Multi-output local Gaussian process regression: Applications to uncertainty quantification

We develop an efficient, Bayesian Uncertainty Quantification framework using a novel treed Gaussian process model. The tree is adaptively constructed using information conveyed by the observed data about the length scales of the underlying process. On each leaf of the tree, we utilize Bayesian Experimental Design techniques in order to learn a multi-output Gaussian process. The constructed surrogate can provide analytical point estimates, as well as error bars, for the statistics of interest. We numerically demonstrate the effectiveness of the suggested framework in identifying discontinuities, local features and unimportant dimensions in the solution of stochastic differential equations.     

Focused microwave-assisted extraction combined with solid-phase microextraction and gas chromatography-mass spectrometry for the selective analysis of cocaine from coca leaves

An effective combination of focused microwave-assisted extraction (FMAE) with solid-phase microextraction (SPME) prior to gas chromatography (GC) is described for the selective extraction and quantitative analysis of cocaine from coca leaves (Erythroxylum coca). This approach required switching from an organic extraction solvent to an aqueous medium more compatible with SPME liquid sampling. SPME was performed in the direct immersion mode with a universal 100 microm polydimethylsiloxane (PDMS) coated fibre. Parameters influencing this extraction step, such as solution pH, sampling time and temperature are discussed. Furthermore, the overall extraction process takes into account the stability of cocaine in alkaline aqueous solutions at different temperatures. Cocaine degradation rate was determined by capillary electrophoresis using the short end injection procedure. In the selected extraction conditions, less than 5% of cocaine was degraded after 60 min. From a qualitative point of view, a significant gain in selectivity was obtained with the incorporation of SPME in the extraction procedure. As a consequence of SPME clean-up, shorter columns could be used and analysis time was reduced to 6 min compared to 35 min with conventional GC. Quantitative results led to a cocaine content of 0.70 +/- 0.04% in dry leaves (RSD <5%) which agreed with previous investigations.     

How To Make Nitroaromatic Compounds Glow: Next‐Generation Large X‐Shaped,Centrosymmetric Diketopyrrolopyrroles

Red‐emissive π‐expanded diketopyrrolopyrroles (DPPs) with fluorescence reaching λ=750 nm can be easily synthesized by a three‐step strategy involving the preparation of diketopyrrolopyrrole followed by N‐arylation and subsequent intramolecular palladium‐catalyzed direct arylation. Comprehensive spectroscopic assays combined with first‐principles calculations corroborated that both N‐arylated and fused DPPs reach a locally excited (S₁) state after excitation, followed by internal conversion to states with solvent and structural relaxation, before eventually undergoing intersystem crossing. Only the structurally relaxed state is fluorescent, with lifetimes in the range of several nanoseconds and tens of picoseconds in nonpolar and polar solvents, respectively. The lifetimes correlate with the fluorescence quantum yields, which range from 6 % to 88 % in nonpolar solvents and from 0.4 % and 3.2 % in polar solvents. A very inefficient (T₁) population is responsible for fluorescence quantum yields as high as 88 % for the fully fused DPP in polar solvents.     

Metabolic Behavior and Enzymatic Aspects of Denitrifying EBPR Sludge in a Continuous-Flow Anaerobic–Anoxic System

The metabolic aspects of enhanced biological phosphorus removal (EBPR) were investigated for the first time in a continuous-flow anaerobic–anoxic plant fed with acetate, propionate, or substrates which are involved in the tricarboxylic acid and/or glyoxylate cycle, i.e., fumarate, malate, or oxaloacetate, as the sole carbon source. Although the polyphosphate-accumulating organisms (PAOs) population remained stable with any carbon source examined, no typical EBPR metabolism was observed during fumarate, malate, or oxaloacetate utilization. Specific enzymatic activities related to EBPR were determined in activated sludge homogenates and directly correlated with the nutrient metabolic rates. The experimental results indicated the direct involvement of alkaline phosphatase, pyrophosphatase, and exopolyphosphatase in the denitrifying EBPR process. Metabolic aspects of glyoxylate cycle enzymes are discussed with regard to the biomass anaerobic and anoxic activity. Process performance was highly influenced by the kind of substrate utilized, indicating that specific metabolic pathways should be followed to favor efficient EBPR.     

Measuring monotony in two-dimensional samples

This note introduces a monotony coefficient as a new measure of the monotone dependence in a two-dimensional sample. Some properties of this measure are derived. In particular, it is shown that the absolute value of the monotony coefficient for a two-dimensional sample is between |r| and 1, where r is the Pearson's correlation coefficient for the sample; that the monotony coefficient equals 1 for any monotone increasing sample and equals ?1 for any monotone decreasing sample. This article contains a few examples demonstrating that the monotony coefficient is a more accurate measure of the degree of monotone dependence for a non-linear relationship than the Pearson's, Spearman's and Kendall's correlation coefficients. The monotony coefficient is a tool that can be applied to samples in order to find dependencies between random variables; it is especially useful in finding couples of dependent variables in a big dataset of many variables. Undergraduate students in mathematics and science would benefit from learning and applying this measure of monotone dependence.     

