer) to support assessments of land-cover change (and validation of global land-cover maps). Authorised users are provided with means to assess land-cover visually and may optionally provide uncertainty information at various levels: from a general rating of their confidence in an assessment to a quantification of the proportions of land-cover types within a reference area. Versions of this tool have been developed for the TREES-3 initiative (Simonetti, Beuchle and Eva, 2011). This monitors tropical land-cover change through ground-truthing at latitude / longitude degree confluence points, and for monitoring of change within and around Important Bird Areas (IBAs) by Birdlife International and the Royal Society for the Protection of Birds (RSPB). In this paper we present results from the second of these applications. We also present further details on the potential use of the land-cover change assessment tool on sites of recognised conservation importance, in combination with NDVI and other time series data from the eStation (a system for receiving, processing and disseminating environmental data). We show how the tool can be used to increase the usability of earth observation data by local stakeholders and experts, and assist in evaluating the impact of protection regimes on land-cover change.

On the Vertex Separation of Cactus Graphs

This paper is part of a work in progress whose goal is to construct a fast, practical algorithm for the vertex separation (VS) of cactus graphs. We prove a \main theorem for cacti", a necessary and sufficient condition for the VS of a cactus graph being k. Further, we investigate the ensuing ramifications that prevent the construction of an algorithm based on that theorem only.

On the Vertex Separation of Maximal Outerplanar Graphs

We investigate the NP-complete problem Vertex Separation (VS) on Maximal Outerplanar Graphs (mops). We formulate and prove a “main theorem for mops”, a necessary and sufficient condition for the vertex separation of a mop being k. The main theorem reduces the vertex separation of mops to a special kind of stretchability, one that we call affixability, of submops.

On the 3-Colouring Vertex Folkman Number F(2,2,4)

In this note we prove that F (2, 2, 4) = 13.

On a Class of Vertex Folkman Numbers

Let a1 , . . . , ar, be positive integers, i=1 ... r, m = ∑(ai − 1) + 1 and p = max{a1 , . . . , ar }. For a graph G the symbol G → (a1 , . . . , ar ) means that in every r-coloring of the vertices of G there exists a monochromatic ai -clique of color i for some i ∈ {1, . . . , r}. In this paper we consider the vertex Folkman numbers F (a1 , . . . , ar ; m − 1) = min |V (G)| : G → (a1 , . . . , ar ) and Km−1 ⊂ G} We prove that F (a1 , . . . , ar ; m − 1) = m + 6, if p = 3 and m ≧ 6 (Theorem 3) and F (a1 , . . . , ar ; m − 1) = m + 7, if p = 4 and m ≧ 6 (Theorem 4).

When does a Bounded Domain Cover a Projective Manifold? (Survey)

* The research has been partially supported by Bulgarian Funding Organizations, sponsoring the Algebra Section of the Mathematics Institute, Bulgarian Academy of Sciences, a Contract between the Humboldt Univestit¨at and the University of Sofia, and Grant MM 412 / 94 from the Bulgarian Board of Education and Technology

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.

Essential Cover and Closure

2000 Mathematics Subject Classification: 16N80, 16S70, 16D25, 13G05.

On the Vertex Folkman Numbers Fv(2,...,2;q)

2000 Mathematics Subject Classification: 05C55.