On the uniqueness of overcomplete dictionaries, and a practical way to retrieve them

A full-rank under-determined linear system of equations Ax = b has in general infinitely many possible solutions. In recent years there is a growing interest in the sparsest solution of this equation—the one with the fewest non-zero entries, measured by ∥x∥₀. Such solutions find applications in signal and image processing, where the topic is typically referred to as “sparse representation”. Considering the columns of A as atoms of a dictionary, it is assumed that a given signal b is a linear composition of few such atoms. Recent work established that if the desired solution x is sparse enough, uniqueness of such a result is guaranteed. Also, pursuit algorithms, approximation solvers for the above problem, are guaranteed to succeed in finding this solution.Armed with these recent results, the problem can be reversed, and formed as an implied matrix factorization problem: Given a set of vectors {b_i}, known to emerge from such sparse constructions, Ax_i = b_i, with sufficiently sparse representations x_i, we seek the matrix A. In this paper we present both theoretical and algorithmic studies of this problem. We establish the uniqueness of the dictionary A, depending on the quantity and nature of the set {b_i}, and the sparsity of {x_i}. We also describe a recently developed algorithm, the K-SVD, that practically find the matrix A, in a manner similar to the K-Means algorithm. Finally, we demonstrate this algorithm on several stylized applications in image processing.     

Peak alignment of urine NMR spectra using fuzzy warping

Proton nuclear magnetic resonance (1H NMR) spectroscopic analysis of mixtures has been used extensively for a variety of applications ranging from the analysis of plant extracts, wine, and food to the evaluation of toxicity in animals. For example, NMR analysis of urine samples has been used extensively for biomarker discovery and, more simply, for the construction of classification models of toxicity, disease, and biochemical phenotype. However, NMR spectra of complex mixtures typically show unwanted local peak shifts caused by matrix and instrument variability, which must be compensated for prior to statistical analysis and interpretation of the data. One approach is to align the spectral peaks across the data set. An efficient and fast warping algorithm is required as the signals typically contain ca. 32,000-64,000 data points and there can be several thousand spectra in a data set. As demonstrated in our study, the iterative fuzzy warping algorithm fulfills these requirements and can be used on-line for an alignment of the NMR spectra. Correlation coefficients between the aligned and target spectra are used as the evaluation function for the algorithm, and its performance is compared with those of other published warping methods.     

Geometric accuracy of three-dimensional molecular overlays

This study examines the dependence of molecular alignment accuracy on a variety of factors including the choice of molecular template, alignment method, conformational flexibility, and type of protein target. We used eight test systems for which X-ray data on 145 ligand-protein complexes were available. The use of X-ray structures allowed an unambiguous assignment of bioactive overlays for each compound set. The alignment accuracy depended on multiple factors and ranged from 6% for flexible overlays to 73% for X-ray rigid overlays, when the conformation of the template ligand came from X-ray structures. The dependence of the overlay accuracy on the choice of templates and molecules to be aligned was found to be the most significant factor in six and seven of the eight ligand-protein complex data sets, respectively. While finding little preference for the overlay method, we observed that the introduction of molecule flexibility resulted in a decrease of overlay accuracy in 50% of the cases. We derived rules to maximize the accuracy of alignment, leading to a more than 2-fold improvement in accuracy (from 19% to 48%). The rules also allowed the identification of compounds with a low (<5%) chance to be correctly aligned. Last, the accuracy of the alignment derived without any utilization of X-ray conformers varied from <1% for the human immunodeficiency virus data set to 53% for the trypsin data set. We found that the accuracy was directly proportional to the product of the overlay accuracy from the templates in their bioactive conformations and the chance of obtaining the correct bioactive conformation of the templates. This study generates a much needed benchmark for the expectations of molecular alignment accuracy and shows appropriate usages and best practices to maximize hypothesis generation success.     

