High performance liquid chromatographic analysis of phytoplankton pigments using a C16-amide column

In this study, a reverse-phase HPLC method incorporating a ternary solvent system was developed to analyze most polar and non-polar chlorophylls and carotenoids present in phytoplankton. The method is based on an RP-C₁₆-Amide column and provided excellent peak resolution of most taxonomically important pigments and an elution profile different than C₈ or C₁₈ columns provide. Analysis of mixed pigment standards, extracts of phytoplankton monocultures, and field samples showed that this method was able to resolve more than sixty pigments, ranging from very polar acidic chlorophylls to the non-polar hydrocarbon carotenes in less than 36 min. This included chlorophylls c₁, c₂ and c₃, divinyl chlorophylls a and b, the carotenoids lutein and zeaxanthin and some recently discovered pigments. The ability of this method to resolve divinyl chl b from monovinyl chl b and divinyl chl a from monovinyl chl a is particularly important for the quantification and identification of the marine cyanobacteria Prochlorococcus spp. in oceanic waters. The described protocol is sensitive and reproducible and can be used to assess the distribution and dynamics of major phytoplankton groups in marine and freshwater ecosystems.     

Validating proofs and counterexamples across content domains: Practices of importance for mathematics majors

Validating proofs and counterexamples across content domains is considered vital practices for undergraduate students to advance their mathematical reasoning and knowledge. To date, not enough is known about the ways mathematics majors determine the validity of arguments in the domains of algebra, analysis, geometry, and number theory—the domains that are central to many mathematics courses. This study reported how 16 mathematics majors, including eight specializing in secondary mathematics education, who had completed more proof-based courses than transition-to-proof classes evaluated various arguments. The results suggest that the students use one of the following strategies in proof and counterexample validation: (1) examination of the argument's structure and (2) line-by-line checking with informal deductive reasoning, example-based reasoning, experience-based reasoning, and informal deductive and example-based reasoning. Most students tended to examine all steps of the argument with informal deductive reasoning across various tasks, suggesting that this approach might be problem dependent. Even though all participating students had taken more proof-related mathematics courses, it is surprising that many of them did not recognize global-structure or line-by-line content-based flaws presented in the argument.     

Stochastic modeling of neurobiological time series: power, coherence, Granger causality, and separation of evoked responses from ongoing activity

In this article we consider the stochastic modeling of neurobiological time series from cognitive experiments. Our starting point is the variable-signal-plus-ongoing-activity model. From this model a differentially variable component analysis strategy is developed from a Bayesian perspective to estimate event-related signals on a single trial basis. After subtracting out the event-related signal from recorded single trial time series, the residual ongoing activity is treated as a piecewise stationary stochastic process and analyzed by an adaptive multivariate autoregressive modeling strategy which yields power, coherence, and Granger causality spectra. Results from applying these methods to local field potential recordings from monkeys performing cognitive tasks are presented.     

Recurrence relations based on minimization

This paper investigates solutions of the general recurrence M(0) = g(0), M(n + 1) = g(n + 1) + min_0?k?n(αM(k) + βM(n ? k)) for various choices of α, β, and g(n). In a large number of cases it is possible to prove that M(n) is a convex function whose values can be computed much more efficiently than would be suggested by the defining recurrence. The asymptotic behavior of M(n) can be deduced using combinatorial methods in conjunction with analytic techniques. In some cases there are strong connections between M(n) and the function H(x) defined by $\text{H(x) = 1}\text{for}\text{x < 1, H(x) = H(}\text{(x ? 1)}\text{α}\text{) + H(}\text{(x ? 1)}\text{β}\text{)}\text{for}\text{x ? 1}$. Special cases of these recurrences lead to a surprising number of interesting problems involving both discrete and continuous mathematics.     

High-throughput cytochrome P450 (CYP) inhibition screening via cassette probe-dosing strategy. I. Development of direct injection/on-line guard cartridge extraction/tandem mass spectrometry for the simultaneous detection of CYP probe substrates and their metabolites

A highly efficient direct injection/on-line guard cartridge extraction/tandem mass spectrometry (DI-GCE/MS/MS) method utilizing electrospray polarity switching was developed for the simultaneous detection of probe substrates and marker metabolites of seven human hepatic cytochrome P450 (CYP) isozymes: CYP1A2, 2A6, 3A4, 2C9, 2C19, 2D6 and 2E1. Microsomal incubations were terminated with formic acid, centrifuged, and the resulting supernatants were injected for analysis by DI-GCE/MS/MS. This method employed an extremely short C(18) cartridge (4 mm in length) which allowed rapid cleanup of sample matrices while retaining the analytes an appropriate time (2. 0-2.2 min). From 1.5 to 2.7 min the effluent was directed to the mass spectrometer for detection otherwise diverted to waste. As a result of the efficient on-line extraction, matrix (e.g., salts and proteins) suppression was minimized. In addition, no visible source contamination was observed and system performance (chromatographic and mass spectrometric) did not significantly deteriorate after 500 consecutive injections. Electrospray polarity switching was strategically executed on a Micromass Quattro II mass spectrometer by establishing dummy ion transitions to protect the analytes from the interference of the overwhelming noise which was unavoidable for the first transition scanned following each polarity switch. This unique strategy led to the simultaneous detection of seven CYP probe substrates and seven corresponding marker metabolites (12 by positive mode and 2 by negative mode).     

On the LambertW function

The LambertW function is defined to be the multivalued inverse of the functionw we ^w . It has many applications in pure and applied mathematics, some of which are briefly described here. We present a new discussion of the complex branches ofW, an asymptotic expansion valid for all branches, an efficient numerical procedure for evaluating the function to arbitrary precision, and a method for the symbolic integration of expressions containingW.     

Fission fragment angular distributions in 16O+181Ta

Time of flight and energy of fission fragments were measured using pulsed beam. Fission fragment mass and energy integrated angular distributions were extracted. Fission fragment anisotropy was explained in the framework of saddle point model.     

The Symmetrical Foundation of Measure,Probability, and Quantum Theories

Quantification starts with sum and product rules that express combination and partition. These rules rest on elementary symmetries that have wide applicability, which explains why arithmetical adding up and splitting into proportions are ubiquitous. Specifically, measure theory formalizes addition, and probability theory formalizes inference in terms of proportions. Quantum theory rests on the same simple symmetries, but is formalized in two dimensions, not just one, in order to track an object through its binary interactions with other objects. The symmetries still require sum and product rules (here known as the Feynman rules), but they apply to complex numbers instead of real scalars, with observable probabilities being modulus squared (known as the Born rule). The standard quantum formalism follows. There is no mystery or weirdness, just ordinary probabilistic inference.