Matrix-free interior point method for compressed sensing problems

We consider a class of optimization problems for sparse signal reconstruction which arise in the field of compressed sensing (CS). A plethora of approaches and solvers exist for such problems, for example GPSR, FPC_AS, SPGL1, NestA, $\mathbf{\ell _1\_\ell _s}$ , PDCO to mention a few. CS applications lead to very well conditioned optimization problems and therefore can be solved easily by simple first-order methods. Interior point methods (IPMs) rely on the Newton method hence they use the second-order information. They have numerous advantageous features and one clear drawback: being the second-order approach they need to solve linear equations and this operation has (in the general dense case) an ${\mathcal {O}}(n^3)$ computational complexity. Attempts have been made to specialize IPMs to sparse reconstruction problems and they have led to interesting developments implemented in $\mathbf{\ell _1\_\ell _s}$ and PDCO softwares. We go a few steps further. First, we use the matrix-free IPM, an approach which redesigns IPM to avoid the need to explicitly formulate (and store) the Newton equation systems. Secondly, we exploit the special features of the signal processing matrices within the matrix-free IPM. Two such features are of particular interest: an excellent conditioning of these matrices and the ability to perform inexpensive (low complexity) matrix–vector multiplications with them. Computational experience with large scale one-dimensional signals confirms that the new approach is efficient and offers an attractive alternative to other state-of-the-art solvers.     

Ab initio potential energy surface and vibration‐rotation energy levels of silicon dicarbide,SiC2

The accurate ground‐state potential energy surface of silicon dicarbide, SiC₂, has been determined from ab initio calculations using the coupled‐cluster approach. Results obtained with the conventional and explicitly correlated coupled‐cluster methods were compared. The core‐electron correlation, higher‐order valence‐electron correlation, and scalar relativistic effects were taken into account. The potential energy barrier to the linear SiCC configuration was predicted to be 1782 cm^?1. The vibration‐rotation energy levels of the SiC₂, ²⁹SiC₂, ³⁰SiC₂, and SiC¹³C isotopologues were calculated using a variational method. The experimental vibration‐rotation energy levels of the main isotopologue were reproduced to high accuracy. In particular, the experimental energy levels of the highly anharmonic vibrational ν₃ mode of SiC₂ were reproduced to within 6.7 cm^?1, up to as high as the v₃ = 16 state.     

Benchmark calculations for He2 and LiH molecules using explicitly correlated Gaussian functions

Explicitly correlated Gaussian (ECG) functions with carefully optimized non-linear parameters are used to calculate the electronic energies of He₂⁺ and LiH at their equilibrium internuclear distances. The obtained variational upper bounds (−4.99464392 and −8.070538 hartree, respectively) are the lowest reported to date. By extrapolating results obtained with various expansion lengths, the estimations of the Born–Oppenheimer limits are made.     

Ultrafast carbene-carbene isomerization

The photochemistry of two isomeric aryl diazo ketones was investigated by fs time-resolved UV-vis and IR spectroscopies. Both diazo ketone excited states decompose in less than 300 fs by multiple pathways. One pathway involves concerted Wolff rearrangement and nitrogen extrusion, most likely in the syn rotomer. In the anti rotomer of one isomer, oxygen migration proceeds in concert with nitrogen extrusion to form rearranged keto carbene. This rotomer excited state also decomposes to form unrearranged carbene, which isomerizes in 5 ps.     

Rime samples characterization and comparison using classical and fuzzy principal components analysis

The main objective of this paper is to introduce principal component analysis and two robust fuzzy principal component algorithms as useful tools in characterizing and comparing rime samples collected in different locations in Poland (2004–2007). The efficiency of the applied procedures was illustrated on a data set containing 108 rime samples and concentration of anions, cations, HCHO, as well as pH and conductivity. The fuzzy principal component algorithms achieved better results mainly because they are more compressible than classical PCA and very robust to outliers. For example, a three component model, fuzzy principal component analysis-first component (FPCA-1) accounts for 62.37% of the total variance and fuzzy principal component analysis-orthogonal (FPCA-o) 90.11%; PCA accounts only for 58.30%. The first two principal components explain 51.41% of the total variance in the case of FPCA-1 and 79.59% in the case of FPCA-o as compared to only 47.55% for PCA. As a direct consequence, PCA showed only a partial differentiation of rime samples onto the plane or in the space described by different combination of two or three principal components, whereas a much sharper differentiation of the samples, regarding their origin and location, is observed when FPCAs are applied.      

Ultrafast spectroscopic study of the photochemistry and photophysics of arylhalodiazirines: direct observation of carbene and zwitterion formation

Ultrafast photolysis (lambdaex = 270, 350, or 360 nm) of bromophenyl, chlorophenyl, fluorophenyl, and fluoro-para-trifluoromethylphenyl diazirines produces transient species which absorb broadly in the UV and visible regions. Transient decay can be fit to either mono- or biexponential functions (tau1 approximately 0.3-10 ps, tau2 approximately 10-350 ps; dependent on solvent and halogen). Fluoro- and chlorophenylcarbene are formed within the time resolution of the spectrometer (300 fs, 270 nm excitation). Bromophenyl diazirine decay (270 nm excitation) correlates with the growth of bromophenylcarbene. Solvent and substituent effects on the slower decays of the transient absorptions are consistent with assigning the carriers of transient absorption in the visible region to ring-opened zwitterionic species.     

