Geometry of Control-Affine Systems

Motivated by control-affine systems in optimal control theory, we introduce the notion of a point-affine distribution on a manifold X - i.e., an affine distribution F together with a distinguished vector field contained in F. We compute local invariants for point-affine distributions of constant type when dim(X)=n, rank(F)=n-1, and when dim(X)=3, rank(F)=1. Unlike linear distributions, which are characterized by integer-valued invariants - namely, the rank and growth vector - when dim(X)<=4, we find local invariants depending on arbitrary functions even for rank 1 point-affine distributions on manifolds of dimension 2

Geometry of Optimal Control for Control-Affine Systems

Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for point-affine distributions of constant type with metric structures for systems with 2 states and 1 control and systems with 3 states and 1 control, and use Pontryagin's maximum principle to find geodesic trajectories for homogeneous examples. Even in these low dimensions, the behavior of these systems is surprisingly rich and varied

Interacting bosons in an optical lattice: Bose-Einstein condensates and Mott insulator

A dense Bose gas with hard-core interaction is considered in an optical lattice. We study the phase diagram in terms of a special mean-field theory that describes a Bose-Einstein condensate and a Mott insulator with a single particle per lattice site for zero as well as for non-zero temperatures. We calculate the densities, the excitation spectrum and the static structure factor for each of these phases.Comment: 17 pages, 5 figures; 1 figure added, typos remove

A renormalized Gross-Pitaevskii Theory and vortices in a strongly interacting Bose gas

We consider a strongly interacting Bose-Einstein condensate in a spherical harmonic trap. The system is treated by applying a slave-boson representation for hard-core bosons. A renormalized Gross-Pitaevskii theory is derived for the condensate wave function that describes the dilute regime (like the conventional Gross-Pitaevskii theory) as well as the dense regime. We calculate the condensate density of a rotating condensate for both the vortex-free condensate and the condensate with a single vortex and determine the critical angular velocity for the formation of a stable vortex in a rotating trap.Comment: 13 pages, 5 figures; revision and extension, figure 2 adde

A Chemical Interpretation of Protein Electron Density Maps in the Worldwide Protein Data Bank

High-quality three-dimensional structural data is of great value for the functional interpretation of biomacromolecules, especially proteins; however, structural quality varies greatly across the entries in the worldwide Protein Data Bank (wwPDB). Since 2008, the wwPDB has required the inclusion of structure factors with the deposition of x-ray crystallographic structures to support the independent evaluation of structures with respect to the underlying experimental data used to derive those structures. However, interpreting the discrepancies between the structural model and its underlying electron density data is difficult, since derived sigma-scaled electron density maps use arbitrary electron density units which are inconsistent between maps from different wwPDB entries. Therefore, we have developed a method that converts electron density values from sigma-scaled electron density maps into units of electrons. With this conversion, we have developed new methods that can evaluate specific regions of an x-ray crystallographic structure with respect to a physicochemical interpretation of its corresponding electron density map. We have systematically compared all deposited x-ray crystallographic protein models in the wwPDB with their underlying electron density maps, if available, and characterized the electron density in terms of expected numbers of electrons based on the structural model. The methods generated coherent evaluation metrics throughout all PDB entries with associated electron density data, which are consistent with visualization software that would normally be used for manual quality assessment. To our knowledge, this is the first attempt to derive units of electrons directly from electron density maps without the aid of the underlying structure factors. These new metrics are biochemically-informative and can be extremely useful for filtering out low-quality structural regions from inclusion into systematic analyses that span large numbers of PDB entries. Furthermore, these new metrics will improve the ability of non-crystallographers to evaluate regions of interest within PDB entries, since only the PDB structure and the associated electron density maps are needed. These new methods are available as a well-documented Python package on GitHub and the Python Package Index under a modified Clear BSD open source license

Hierarchical Harmonization of Atom-Resolved Metabolic Reactions across Metabolic Databases

