Regularizing Flows over Lie Groups

In this paper we discuss regularization of images that take their value in matrix Lie groups. We describe an image as a section in a principal bundle which is a fibre bundle where the fiber (the feature space) is a Lie group. Via the scalar product on the Lie algebra, we define a bi-invariant metric on the Lie-group manifold. Thus, the fiber becomes a Riemannian manifold with respect to this metric. The induced metric from the principal bundle to the image manifold is obtained by means of the bi-invariant metric. A functional over the space of sections, i.e., the image manifolds, is defined. The resulting equations of motion generate a flow which evolves the sections in the spatial-Lie-group manifold. We suggest two different approaches to treat this functional and the corresponding PDEs. In the first approach we derive a set of coupled PDEs for the local coordinates of the Lie-group manifold. In the second approach a coordinate-free framework is proposed where the PDE is defined directly with respect to the Lie-group elements. This is a parameterization-free method. The differences between these two methods are discussed. We exemplify this framework on the well-known orientation diffusion problem, namely, the unit-circle S ¹ which is identified with the group of rotations in two dimensions, SO(2). Regularization of the group of rotations in 3D and 4D, SO(3) and SO(4), respectively, is demonstrated as well.

Evaluation of peak picking quality in LC-MS metabolomics data

The output of LC-MS metabolomics experiments consists of mass-peak intensities identified through a peak-picking/alignment procedure. Besides imperfections in biological samples and instrumentation, data accuracy is highly dependent on the applied algorithms and their parameters. Consequently, quality control (QC) is essential for further data analysis. Here, we present a QC approach that is based on discrepancies between replicate samples. First, the quantile normalization of per-sample log-signal distributions is applied to each group of biologically homogeneous samples. Next, the overall quality of each replicate group is characterized by the Z-transformed correlation coefficients between samples. This general QC allows a tuning of the procedure's parameters which minimizes the inter-replicate discrepancies in the generated output. Subsequently, an in-depth QC measure detects local neighborhoods on a template of aligned chromatograms that are enriched by divergences between intensity profiles of replicate samples. These neighborhoods are determined through a segmentation algorithm. The retention time (RT)-m/z positions of the neighborhoods with local divergences are indicative of either: incorrect alignment of chromatographic features, technical problems in the chromatograms, or to a true biological discrepancy between replicates for particular metabolites. We expect this method to aid in the accurate analysis of metabolomics data and in the development of new peak-picking/alignment procedures.     

Direction of Arrival Estimation in the Presence of Noise Coupling in Antenna Arrays

The direction of arrival (DOA) estimation problem in the presence of signal and noise coupling in antenna arrays is addressed. In many applications, such as smart antenna, radar and navigation systems, the noise coupling between different antenna array elements is often neglected in the antenna modeling and thus, may significantly degrade the system performance. Utilizing the exact noise covariance matrix enables to achieve high-performance source localization by taking into account the colored properties of the array noise. The noise covariance matrix of the antenna array consists of both the external noise sources from sky, ground and interference, and the internal noise sources from amplifiers and loads. Computation of the internal noise covariance matrix is implemented using the theory of noisy linear networks combined with the method of moments (MoM). Based on this noise statistical analysis, a new four-port antenna element consisting of two orthogonal loops is proposed with enhanced source localization performance. The maximum likelihood (ML) estimator and the Cramer-Rao lower bound (CRLB) for DOA estimation in the presence of noise coupling is derived. Simulation results show that the noise coupling in antenna arrays may substantially alter the source localization performance. The performance of a mismatched ML estimator based on a model which ignores the noise coupling shows significant performance degradation due to noise coupling. These results demonstrate the importance of the noise coupling modeling in the DOA estimation algorithms.     

S-states of helium-like ions

A simple Mathematica (version 7) code for computing S-state energies and wave functions of two-electron (helium-like) ions is presented. The elegant technique derived from the classical papers of Pekeris (1958, 1959, 1962, 1965, 1971) [1], [2] and [3] is applied. The basis functions are composed of the Laguerre functions. The method is based on the perimetric coordinates and specific properties of the Laguerre polynomials. Direct solution of the generalized eigenvalues and eigenvectors problem is used, distinct from the Pekeris works. No special subroutines were used, only built-in objects supported by Mathematica. The accuracy of the results and computation times depend on the basis size. The ground state and the lowest triplet state energies can be computed with a precision of 12 and 14 significant figures, respectively. The accuracy of the higher excited states calculations is slightly worse. The resultant wave functions have a simple analytical form, that enables calculation of expectation values for arbitrary physical operators without any difficulties. Only three natural parameters are required in the input.The above Mathematica code is simpler than the earlier version (Liverts and Barnea, 2010 [4]). At the same time, it is faster and more accurate.

