Conceptual knowledge discovery with frequent concept lattices

Knowledge discovery support environments include beside classical data analysis tools also data mining tools. For supporting both kinds of tools, a unified knowledge representation is needed. We show that concept lattices which are used as knowledge representation in Conceptual Information Systems can also be used for structuring the results of mining association rules. Vice versa, we use ideas of association rules for reducing the complexity of the visualization of Conceptual Information Systems.

Fast computation of concept lattices using data mining techniques

We present a new algorithm called TITANIC for computing concept lattices. It is based on data mining techniques for computing frequent itemsets. The algorithm is experimentally evaluated and compared with B. Ganter's Next-Closure algorithm.

Iceberg query lattices for datalog

In this paper we study two orthogonal extensions of the classical data mining problem of mining association rules, and show how they naturally interact. The first is the extension from a propositional representation to datalog, and the second is the condensed representation of frequent itemsets by means of Formal Concept Analysis (FCA). We combine the notion of frequent datalog queries with iceberg concept lattices (also called closed itemsets) of FCA and introduce two kinds of iceberg query lattices as condensed representations of frequent datalog queries. We demonstrate that iceberg query lattices provide a natural way to visualize relational association rules in a non-redundant way.

On Solutions of Holonomic Divided-Difference Equations on Non-Uniform Lattices

The main aim of this paper is the development of suitable bases (replacing the power basis x^n (n\in\IN_\le 0) which enable the direct series representation of orthogonal polynomial systems on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this type, the first of which allows to write solutions of arbitrary divided-difference equations in terms of series representations extending results given in [16] for the q-case. Furthermore it enables the representation of the Stieltjes function which can be used to prove the equivalence between the Pearson equation for a given linear functional and the Riccati equation for the formal Stieltjes function. If the Askey-Wilson polynomials are written in terms of this basis, however, the coefficients turn out to be not q-hypergeometric. Therefore, we present a second basis, which shares several relevant properties with the first one. This basis enables to generate the defining representation of the Askey-Wilson polynomials directly from their divided-difference equation. For this purpose the divided-difference equation must be rewritten in terms of suitable divided-difference operators developed in [5], see also [6].

Characterization theorem for classical orthogonal polynomials on non-uniform lattices: The functional approach

Using the functional approach, we state and prove a characterization theorem for classical orthogonal polynomials on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable) including the Askey-Wilson polynomials. This theorem proves the equivalence between seven characterization properties, namely the Pearson equation for the linear functional, the second-order divided-difference equation, the orthogonality of the derivatives, the Rodrigues formula, two types of structure relations,and the Riccati equation for the formal Stieltjes function.

An unprecedented mononuclear double helicate with a square planar metal ion

Reactions of the 1:2 condensate (L) of benzil dihydrazone and 1-methyl-2-imidazole carboxaldehyde with Cd(ClO4)(2)center dot xH(2)O and CdI2 yield [CdL2]( ClO4)(2) (1) and LCdI2 (2), respectively. The yellow ligand L, and its yellow complexes 1 and 2 are characterized by NMR and single crystal X-ray diffraction. Though L contains four N-donor centers, 1 is found to be a four-coordinate double helicate with a square planar Cd(II)N-4 core and 2 a spiral coordination polymer with tetrahedral Cd(II)N2I2 moieties. The bidentate nature of L and the occurrence of the square planar coordination of Cd( II) is explained by DFT calculations. (c) 2007 Elsevier B. V. All rights reserved.

Square planar mononuclear Pd(II) complexes of substituted 2-(pyrazole-1-yl)phenylamines with a helical twist

X-ray crystal structure shows that 3,5-dimethyl-1-(2-nitrophenyl)-1H-pyrazole (DNP) belongs to the rare class of helically twisted synthetic organic molecules. Hydrogenation of DNP gives 2-(3,5-dimethylpyrazole-1-yl)phenylamine (L) which on methylation yields [2-(3,5-dimethylpyrazole-1-yl)phenyl]dimethylamine (L'). Two Pd(II) complexes, PdLCl2 (1) and PdL'Cl-2 (2), are synthesized and characterized by NMR. X-ray crystallography reveals that 1 and 2 are unprecedented square planar complexes which possess well discernible helical twists. (C) 2007 Elsevier B.V. All rights reserved.

A new tetrameric Cu-II cluster with square topology exhibiting ferro- and antiferromagnetic magnetic pathways: which is which?

[Cu4L2(bpy)(4)(H2O)(3)](ClO4)(4).2.5H(2)O, 1, a new tetranuclear Cu-II cluster showing square planar geometry, formed with aspartate bridging ligand (L) has been synthesized. The global magnetic coupling is ferromagnetic but theoretical DFT/B3LYP calculations are necessary to assign which Cu-L-Cu side is ferro or antiferromagnetically coupled.

Sparse multioutput radial basis function network construction using combined locally regularised orthogonal least square and D-optimality experimental design

A construction algorithm for multioutput radial basis function (RBF) network modelling is introduced by combining a locally regularised orthogonal least squares (LROLS) model selection with a D-optimality experimental design. The proposed algorithm aims to achieve maximised model robustness and sparsity via two effective and complementary approaches. The LROLS method alone is capable of producing a very parsimonious RBF network model with excellent generalisation performance. The D-optimality design criterion enhances the model efficiency and robustness. A further advantage of the combined approach is that the user only needs to specify a weighting for the D-optimality cost in the combined RBF model selecting criterion and the entire model construction procedure becomes automatic. The value of this weighting does not influence the model selection procedure critically and it can be chosen with ease from a wide range of values.

OFDM joint data detection and phase noise cancellation based on minimum mean square prediction error

This paper proposes a new iterative algorithm for orthogonal frequency division multiplexing (OFDM) joint data detection and phase noise (PHN) cancellation based on minimum mean square prediction error. We particularly highlight the relatively less studied problem of "overfitting" such that the iterative approach may converge to a trivial solution. Specifically, we apply a hard-decision procedure at every iterative step to overcome the overfitting. Moreover, compared with existing algorithms, a more accurate Pade approximation is used to represent the PHN, and finally a more robust and compact fast process based on Givens rotation is proposed to reduce the complexity to a practical level. Numerical Simulations are also given to verify the proposed algorithm. (C) 2008 Elsevier B.V. All rights reserved.