The Expected Number of Local Maxima of a Random Algebraic Polynomial

In this work we obtain an asymptotic estimate for the expected number of maxima of the random algebraic polynomial , where a _j (j=0, 1,...,n–1) are independent, normally distributed random variables with mean and variance one. It is shown that for nonzero , the expected number of maxima is asymptotic to log n, when n is large.     

Directed random walks in random environments

We use holding time methods to study the asymptotic behavior of pure birth processes with random transition rates. Both the normal and slow approaches to infinity are studied. Fluctuations are shown to obey the central limit theorem for almost all sample-transition rates. Our results are stronger, and our proofs simpler, then those of recently published studies.     

Cell-cycle delay is induced in cells of a U937 promonocytic cell line by low-intensity light irradiation at 660 nm

Visible-light irradiation (VLI) at 660 nm and 11.5 J/cm2 inhibits proliferation of cells of the U937 promonocytic cell line, as monitored by autoradiographical analysis. The S-phase cell population is reduced at 6 h post-radiation treatment. Flow cytometric analysis confirms this, and also shows that light irradiation of cells induces a statistically significant increase in G2/M cells at 6 h post-radiation treatment. It has been postulated that VLI at 660 nm can alter cell-cycle progression by affecting intracellular concentrations of ions, in particular pH and calcium. However, no significant effects of light irradiation on these intracellular ions have been observed. These effects of VLI are not a consequence of radiation-induced DNA strand breaks, therefore events other than direct DNA damage are involved. These findings demonstrate a direct photobiological effect of VLI at 660 nm on the cell cycle, and indicate a previously unsuspected mechanism for the induction of cell-cycle delay that is neither a result of changes in the concentration of intracellular ions nor initiated by DNA strand breaks.     

Long-term evolution in the tropospheric concentration of chlorofluorocarbon 12 (CCl2F2) derived from high-spectral resolution infrared solar absorption spectra: retrieval and comparison with in situ surface measurements

The average tropospheric volume mixing ratios of chlorofluorocarbon 12 (CCl₂F₂) have been retrieved from high-spectral resolution ground-based infrared solar-absorption spectra recorded from March 1982 to October 2003 with the McMath Fourier transform spectrometer at the US National Solar Observatory facility on Kitt Peak in southern Arizona (31.9°N, 111.6°W, 2.09 km altitude). The retrievals are based on fits to the unresolved ν₈ band Q-branches near using the SFIT2 retrieval algorithm. The annual increase rate was equal to (16.88±1.37) parts per trillion (10^-12) by volume at the beginning of the time series, March 1982, or (4.77±0.04)%, 1 sigma, declining progressively to (2.49±1.24) parts per trillion, by volume at the end, October 2003, or (0.46±0.24)%, 1 sigma. Average tropospheric mixing ratios from the solar spectra have been compared with average surface flask and in situ sampling measurements from the Climate Monitoring and Diagnostics Laboratory (CMDL) station at Niwot Ridge, CO, (USA) (40.0°N, 105.5°W, 3013 m altitude). The average ratio and standard deviation of the monthly means of the retrieved tropospheric mixing ratios relative to the CMDL surface mixing ratios is (1.01±0.03) for the overlapping time period. Both datasets demonstrate the progressive impact of the Montreal protocol and its strengthening amendments on the trend of CCl₂F₂, though a tropospheric decrease has yet to be observed.     

Structural informatics,modeling, and design with an open‐source Molecular Software Library (MSL)

We present the Molecular Software Library (MSL), a C++ library for molecular modeling. MSL is a set of tools that supports a large variety of algorithms for the design, modeling, and analysis of macromolecules. Among the main features supported by the library are methods for applying geometric transformations and alignments, the implementation of a rich set of energy functions, side chain optimization, backbone manipulation, calculation of solvent accessible surface area, and other tools. MSL has a number of unique features, such as the ability of storing alternative atomic coordinates (for modeling) and multiple amino acid identities at the same backbone position (for design). It has a straightforward mechanism for extending its energy functions and can work with any type of molecules. Although the code base is large, MSL was created with ease of developing in mind. It allows the rapid implementation of simple tasks while fully supporting the creation of complex applications. Some of the potentialities of the software are demonstrated here with examples that show how to program complex and essential modeling tasks with few lines of code. MSL is an ongoing and evolving project, with new features and improvements being introduced regularly, but it is mature and suitable for production and has been used in numerous protein modeling and design projects. MSL is open‐source software, freely downloadable at http://msl‐libraries.org . We propose it as a common platform for the development of new molecular algorithms and to promote the distribution, sharing, and reutilization of computational methods. © 2012 Wiley Periodicals, Inc.     

