SUMMARY: PINE-SPARKY supports the rapid, user-friendly and efficient visualization of probabilistic assignments of NMR chemical shifts to specific atoms in the covalent structure of a protein in the context of experimental NMR spectra. PINE-SPARKY is based on the very popular SPARKY package for visualizing multidimensional NMR spectra (T. D. Goddard and D. G. Kneller, SPARKY 3, University of California, San Francisco). PINE-SPARKY consists of a converter (PINE2SPARKY), which takes the output from an automated PINE-NMR analysis and transforms it into SPARKY input, plus a number of SPARKY extensions. Assignments and their probabilities obtained in the PINE-NMR step are visualized as labels in SPARKY's spectrum view. Three SPARKY extensions (PINE Assigner, PINE Graph Assigner, and Assign the Best by PINE) serve to manipulate the labels that signify the assignments and their probabilities. PINE Assigner lists all possible assignments for a peak selected in the dialog box and enables the user to choose among these. A window in PINE Graph Assigner shows all atoms in a selected residue along with all atoms in its adjacent residues; in addition, it displays a ranked list of PINE-derived connectivity assignments to any selected atom. Assign the Best-by-PINE allows the user to choose a probability threshold and to automatically accept as "fixed" all assignments above that threshold; following this operation, only the less certain assignments need to be examined visually. Once assignments are fixed, the output files generated by PINE-SPARKY can be used as input to PINE-NMR for further refinements. AVAILABILITY: The program, in the form of source code and binary code along with tutorials and reference manuals, is available at http://pine.nmrfam.wisc.edu/PINE-SPARKY.

The process of assigning a finite set of tags or labels to a collection of observations, subject to side conditions, is notable for its computational complexity. This labeling paradigm is of theoretical and practical relevance to a wide range of biological applications, including the analysis of data from DNA microarrays, metabolomics experiments, and biomolecular nuclear magnetic resonance (NMR) spectroscopy. We present a novel algorithm, called Probabilistic Interaction Network of Evidence (PINE), that achieves robust, unsupervised probabilistic labeling of data. The computational core of PINE uses estimates of evidence derived from empirical distributions of previously observed data, along with consistency measures, to drive a fictitious system M with Hamiltonian H to a quasi-stationary state that produces probabilistic label assignments for relevant subsets of the data. We demonstrate the successful application of PINE to a key task in protein NMR spectroscopy: that of converting peak lists extracted from various NMR experiments into assignments associated with probabilities for their correctness. This application, called PINE-NMR, is available from a freely accessible computer server (http://pine.nmrfam.wisc.edu). The PINE-NMR server accepts as input the sequence of the protein plus user-specified combinations of data corresponding to an extensive list of NMR experiments; it provides as output a probabilistic assignment of NMR signals (chemical shifts) to sequence-specific backbone and aliphatic side chain atoms plus a probabilistic determination of the protein secondary structure. PINE-NMR can accommodate prior information about assignments or stable isotope labeling schemes. As part of the analysis, PINE-NMR identifies, verifies, and rectifies problems related to chemical shift referencing or erroneous input data. PINE-NMR achieves robust and consistent results that have been shown to be effective in subsequent steps of NMR structure determination.

Models of processes underlying human perception of geometric forms are helpful in addressing the nature of computations performed by the brain in understanding images from environment. Perceptual geometry is an emerging field of interdisciplinary research whose objectives focus on study of geometry from the perspective of visual perception, and in turn, apply such geometric findings to the ecological study of vision. Perceptual geometry attempts to answer fundamental questions in perception of form and representation of space through synthesis of cognitive and biological theories of visual perception with geometric theories of the physical world. The following model appeals to perceptual geometry as a framework that takes advantage of "almost regularity" of 2-dimensional images of surfaces, in order to estimate of their shape, orientation and other geometric features.

Pattern recognition and feature extraction tasks in massive and noisy data sets are often plagued by a formidable amount of necessary computations. A common remedy is the application of techniques such as PCA to reduce the dimensionality of data and therefore the amount of computation. While PCA is a useful and popular method, its strict linearity drastically limits its domain of applicability. A number of approaches such as nonlinear formulations of PCA as well as alternatives such as independent component analysis has been proposed. We propose non-linear methods that generalize the PCA and ICA, and lead to the same answer for the cases in which the nonlinearity in the data set is negligible. The main contribution of our research is to develop the nonlinear algorithms based on the geometric ideas in the theory of Riemannian Foliations in differential topology.

Analysis of data in computational finance and computational neuroscience share a number of common traits: data are typically massive, noisy, very high dimensional, and governed by complete multi-scale time dynamics. The set of known parameters forms a small subset of the true variates that control the dynamics of the systems from which data is collected. Reduction of dimensionality of the data, and clustering of system parameters according to a relevant measure of independence, and improving signal to noise ratio, are among the core problems of both disciplines. We propose a nonlinear version of independent component analysis for clustering of parameters and separating clusters according to their measure of statistical independence. Analogously, we propose a nonlinear version of principal component analysis for reducing the dimensionality of data. The combination of these two methods forms the basis for a dynamic pattern recognition paradigm. This approach is inspired by a mathematical analogy to a successful method for estimation of patterns of functional connectivity in neuro-imaging.