Possibilities and limitations of fast GC with narrow-bore columns

In this work, two narrow-bore capillary columns with different internal diameters (I.D.) 0.15 mm (15 m length, 0.15 microm film thickness) and 0.10 mm (10 m length, 0.10 microm film thickness) with the same stationary phase (5% diphenyl 95% dimethylsiloxane), phase ratio and separation power were compared with regard to their advantages, practical limitations and applicability in fast GC on commercially available instrumentation. The column comparison concerns fast GC method development, speed and separation efficiency, the sample transfer into the column utilizing split and splitless inlet, sample capacity, detection (analysing compounds of a wide range of polarities and volatilities--even n-alkanes C16-C28 and selected pesticides) and ruggedness (in the field of ultratrace analysis of pesticide residues in real matrix). Under conditions corresponding to speed/separation efficiency trade-off 0.10 mm I.D. versus 0.15 mm I.D. column provides a speed gain of 1.74, but all other parameters investigated were better for the 0.15 mm I.D. column concerning more efficient sample transfer from inlet to the column using splitless injection, no discrimination with split injection. Better sample capacity (three times higher for the 0.15 mm than for the 0.10 mm I.D. column) resulted in improved ruggedness and simpler fast GC-MS method development.     

Optical and X-ray emission spectroscopy of high-power laser-induced dielectric breakdown in molecular gases and their mixtures

Large-scale plasma was created in molecular gases (CO, CO2, N2, H2O) and their mixtures by high-power laser-induced dielectric breakdown (LIDB). Compositions of the mixtures used are those suggested for the early earth's atmosphere of neutral and/or mildly reducing character. Time-integrated optical spectra emitted from the laser spark have been measured and analyzed. The spectra of the plasma generated in the CO-containing mixtures are dominated by emission of both C2 and CN radicals. A vibrational temperature of approximately 10(4) K was determined according to an intensity distribution in a vibronic structure of the CN (B2Sigma(+)u-X2Sigma(+)g) violet band. For comparison, the NH3-CH4-H2-H2O mixture has been irradiated as a model of the strongly reducing version of the early earth's atmosphere. In this mixture, excited CN seems to be significantly less abundant than C2. The LIDB experiments were in the molecular gases carried out not only in the static cell but also using a large, double stream pulse jet (gas puff target) placed in the vacuum interaction chamber. The obtained soft X-ray emission spectra indicate the presence of highly charged atomic ions in the hot core of high-power laser sparks.     

Optical sensing system for ATP using porphyrin-alkaloid conjugates

Tetrabrucin-porphyrin as a sensor for ATP was designed and tested; selectivity for ATP was proved in the presence of ADP and AMP.     

Recording 2-D Nutation NQR Spectra by Random Sampling Method

The method of random sampling was introduced for the first time in the nutation nuclear quadrupole resonance (NQR) spectroscopy where the nutation spectra show characteristic singularities in the form of shoulders. The analytic formulae for complex two-dimensional (2-D) nutation NQR spectra (I = 3/2) were obtained and the condition for resolving the spectral singularities for small values of an asymmetry parameter η was determined. Our results show that the method of random sampling of a nutation interferogram allows significant reduction of time required to perform a 2-D nutation experiment and does not worsen the spectral resolution.     

Graph algorithms for DNA sequencing – origins,current models and the future

With the ubiquitous presence of next-generation sequencing in modern biological, genetic, pharmaceutical and medical research, not everyone pays attention to the underlying computational methods. Even fewer researchers know what were the origins of the current models for DNA assembly. We present original graph models used in DNA sequencing by hybridization, discuss their properties and connections between them. We also explain how these graph models evolved to adapt to the characteristics of next-generation sequencing. Moreover, we present a practical comparison of state-of-the-art DNA de novo assembly tools representing these transformed models, i.e. overlap and decomposition-based graphs. Even though the competition is tough, some assemblers perform better and certainly large differences may be observed in hardware resources utilization. Finally, we outline the most important trends in the sequencing field, and try to predict their impact on the computational models in the future.