The fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning.     

A genetic algorithm for structure-based de novo design

Genetic algorithms have properties which make them attractive in de novo drug design. Like other de novo design programs, genetic algorithms require a method to reduce the enormous search space of possible compounds. Most often this is done using information from known ligands. We have developed the ADAPT program, a genetic algorithm which uses molecular interactions evaluated with docking calculations as a fitness function to reduce the search space. ADAPT does not require information about known ligands. The program takes an initial set of compounds and iteratively builds new compounds based on the fitness scores of the previous set of compounds. We describe the particulars of the ADAPT algorithm and its application to three well-studied target systems. We also show that the strategies of enhanced local sampling and re-introducing diversity to the compound population during the design cycle provide better results than conventional genetic algorithm protocols.     

Single-shot measurement of quantum optical phase

Although the canonical phase of light, which is defined as the complement of photon number, has been described theoretically by a variety of distinct approaches, there have been no methods proposed for its measurement. Indeed doubts have been expressed about whether or not it is measurable. Here we show how it is possible, at least in principle, to perform a single-shot measurement of the canonical phase using beam splitters, mirrors, phase shifters, and photodetectors.     

Vanadium and chromium redox behavior in borosilicate nuclear waste glasses

X-ray absorption spectroscopy (XAS) was used to characterize vanadium (V) and chromium (Cr) environments in low activity nuclear waste (LAW) glasses synthesized under a variety of redox conditions. V₂O₅ was added to the melt to improve sulfur incorporation from the waste; however, at sufficiently high concentrations, V increased melt foaming, which lowered melt processing rates. Foaming may be reduced by varying the redox conditions of the melt, while small amounts of Cr are added to reduce melter refractory corrosion. Three parent glasses were studied, where CO-CO₂ mixtures were bubbled through the corresponding melt for increasing time intervals so that a series of redox-adjusted-glasses was synthesized from each parent glass. XAS data indicated that V and Cr behaviors are significantly different in these glasses with respect to the cumulative gas bubbling times: V⁴⁺/V_total ranges from 8 to 35%, while Cr³⁺/Cr_total can range from 15 to 100% and even to population distributions including Cr²⁺. As Na-content decreased, V, and especially, Cr became more reduced, when comparing equivalent glasses within a series. The Na-poor glass series show possible redox coupling between V and Cr, where V⁴⁺ populations increase after initial bubbling, but as bubbling time increases, V⁴⁺ populations drop to near the level of the parent glass, while Cr becomes more reduced to the point of having increasing Cr²⁺ populations.     

Retrocausality and Quantum Measurement

A retrocausal interpretation of quantum mechanics is examined and is applied to the problem of measuring an optical qubit before the qubit is actually created. Although the predictions of the retrocausal interpretation are the same as for the conventional causal picture, it provides a new perspective which should give a useful way of understanding some quantum mechanical processes.