Translation-Invariant Kernels for Multivariable Approximation.

Suitability of shallow (one-hidden-layer) networks with translation-invariant kernel units for function approximation and classification tasks is investigated. It is shown that a critical property influencing the capabilities of kernel networks is how the Fourier transforms of kernels converge to zero. The Fourier transforms of kernels suitable for multivariable approximation can have negative values but must be almost everywhere nonzero. In contrast, the Fourier transforms of kernels suitable for maximal margin classification must be everywhere nonnegative but can have large sets where they are equal to zero (e.g., they can be compactly supported). The behavior of the Fourier transforms of multivariable kernels is analyzed using the Hankel transform. The general results are illustrated by examples of both univariable and multivariable kernels (such as Gaussian, Laplace, rectangle, sinc, and cut power kernels).

Comparison of six methods for the detection of causality in a bivariate time series.

In this comparative study, six causality detection methods were compared, namely, the Granger vector autoregressive test, the extended Granger test, the kernel version of the Granger test, the conditional mutual information (transfer entropy), the evaluation of cross mappings between state spaces, and an assessment of predictability improvement due to the use of mixed predictions. Seven test data sets were analyzed: linear coupling of autoregressive models, a unidirectional connection of two Hénon systems, a unidirectional connection of chaotic systems of Rössler and Lorenz type and of two different Rössler systems, an example of bidirectionally connected two-species systems, a fishery model as an example of two correlated observables without a causal relationship, and an example of mediated causality. We tested not only 20000 points long clean time series but also noisy and short variants of the data. The standard and the extended Granger tests worked only for the autoregressive models. The remaining methods were more successful with the more complex test examples, although they differed considerably in their capability to reveal the presence and the direction of coupling and to distinguish causality from mere correlation.

Detection of coupling delay: A problem not yet solved.

Nonparametric detection of coupling delay in unidirectionally and bidirectionally coupled nonlinear dynamical systems is examined. Both continuous and discrete-time systems are considered. Two methods of detection are assessed-the method based on conditional mutual information-the CMI method (also known as the transfer entropy method) and the method of convergent cross mapping-the CCM method. Computer simulations show that neither method is generally reliable in the detection of coupling delays. For continuous-time chaotic systems, the CMI method appears to be more sensitive and applicable in a broader range of coupling parameters than the CCM method. In the case of tested discrete-time dynamical systems, the CCM method has been found to be more sensitive, while the CMI method required much stronger coupling strength in order to bring correct results. However, when studied systems contain a strong oscillatory component in their dynamics, results of both methods become ambiguous. The presented study suggests that results of the tested algorithms should be interpreted with utmost care and the nonparametric detection of coupling delay, in general, is a problem not yet solved.

Two-dimensional electrophoretic comparison of metastatic and non-metastatic human breast tumors using in vitro cultured epithelial cells derived from the cancer tissues.

BACKGROUND: Breast carcinomas represent a heterogeneous group of tumors diverse in behavior, outcome, and response to therapy. Identification of proteins resembling the tumor biology can improve the diagnosis, prediction, treatment selection, and targeting of therapy. Since the beginning of the post-genomic era, the focus of molecular biology gradually moved from genomes to proteins and proteomes and to their functionality. Proteomics can potentially capture dynamic changes in protein expression integrating both genetic and epigenetic influences. METHODS: We prepared primary cultures of epithelial cells from 23 breast cancer tissue samples and performed comparative proteomic analysis. Seven patients developed distant metastases within three-year follow-up. These samples were included into a metastase-positive group, the others formed a metastase-negative group. Two-dimensional electrophoretical (2-DE) gels in pH range 4-7 were prepared. Spot densities in 2-DE protein maps were subjected to statistical analyses (R/maanova package) and data-mining analysis (GUHA). For identification of proteins in selected spots, liquid chromatography-tandem mass spectrometry (LC-MS/MS) was employed. RESULTS: Three protein spots were significantly altered between the metastatic and non-metastatic groups. The correlations were proven at the 0.05 significance level. Nucleophosmin was increased in the group with metastases. The levels of 2,3-trans-enoyl-CoA isomerase and glutathione peroxidase 1 were decreased. CONCLUSION: We have performed an extensive proteomic study of mammary epithelial cells from breast cancer patients. We have found differentially expressed proteins between the samples from metastase-positive and metastase-negative patient groups.