We present a method of fast factorization in formal concept analysis (FCA) of data with fuzzy attributes. The output of FCA consists of a partially ordered collection of clusters extracted from a data table describing objects and their attributes. The collection is called a concept lattice. Factorization by similarity enables us to obtain, instead of a possibly large concept lattice, its factor lattice. The elements of the factor lattice are maximal blocks of clusters which are pairwise similar to degree exceeding a userspecified threshold. The factor lattice thus represents an approximate version of the original concept lattice. We describe a fuzzy closure operator the fixed points of which are just clusters which uniquely determine the blocks of clusters of the factor lattice. This enables us to compute the factor lattice directly from the data without the need to compute the whole concept lattice. We present theoretical solution and examples demonstrating the speed-up of our method.
We consider the problem of non-parametric testing of independence of two components of a stationary bivariate spatial process. In particular, we revisit the random shift approach that has become a standard method for testing the independent superposition hypothesis in spatial statistics, and it is widely used in a plethora of practical applications. However, this method has a problem of liberality caused by breaking the marginal spatial correlation structure due to the toroidal correction. This indeed causes that the assumption of exchangability, which is essential for the Monte Carlo test to be exact, is not fulfilled.We present a number of permutation strategies and show that the random shift with the variance correction brings a suitable improvement compared to the torus correction in the random field case. It reduces the liberality and achieves the largest power from all investigated variants. To obtain the variance for the variance correction method, several approaches were studied. The best results were achieved, for the sample covariance as the test statistics, with the correction factor 1/n. This corresponds to the asymptotic order of the variance of the test statistics.In the point process case, the problem of deviations from exchangeability is far more complex and we propose an alternative strategy based on the mean cross nearest-neighbor distance and torus correction. It reduces the liberality but achieves slightly lower power than the usual cross K-function. Therefore we recommend it, when the point patterns are clustered, where the cross Kfunction achieves liberality.
The present state of information communication technology makes it possible to devise and run computer-based e-laboratories accessible to any user with a connection to the Internet, equipped with very simple technical means and making full use of web services. Thus, the way is open for a new strategy of physics education with strongly global features, based on experiment and experimentation. We name this strategy integrated e-learning, and remote experiments across the Internet are the foundation for this strategy. We present both pedagogical and technical reasoning for the remote experiments and outline a simple system based on a server–client approach, and on web services and Java applets. We give here an outline of the prospective remote laboratory system with data transfer using the Internet School Experimental System (ISES) as hardware and ISES WEB Control kit as software. This approach enables the simple construction of remote experiments without building any hardware and virtually no programming, using a paste and copy approach with typical prebuilt blocks such as a camera view, controls, graphs, displays, etc. We have set up and operate at present seven experiments, running round the clock, with more than 12 000 connections since 2005. The experiments are widely used in practical teaching of both university and secondary level physics. The recording of the detailed steps the experimentor takes during the measurement enables detailed study of the psychological aspects of running the experiments. The system is ready for a network of universities to start covering the basic set of physics experiments. In conclusion we summarize the results achieved and experiences of using remote experiments built on the ISES hardware system.
In the present paper we develop several two-step estimation procedures for inhomogeneous shot-noise Cox processes. The intensity function is parametrized by the inhomogeneity parameters while the pair-correlation function is parametrized by the interaction parameters. The suggested procedures are based on a combination of Poisson likelihood estimation of the inhomogeneity parameters in the first step and an adaptation of a method from the homogeneous case for estimation of the interaction parameters in the second step. The adapted methods, based on minimum contrast estimation, composite likelihood and Palm likelihood, are compared both theoretically and by means of a simulation study. Two-step estimation with Palm likelihood has not been considered before. Asymptotic normality of the two-step estimator with Palm likelihood is proved.
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