Monotonicity and the principle of optimality

This paper explores some of the theoretical and algorithmic implications of the fact that the Monotonicity Assumption does not ensure either the validity of the Principle of Optimality or the discovery of all optimal solutions in finite dynamic programs, even though it is sufficient to ensure the validity of the functional equations. A slightly stronger assumption is introduced to resolve these problems. Our analysis is illustrated with some extremely simple examples.     

Considerations on the possibilities and limitations of comprehensive normal phase-reversed phase liquid chromatography (NPLC x RPLC)

A comprehensive normal phase system LC-reversed phase LC (NPLC x RPLC) was evaluated for the separation of a pharmaceutical mixture and citrus oil extracts. NPLC was performed on a 25 cm x 1 mm ID x 5 microm dp diol phase. In the second dimension, an RP 18 monolithic column (10 cm L x 4.6 mm ID x 2 microm macropore size) and an octadecyl silicagel-packed column (5 cm L x 4.6 mm ID x 3.5 microm dp) were applied for the analyses of the pharmaceutical sample and the citrus oil extracts, respectively. A two-position/ten-port switching valve was used as interface. Under optimised LC conditions, the high degree of orthogonality between NP and RP resulted in peak capacities of 300 for the pharmaceutical sample and of 450 for the citrus oil extract composed of lemon and orange oil. Despite the features of NPLC x RPLC, several shortcomings related with the solvent incompatibility between the two LC modes were identified and the practical consequences were discussed.     

A stability result using the matrix norm to bound the permanent

We prove a stability version of a general result that bounds the permanent of a matrix in terms of its operator norm. More specifically, suppose A is an n × n matrix over C (resp. R), and let P denote the set of n × n matrices over C (resp. R) that can be written as a permutation matrix times a unitary diagonal matrix. Then it is known that the permanent of A satisfies |per(A)| ≤ ||A|| ⁿ ₂ with equality iff A/||A||₂ ∈ P (where ||A||₂ is the operator 2-norm of A). We show a stability version of this result asserting that unless A is very close (in a particular sense) to one of these extremal matrices, its permanent is exponentially smaller (as a function of n) than ||A|| ⁿ ₂. In particular, for any fixed α, β > 0, we show that |per(A)| is exponentially smaller than ||A|| ⁿ ₂ unless all but at most αn rows contain entries of modulus at least ||A||₂(1?β).     

Assessing induced folding of an intrinsically disordered protein by site-directed spin-labeling electron paramagnetic resonance spectroscopy

We used site-directed spin-labeling electron paramagnetic resonance (EPR) spectroscopy to study the induced folding of the intrinsically disordered C-terminal domain of measles virus nucleoprotein (N(TAIL)). Four single-site N(TAIL) mutants (S407C, S488C, L496C, and V517C), located in three conserved regions, were prepared and labeled with a nitroxide paramagnetic probe. We could monitor the gain of rigidity that N(TAIL) undergoes in the presence of either the secondary structure stabilizer 2,2,2-trifluoroethanol (TFE) or one of its physiological partners, namely, the C-terminal domain (XD) of the viral phosphoprotein. The mobility of the spin label grafted at positions 488, 496, and 517 was significantly reduced upon addition of XD, contrary to that of the spin label bound to position 407, which was unaffected. Furthermore, the EPR spectra of spin-labeled S488C and L496C bound to XD in the presence of 30% sucrose are indicative of the formation of an alpha-helix in the proximity of the spin labels. Such an alpha-helix had been already identified by previous biochemical and structural studies. Using TFE we unveiled a previously undetected structural propensity within the N-terminal region of N(TAIL) and showed that its C-terminal region "resists" gaining structure even at high TFE concentrations. Finally, we for the first time showed the reversibility of the induced folding process that N(TAIL) undergoes in the presence of XD. These results highlight the suitability of site-directed spin-labeling EPR spectroscopy to identify protein regions involved in binding and folding events, while providing insights at the residue level.     

MODELS AND SUPER-MODELS: WAYS OF THINKING ABOUT PROFESSIONAL KNOWLEDGE IN MATHEMATICS TEACHING[1]

Teaching about teaching is a complex process requiring knowledge about teaching as well as knowledge about teaching about teaching. We have published findings on research carried out over the last few years about teachers’ subject knowledge. This research led to the proposal of a model for thinking about subject knowledge which distinguishes between knowledge needed to pass an examination and knowledge needed to help someone else to come to know that knowledge. The first is necessary but not sufficient for the latter. This model for thinking about subject knowledge has led to proposals for similar models for thinking about other aspects of teacher knowledge and has more recently developed into a parallel model for thinking about teacher education.     

Theory and experiment of large numerical aperture objective Raman microscopy: application to the stress‐tensor determination in strained cubic materials

We present the theory underlying the large numerical aperture objective micro‐Raman backscattering experiment and apply it to the elaboration of a characterization methodology for the determination of the stress tensor in strained cubic semiconductor structures. The presented stress characterization technique consists in monitoring the variations of the stress‐sensitive optical phonon peak position and linewidth while rotating stepwise the sample about its normal. The practical application of the technique is illustrated on a silicon‐on‐insulator (SOI) microelectronic structure demonstrating a plane stress‐tensor determination. Copyright © 2008 John Wiley & Sons, Ltd.