A new kernel method for hyperspectral image feature extraction

Hyperspectral image provides abundant spectral information for remote discrimination of subtle differences in ground covers. However, the increasing spectral dimensions, as well as the information redundancy, make the analysis and interpretation of hyperspectral images a challenge. Feature extraction is a very important step for hyperspectral image processing. Feature extraction methods aim at reducing the dimension of data, while preserving as much information as possible. Particularly, nonlinear feature extraction methods (e.g. kernel minimum noise fraction (KMNF) transformation) have been reported to benefit many applications of hyperspectral remote sensing, due to their good preservation of high-order structures of the original data. However, conventional KMNF or its extensions have some limitations on noise fraction estimation during the feature extraction, and this leads to poor performances for post-applications. This paper proposes a novel nonlinear feature extraction method for hyperspectral images. Instead of estimating noise fraction by the nearest neighborhood information (within a sliding window), the proposed method explores the use of image segmentation. The approach benefits both noise fraction estimation and information preservation, and enables a significant improvement for classification. Experimental results on two real hyperspectral images demonstrate the efficiency of the proposed method. Compared to conventional KMNF, the improvements of the method on two hyperspectral image classification are 8 and 11%. This nonlinear feature extraction method can be also applied to other disciplines where high-dimensional data analysis is required

Charges and fluxes in Maxwell theory on compact manifolds with boundary

We investigate the charges and fluxes that can occur in higher-order Abelian gauge theories defined on compact space-time manifolds with boundary. The boundary is necessary to supply a destination to the electric lines of force emanating from brane sources, thus allowing non-zero net electric charges, but it also introduces new types of electric and magnetic flux. The resulting structure of currents, charges, and fluxes is studied and expressed in the language of relative homology and de Rham cohomology and the corresponding abelian groups. These can be organised in terms of a pair of exact sequences related by the Poincar\'e-Lefschetz isomorphism and by a weaker flip symmetry exchanging the ends of the sequences. It is shown how all this structure is brought into play by the imposition of the appropriately generalised Maxwell's equations. The requirement that these equations be integrable restricts the world-volume of a permitted brane (assumed closed) to be homologous to a cycle on the boundary of space-time. All electric charges and magnetic fluxes are quantised and satisfy the Dirac quantisation condition. But through some boundary cycles there may be unquantised electric fluxes associated with quantised magnetic fluxes and so dyonic in nature.Comment: 28 pages, plain Te

Comparative analysis of knowledge representation and reasoning requirements across a range of life sciences textbooks.

BackgroundUsing knowledge representation for biomedical projects is now commonplace. In previous work, we represented the knowledge found in a college-level biology textbook in a fashion useful for answering questions. We showed that embedding the knowledge representation and question-answering abilities in an electronic textbook helped to engage student interest and improve learning. A natural question that arises from this success, and this paper's primary focus, is whether a similar approach is applicable across a range of life science textbooks. To answer that question, we considered four different textbooks, ranging from a below-introductory college biology text to an advanced, graduate-level neuroscience textbook. For these textbooks, we investigated the following questions: (1) To what extent is knowledge shared between the different textbooks? (2) To what extent can the same upper ontology be used to represent the knowledge found in different textbooks? (3) To what extent can the questions of interest for a range of textbooks be answered by using the same reasoning mechanisms?ResultsOur existing modeling and reasoning methods apply especially well both to a textbook that is comparable in level to the text studied in our previous work (i.e., an introductory-level text) and to a textbook at a lower level, suggesting potential for a high degree of portability. Even for the overlapping knowledge found across the textbooks, the level of detail covered in each textbook was different, which requires that the representations must be customized for each textbook. We also found that for advanced textbooks, representing models and scientific reasoning processes was particularly important.ConclusionsWith some additional work, our representation methodology would be applicable to a range of textbooks. The requirements for knowledge representation are common across textbooks, suggesting that a shared semantic infrastructure for the life sciences is feasible. Because our representation overlaps heavily with those already being used for biomedical ontologies, this work suggests a natural pathway to include such representations as part of the life sciences curriculum at different grade levels

Exploring the episodic structure of algebra story problem solving

This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem-solving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses of written protocols compare the strategic, tactical, and conceptual content of solution attampts, looking within these attempts at the interplay between problem comprehension and solution. Comprehension and solution of algebra story problems are complimentary activities, giving rise to a succession of problem solving episodes. While direct algebraic problem solving is sometimes effective, results suggest that the algebraic formalism may be of little help in comprehending the quantitative constraints posed in a problem text. Instead, competent problem solvers often reason within the situational context presented by a story problem, using various forms of "model-based reasoning" to identify, pursue, and verify quantitative constraints required for solution. The paper concludes by discussing the implications of these findings for acquiring mathematical concepts (e.g., related linear functions) and for supporting their acquisition through instruction