Thickness-induced violation of de Haas-van Alphen effect through exact analytical solutions at a one-electron and a one-composite fermion level

A systematic study of the energetics of electrons in an interface in a magnetic field is reported with exact analytical calculations based on a Landau level (LL) picture, by serious consideration of the finite thickness of the quantum well (QW). The approach is physically transparent and subtly different in its line of reasoning from standard methods avoiding any semi-classical approximation. We find “internal” phase transitions (at partial LL filling) for magnetisation and susceptibility that are not captured by other approaches and that give rise to nontrivial violations of the standard de Haas-van Alphen periods, in a manner that reproduces the exact quantal astrophysical behaviours in the limit of full three-dimensional (3D) space. Upon inclusion of Zeeman splitting, additional features are also found, such as global energy minima originating from the interplay of QW, Zeeman and LL Physics, while a corresponding calculation in a composite fermion picture with Λ-levels, leads to new predictions on magnetic properties of an interacting electron liquid. By pursuing the same line of reasoning for a topologically nontrivial system with a relativistic spectrum, we find evidence that similar effects might be operative in the dimensionality crossover of 3D strong topological insulators to 2D topological insulator quantum wells.     

A comparative study on the use of the extended-Cauchy dispersion equation for fitting refractive index data in crystals

This study attempts a comparative evaluation of chromatic dispersion equations in 61 crystalline solids. Based on previously published data, it is demonstrated that the extended-Cauchy equation (which in the past has been mainly used with glasses) outperforms Sellmeier models and other alternative approaches in the cases of 43 crystals, including BBO, BiBO, KTP, etc. Accumulated Cauchy coefficients for these 43 materials are presented. Performance characteristics of the extended-Cauchy model are related to specific experimental conditions, such as the number of available refractive index data, as well as the spectral location and bandwidth of measurement. The number of Cauchy coefficients required for reaching practically maximum fitting accuracy is determined. It is shown that typically, extended-Cauchy equations constructed by use of only five experimental data may be used for precise modeling of two-octave spanning spectral bandwidths.     

The “Forgotten” Pseudomomenta and Gauge Changes in Generalized Landau Level Problems: Spatially Nonuniform Magnetic and Temporally Varying Electric Fields

By perceiving gauge invariance as an analytical tool in order to get insight into the states of the “generalized Landau problem” (a charged quantum particle moving inside a magnetic, and possibly electric field), and motivated by an early article that correctly warns against a naive use of gauge transformation procedures in the usual Landau problem (i.e. with the magnetic field being static and uniform), we first show how to bypass the complications pointed out in that article by solving the problem in full generality through gauge transformation techniques in a more appropriate manner. Our solution provides in simple and closed analytical forms all Landau Level-wavefunctions without the need to specify a particular vector potential. This we do by proper handling of the so-called pseudomomentum \(\vec {{K}}\) (or of a quantity that we term pseudo-angular momentum L _z ), a method that is crucially different from the old warning argument, but also from standard treatments in textbooks and in research literature (where the usual Landau-wavefunctions are employed - labeled with canonical momenta quantum numbers). Most importantly, we go further by showing that a similar procedure can be followed in the more difficult case of spatially-nonuniform magnetic fields: in such case we define \(\vec {{K}}\) and L _z as plausible generalizations of the previous ordinary case, namely as appropriate line integrals of the inhomogeneous magnetic field – our method providing closed analytical expressions for all stationary state wavefunctions in an easy manner and in a broad set of geometries and gauges. It can thus be viewed as complementary to the few existing works on inhomogeneous magnetic fields, that have so far mostly focused on determining the energy eigenvalues rather than the corresponding eigenkets (on which they have claimed that, even in the simplest cases, it is not possible to obtain in closed form the associated wavefunctions). The analytical forms derived here for these wavefunctions enable us to also provide explicit Berry’s phase calculations and a quick study of their connection to probability currents and to some recent interesting issues in elementary Quantum Mechanics and Condensed Matter Physics. As an added feature, we also show how the possible presence of an additional electric field can be treated through a further generalization of pseudomomenta and their proper handling.     

Sample pretreatment method for the determination of polychlorinated biphenyls in bird livers using ultrasonic extraction followed by headspace solid-phase microextraction and gas chromatography-mass spectrometry

A simple and reliable sample methodology based on simultaneous ultrasonic extraction, sulfuric acid clean-up and headspace solid-phase microextraction (SPME)-gas chromatography-mass spectrometry has been developed as an advantageous analytical tool for the determination of seven polychlorinated biphenyl congeners in bird livers at low levels. The influence of several parameters on the efficiency of the proposed method was systematically investigated. The clean-up efficiency of sulfuric acid treatment was tested and compared with those of column chromatography (Flosiril, silica gel and alumina) and solid-phase extraction (SPE) (Supelclean ENVI-Carb cartridge) procedures. The use of sulfuric acid in the clean-up step prior to headspace solid-phase microextraction analysis allows the removal of interfering matrix compounds present in the liver extracts that would otherwise cause severe ionization suppression of the polychlorinated biphenyls (PCBs) during the ionization process. The optimized method had good linearity (R2>0.99) over the range studied (5-500 ng/g wet weight) and showed satisfactory level of precision, with RSD values lower than 10.6%. The obtained relative recoveries ranged between 63 and 94%. The limits of detection (0.06-0.63 ng/g wet weight) were low enough to check for harmful levels of polychlorinated biphenyls in biological samples, and were well below most of the restrictive limits established by European Union regulations. The method was found to be reliable under the operational conditions proposed and was applied successfully to the analysis of individual polychlorinated biphenyls in liver tissues. The results obtained from five bird species from Greece revealed the presence of the target compounds in all samples analyzed, at levels ranging between 0.54 and 39.45 ng/g wet weight.