Metabolic models have been proven to be useful tools in system biology and have been successfully applied to various research fields in a wide range of organisms. A relatively complete metabolic network is a prerequisite for deriving reliable metabolic models. The first step in constructing metabolic network is to harmonize compounds and reactions across different metabolic databases. However, effectively integrating data from various sources still remains a big challenge. Incomplete and inconsistent atomistic details in compound representations across databases is a very important limiting factor. Here, we optimized a subgraph isomorphism detection algorithm to validate generic compound pairs. Moreover, we defined a set of harmonization relationship types between compounds to deal with inconsistent chemical details while successfully capturing atom-level characteristics, enabling a more complete enabling compound harmonization across metabolic databases. In total, 15,704 compound pairs across KEGG (Kyoto Encyclopedia of Genes and Genomes) and MetaCyc databases were detected. Furthermore, utilizing the classification of compound pairs and EC (Enzyme Commission) numbers of reactions, we established hierarchical relationships between metabolic reactions, enabling the harmonization of 3856 reaction pairs. In addition, we created and used atom-specific identifiers to evaluate the consistency of atom mappings within and between harmonized reactions, detecting some consistency issues between the reaction and compound descriptions in these metabolic databases

New measurements of the cosmic infrared background fluctuations in deep Spitzer/IRAC survey data and their cosmological implications

We extend previous measurements of cosmic infrared background (CIB) fluctuations to ~ 1 deg using new data from the Spitzer Extended Deep Survey. Two fields, with depths of ~12 hr/pixel over 3 epochs, are analyzed at 3.6 and 4.5 mic. Maps of the fields were assembled using a self-calibration method uniquely suitable for probing faint diffuse backgrounds. Resolved sources were removed from the maps to a magnitude limit of AB mag ~ 25, as indicated by the level of the remaining shot noise. The maps were then Fourier-transformed and their power spectra were evaluated. Instrumental noise was estimated from the time-differenced data, and subtracting this isolates the spatial fluctuations of the actual sky. The power spectra of the source-subtracted fields remain identical (within the observational uncertainties) for the three epochs indicating that zodiacal light contributes negligibly to the fluctuations. Comparing to 8 mic power spectra shows that Galactic cirrus cannot account for the fluctuations. The signal appears isotropically distributed on the sky as required for an extragalactic origin. The CIB fluctuations continue to diverge to > 10 times those of known galaxy populations on angular scales out to < 1 deg. The low shot noise levels remaining in the diffuse maps indicate that the large scale fluctuations arise from the spatial clustering of faint sources well below the confusion noise. The spatial spectrum of these fluctuations is in reasonable agreement with an origin in populations clustered according to the standard cosmological model (LCDM) at epochs coinciding with the first stars era.Comment: ApJ, to be publishe

The mwtab Python Library for RESTful Access and Enhanced Quality Control, Deposition, and Curation of the Metabolomics Workbench Data Repository

The Metabolomics Workbench (MW) is a public scientific data repository consisting of experimental data and metadata from metabolomics studies collected with mass spectroscopy (MS) and nuclear magnetic resonance (NMR) analyses. MW has been constantly evolving; updating its ‘mwTab’ text file format, adding a JavaScript Object Notation (JSON) file format, implementing a REpresentational State Transfer (REST) interface, and nearly quadrupling the number of datasets hosted on the repository within the last three years. In order to keep up with the quickly evolving state of the MW repository, the ‘mwtab’ Python library and package have been continuously updated to mirror the changes in the ‘mwTab’ and JSONized formats and contain many new enhancements including methods for interacting with the MW REST interface, enhanced format validation features, and advanced features for parsing and searching for specific metabolite data and metadata. We used the enhanced format validation features to evaluate all available datasets in MW to facilitate improved curation and FAIRness of the repository. The ‘mwtab’ Python package is now officially released as version 1.0.1 and is freely available on GitHub and the Python Package Index (PyPI) under a Clear Berkeley Software Distribution (BSD) license with documentation available on ReadTheDocs

BaMORC: A Software Package for Accurate and Robust \u3csup\u3e13\u3c/sup\u3eC Reference Correction of Protein NMR Spectra

We describe Bayesian Model Optimized Reference Correction (BaMORC), a software package that performs 13C chemical shifts reference correction for either assigned or unassigned peak lists derived from protein NMR spectra. BaMORC provides an intuitive command line interface that allows non-nuclear magnetic resonance (NMR) experts to detect and correct 13C chemical shift referencing errors of unassigned peak lists at the very beginning of NMR data analysis, further lowering the bar of expertise required for effective protein NMR analysis. Furthermore, BaMORC provides an application programming interface for integration into sophisticated protein NMR data analysis pipelines, both before and after the protein resonance assignment step