Quantitative measurement of different ceramide species from crude cellular extracts by normal-phase high-performance liquid chromatography coupled to atmospheric pressure ionization mass spectrometry

Normal-phase high-performance liquid chromatography (NP-HPLC) coupled to atmospheric pressure ionization mass spectrometry (APCI-MS) allows quantitative analysis of endogenous ceramide and dihydroceramide species from crude lipid extracts. Qualitative information for the species comes from observation of differences in chromatographic and mass spectrometric behavior between species (Pettus et al. Rapid Commun. Mass Spectrom. 2003; 17: 1017-1026). Quantitative analysis is achieved by (1) use of a synthetic internal standard as an extraction and injection control, (2) lack of salt adduction, ion suppression, or other matrix effects in APCI mode, and (3) consistent fragmentation and ionization of external standards across the physiologically relevant concentration range found in endogenous lipid samples. Application to the analysis and quantitation of ceramide and dihydroceramide from various cell lines is demonstrated. The results from APCI-MS analysis corroborate and enhance information acquired from use of the diacylglycerol kinase assay for total ceramide measurement. This technique readily allows simultaneous quantitation of ceramide and dihydroceramide species.     

Assessment of 4-nitrogenated benzyloxymethyl groups for 2'-hydroxyl protection in solid-phase RNA synthesis

The search for a 2'-OH protecting group that would impart ribonucleoside phosphoramidites with coupling kinetics and coupling efficiencies comparable to those of deoxyribonucleoside phosphoramidites led to an assessment of 2'-O-(4-nitrogenated benzyloxy)methyl groups through solid-phase RNA synthesis using phosphoramidites 2a-d, 12a, and 14a. These phosphoramidites exhibited rapid and efficient coupling properties. Particularly noteworthy is the cleavage of the 2'-O-[4-(N-methylamino)benzyloxy]methyl groups in 0.1 M AcOH, which led to U19dT within 15 min at 90 degrees C. [reaction: see text]     

Monitoring and analytics of semivolatile organic compounds (SVOCs) in indoor air

This paper reviews literature information on the behaviour of semivolatile organic compounds (SVOCs) in the indoor environment, as well as the most likely emission sources. The consecutive stages of analytical procedures used for monitoring SVOCs in indoor environments are described. The most common approaches used for collecting samples from the gas and particulate phases are mentioned. The paper discusses and compares various types of sorbents and filters applied in dynamic, passive and denudational techniques, as well as the techniques used to liberate the SVOCs, including Soxhlet, sonication and microwave extraction. The main advantages and disadvantages of each technique are discussed, together with possible future trends. The approaches commonly used during the final determination step, such as gas chromatography and liquid chromatography, are presented together with their possible drawbacks, and ways of eliminating them are suggested. The review makes brief reference to the effects of human exposure to SVOCs in house dust and discusses the main aspects of the analytical procedures used to monitor the presence of SVOCs in this medium.     

Determination of total carbon and total organic carbon from volatile air pollutants. Part I

Summary A new method of collection of representative air samples for the determination of TC and TOC from volatile air pollutants has been developed. The organic substances undergo combustion and only the carbon dioxide produced is concentrated on molecular sieve 5 A at ambient temperature. The CO₂ is subsequently liberated by thermal desorption at ca. 380°C in a stream of purified gas. Atmospheric CO₂ must be removed first and this can be done (at the sample flow rate of 700 ml/min) by a layer of Ascarite heated at 90° C. Organic compounds passing through the layer are then combusted by a dynamic method utilizing Körbl catalyst and the CO₂ formed is concentrated on a molecular sieve 5 A, followed by thermal desorption and final determination. Organic acids are also retained by the first CO₂ absorber. A diffusion cell for preparation of the mixtures of purified air with vapours of organic compounds is described.

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Zusammenfassung Eine neue Anreicherungsmethode zur Gewinnung representativer Luftproben zur Bestimmung des Gesamtkohlenstoffgehaltes und des Gehaltes an organischem Kohlenstoff (TOC) aus flüchtigen Luftverunreinigungen wurde entwickelt. Während der Probenahme werden die flüchtigen Verunreinigungen verbrannt und nur das entstandene Kohlendioxid bei Zimmertemperatur am Molekularsieb 5A angereichert. Anschließend wird CO₂ bei ca. 380° C im gereinigten Gasstrom thermisch desorbiert. Bei der TOC-Bestimmung muß atmosphärisches CO₂ vorangehend aus dem Luftstrom entfernt werden und wird an einer auf 90° C erwärmten Ascariteschicht gebunden. Die durchfließenden organischen Verbindungen werden dann im dynamischen System am Körblkatalysator oxydiert, das entstandene CO₂ am Molekularsieb 5A angereichert, thermisch desorbiert und einer Endbestimmung zugeführt. Organische Säuren werden gleichfalls durch den ersten CO₂-Absorber gebunden. Eine Diffusionszelle zur Herstellung von Gemischen gereinigter Luft mit Dämpfen organischer Verbindungen wurde beschrieben.