Program summary

Program title: TwoElAtomSL(SH)Catalogue identifier: AEHY_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHY_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 11 434No. of bytes in distributed program, including test data, etc.: 540 063Distribution format: tar.gzProgramming language: Mathematica 7.0Computer: Any PCOperating system: Any which supports Mathematica; tested under Microsoft Windows XP and Linux SUSE 11.0RAM:?¹⁰⁹ bytesClassification: 2.1, 2.2, 2.7, 2.9Nature of problem: The Schrödinger equation for atoms (ions) with more than one electron has not been solved analytically. Approximate methods must be applied in order to obtain the wave functions or another physical attributes from quantum mechanical calculations.Solution method: The S-wave function is expanded into a triple set of basis functions which are composed of the exponentials combined with the Laguerre polynomials in the perimetric coordinates. Using specific properties of the Laguerre polynomials, solution of the two-electron Schrödinger equation reduces to solving the generalized eigenvalues and eigenvector problem for the proper Hamiltonian. The unknown exponential parameter is determined by means of minimization of the corresponding eigenvalue (energy).Restrictions: First, the too large length of expansion (basis size) takes the too large computation time and operative memory giving no perceptible improvement in accuracy. Second, the number of shells Ω in the wave function expansion enables one to calculate the excited nS-states up to n=Ω+1 inclusive.Running time: 2–60 minutes (depends on basis size and computer speed).     

Simple iterative receivers for MIMO LP-OFDM systems

In this paper,Lp-ofdm is combined with differentMimo schemes in order to improve performance in terms of diversity gain and to exploit capacity brought by theMimo channel. The original contribution is the development of a generic iterative receiver designed forLp mimo transmission able to work whatever the antenna configuration and the spatial coding scheme. By using a globalMmse criterion, interference terms coming from space-time coding and linear precoding are jointly treated leading to a very good trade-off between performance and complexity compared to trellis based detectors particularly for high order modulations, high number of antennas and/or large size of precoding matrices.     

Threshold of stimulated Brillouin scattering by use of a solar pumped laser

What is to our knowledge the first stimulated Brillouin scattering experiment using a high-power low-gain solar pumped laser is presented. A threshold reflectivity of 0.23% was reached when a peak power of 20.7 kW was used at 7.6 GHz. A cw solar pumped laser was Q-switched with an acousto-optic modulator, and the bandwidth was narrowed with an intracavity etalon. A high polarization ratio (>99.4%) was achieved by use of an intracavity configuration. Higher reflectivity values were limited because of the lack of availability of optical switches.     

Inhibition of FLT3: A Prototype for Molecular Targeted Therapy in Acute Myeloid Leukemia

Modern therapy of acute myeloid leukemia (AML) began in 1973 with the first report of the successful combination of daunorubicin and cytarabine, which led to complete remission in approximately 45% of patients. Accurate AML diagnosis was dependent on morphology, aided initially only by cytochemistry. Unlike acute lymphoblastic leukemia (ALL), immunophenotyping offered little in the diagnosis of AML, at least during the 1970s and 1980s. The advent of reliable cytogenetics changed the entire prognostic outlook of AML. With karyotypic analysis, different groups of AML could be classified and stratified for various therapies. Unique mutational profiling was a major advance in further categorizing AML patients, aided by the immunophenotypic identification of antigenic markers on the cells. All these advances were occurring as the understanding of the importance of the tumor burden—known as minimal residual disease (MRD)—became crucial for the management of AML patients. The efficacy of MRD has rapidly progressed in the past decade, from a specificity of 10⁻³ with immunophenotyping to 10⁻⁴ with polymerase chain reaction (PCR), which is only appropriate for some patients with AML, and finally to 10⁻⁵ or even 10⁻⁶ cells with the extraordinary sensitivity of next-generation sequencing (NGS). All of these advances have promoted the concept of personalized medicine, which has led to the advent of targeted agents that can accurately be used for specific diagnostic subtypes. Responses can be predicted and measured accurately. Such targeted agents have now become a cornerstone in the management of AML, increasing efficacy and dramatically reducing toxicity. The focus of this review is on one of the most well-studied targeted agents in AML: the FMS-like tyrosine kinase 3 (FLT3) inhibitors, which have impacted the prognostication and therapeutics of AML. This review selectively discusses the FLT3 inhibitors in detail, as a model for the other burgeoning targeted agents that have already been approved, as well as those that are currently in development.     

Study of DNA Origami Dimerization and Dimer Dissociation Dynamics and of the Factors that Limit Dimerization

Organizing DNA origami building blocks into higher order structures is essential for fabrication of large structurally and functionally diverse devices and molecular machines. Unfortunately, the yields of origami building block attachment reactions are typically not sufficient to allow programed assembly of DNA devices made from more than a few origami building blocks. To investigate possible reasons for these low yields, a detailed single‐molecule fluorescence study of the dynamics of rectangular origami dimerization and origami dimer dissociation reactions is conducted. Reactions kinetics and yields are investigated at different origami and ion concentrations, for different ion types, for different lengths of bridging strands, and for the “sticky end” and “weaving welding” attachment techniques. Dimerization yields are never higher than 86%, which is typical for such systems. Analysis of the dynamic data shows that the low yield cannot be explained by thermodynamic instability or structural imperfections of the origami constructs. Atomic force microscopy and gel electrophoresis evidence reveal self‐dimerization of the origami monomers, likely via blunt‐end interactions made possible by the presence of bridging strands. It is suggested that this mechanism is the major factor that inhibits correct dimerization and means to overcome it are discussed.