The discretized flow on domains of attraction: a structural stability result

It is well known that, for stepsize sufficiently small, compactattractors of ordinary differential equations persist underdiscretization. The present paper describes the structure ofthe discrete-time dynamical system obtained via discretizationon A(M_h)\M_h where M_h is the approximate attractor and A(M_h)is its domain of attraction. The existence of a smooth embeddinginto a continuous-time parallelizable flow is proved. The constructioncan be used to define sections for discretizations and can beinterpreted as a justification of the method of modified equations.     

Air-tolerant poly(3-hexylthiophene) synthesis via catalyst-transfer polymerization

The discovery of catalyst-transfer polymerization and its further developments have led to unprecedented control over the length and sequence of conjugated polymers. However, the methods themselves are technically challenging to perform due to the air- and moisture-sensitivities of the monomers and catalysts. Herein, we report a catalyst-transfer polymerization method that affords poly(3-hexylthiophene) in high yields without using an inert atmosphere. The synthesis capitalizes on a rapid Negishi cross-coupling using a moisture-tolerant organozinc monomer mediated by an air-stable Pd precatalyst. This simple method should make conjugated polymer synthesis more accessible to a broader range of researchers and may be generalizable to other monomer scaffolds.     

The role of prior mathematical experience in predicting mathematics performance in higher education

Evidence of deficiencies in basic mathematical skills of beginning undergraduates has been documented worldwide. Many different theories have been set out as to why these declines in mathematical competency levels have occurred over time. One such theory is the widening access to higher education which has resulted in a less mathematically prepared profile of beginning undergraduates than ever before. In response to this situation, the present study details the examination of a range of methods through which a student's mathematical performance in higher education could be predicted at the beginning of their third-level studies. Several statistical prediction methods were examined and the most effective method in predicting students’ mathematical performance was discriminant analysis. The discriminant analysis correctly classified 71.3% of students in terms of mathematics performance. An ability to carry out such a prediction in turn allows for appropriate mathematics remediation to be offered to students predicted to fail third-level mathematics. The results of the prediction of mathematical performance, which was carried out using a database consisting of over 1000 beginning undergraduates over a 3-year period, are detailed in this article along with the implications of such findings to educational policy and practice.     

The characterisation of selected antidepressant drugs using electrospray ionisation with ion trap mass spectrometry and with quadrupole time-of-flight mass spectrometry and their determination by high-performance liquid chromatography/electrospray ionisation tandem mass spectrometry

The electrospray ionisation ion trap tandem mass spectrometry (ESI-MS(n)) of selected antidepressant drugs, i.e., citalopram, fluoxetine, mirtazapine, paroxetine, sertraline, and venlafaxine, has been investigated. Sequential product ion fragmentation experiments (MS(n)) have been performed in order to elucidate the degradation pathways for the [M+H](+) ions and their predominant product ions. These MS(n) experiments show certain characteristic fragmentations in that functional groups are generally cleaved from the ring systems as molecules such as H(2)O, amines and phenols. When an aromatic entity is present in a drug molecule together with a nitrogen-containing saturated ring structure as with mirtazapine, fragmentation initially occurs at the latter ring with the former being predictably resistant to fragmentation. Also, when an amine-containing drug molecule such as fluoxetine also contains a functional group, which liberates a phenol with a significantly lower DeltaH(f) (0) value than that of the corresponding amine, the phenol is preferentially liberated. The structures of product ions proposed for ESI-MS(n) can be supported by electrospray ionisation quadrupole-time-of-flight tandem mass spectrometry (ESI-QToF-MS/MS). These molecules can be identified and determined in mixtures at low ng/mL concentrations by the application of high-performance liquid chromatography/electrospray ionisation tandem mass spectrometry (HPLC/ESI-MS(2)), which can also be used for their analysis in hair samples.