Problem modification as a tool for detecting cognitive flexibility in school children

This paper presents the results of an experiment in which fourth to sixth graders with above-average mathematical abilities modified a given problem. The experiment found evidence of links between problem posing and cognitive flexibility. Emerging from organizational theory, cognitive flexibility is conceptualized through three primary constructs: cognitive variety, cognitive novelty, and changes in cognitive framing. Among these components, changes in cognitive framing could be effectively detected in problem-posing situations, giving a relevant indication of students’ creative potential. The students’ capacity to generate coherent and consistent problems in the context of problem modification may indicate the existence of a strategy of functional type for generalizations, which seems to be specific to mathematical creativity.     

From Heisenberg to Gödel via Chaitin

In 1927 Heisenberg discovered that the “more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa.” Four years later Gödel showed that a finitely specified, consistent formal system which is large enough to include arithmetic is incomplete. As both results express some kind of impossibility it is natural to ask whether there is any relation between them, and, indeed, this question has been repeatedly asked for a long time. The main interest seems to have been in possible implications of incompleteness to physics. In this note we will take interest in the converse implication and will offer a positive answer to the question: Does uncertainty imply incompleteness? We will show that algorithmic randomness is equivalent to a “formal uncertainty principle” which implies Chaitin’s information-theoretic incompleteness. We also show that the derived uncertainty relation, for many computers, is physical. In fact, the formal uncertainty principle applies to all systems governed by the wave equation, not just quantum waves. This fact supports the conjecture that uncertainty implies algorithmic randomness not only in mathematics, but also in physics.     

Transverse oriented electric field re-entrant resonator (TERR) with automatic tuning and coupling control for EPR spectroscopy and imaging of the beating heart

Sample motion, particularly that of a beating heart, induces baseline noise and spectral distortion on an EPR spectrum. In order to quench motional noise and restore the EPR signal amplitude and line-width, an L-band transverse oriented electric field re-entrant resonator (TERR) was designed and constructed with provisions for automatic tuning control (ATC) and automatic coupling control (ACC) suited for studies of isolated beating rat hearts. Two sets of electronic circuits providing DC biased voltage to two varactor diodes were implemented to electronically adjust coupling and tuning. The resonator has a rectangular cross-sectional sample arm of 25 mm diameter with a Q value of 1100 without sample. Once inserted with lossy aqueous samples of 0.45% NaCl, Q value drops to 400 with a volume of 0.5 ml and 150 with 5 ml. The ATC/ACC functions were tested with a moving phantom and isolated beating rat hearts with the improvement of signal to noise ratio (S/N, peak amplitude of signal over peak amplitude of baseline noise) of 6.7-, and 4 to 6-fold, respectively. With these improvements, EPR imaging could be performed on an isolated beating rat heart. Thus, this TERR resonator with ATC/ACC enables application of EPR spectroscopy and imaging for the measurement and imaging of radical metabolism, redox state, and oxygenation in the isolated beating rat heart.     

Kinetics of N-glutaryl-L-phenylalanine p-nitroanilide hydrolysis catalyzed by alpha-chymotrypsin in aqueous solutions of alkyltrimethylammonium bromides

The rate of N-glutaryl-L-phenylalanine p-nitroanilide hydrolysis catalyzed by alpha-chymotripsin has been measured in aqueous solutions of cetyltrimethylammonium bromide, tetradecyltrimethylammonium bromide, and dodecyltrimethylammonium bromide at concentrations below and above their critical micellar concentrations (CMC). For the three surfactants considered superactivity was observed, with maximum catalytic efficiencies taking place near the corresponding CMCs. The effect of the surfactants after the CMCs is mostly due to a decreased thermodynamic activity of the substrate due to its incorporation into the micelles. After addition of the surfactants, the Michaelis constant values (corrected to take into account the free substrate concentration) tend to decrease, passing through an ill defined minimum, afterwards reaching a constant value. The catalytic rate constants show the same profiles that the catalytic efficiency, being maxima near the surfactants CMCs. This maximum is more important for the surfactant having the shorter tail. This result is explained by considering that the hydrophobicity of the surfactant influences more the CMC than its association to the enzyme.     

The first trialkylphosphane telluride complexes of Ag(I): molecular, ionic and supramolecular structural alternatives

The structures of the first phosphane telluride complexes of silver(I), obtained from i-Pr3PTe (1) with AgNMs2 [Ms = SO2CH3] and with AgSbF6, reveal the superior coordinating ability of 1, particularly as a bridging ligand, compared with related i-Pr3PS and i-Pr3PSe ligands.     

High-temperature phase transitions in CsH2PO4 under ambient and high-pressure conditions: a synchrotron x-ray diffraction study

To clarify the microscopic origin of the temperature-induced three-order-of-magnitude jump in the proton conductivity of CsH(2)PO(4) (superprotonic behavior), we have investigated its crystal structure modifications within the 25-300 degrees C temperature range under both ambient- and high-pressure conditions using synchrotron x-ray diffraction. Our high-pressure data show no indication of the thermal decomposition/polymerization at the crystal surface recently proposed as the origin of the enhanced proton conductivity [Phys. Rev. B 69, 054104 (2004)]. Instead, we found direct evidence that the superprotonic behavior of the title material is associated with a polymorphic structural transition to a high-temperature cubic phase. Our results are in excellent agreement with previous high-pressure ac impedance measurements.     

Comparative evaluation of MMPBSA and XSCORE to compute binding free energy in XIAP-peptide complexes

Evaluation of binding free energy in receptor-ligand complexes is one of the most important challenges in theoretical drug design. Free energy is directly correlated to the thermodynamic affinity constant, and, as a first step in druglikeness, a lead compound must have this constant in the range of micro- to nanomolar activity. Many efforts have been made to calculate it by rigorous computational approaches, such as free energy perturbation or linear response approximation. However, these methods are still computationally expensive. We focus our work on XIAP, an antiapoptotic protein whose inhibition can lead to new drugs against cancer disease. We report here a comparative evaluation of two completely different methodologies to estimate binding free energy, MMPBSA (a force field based function) and XSCORE (an empirical scoring function), in seven XIAP-peptide complexes using a representative set of structures generated by previous molecular dynamics simulations. Both methods are able to predict the experimental binding free energy with acceptable errors, but if one needs to identify slight differences upon binding, MMPBSA performs better, although XSCORE is not a bad choice taking into account the low computational cost of this method.     

Experimental and theoretical evidence of the first Au(i)...Bi(iii) interaction

Complex [Au(C6F5)2][Bi(C6H4CH2NMe(2)-2)2] displays the first example of an interaction between Au(I) and Bi(III), the nature of which is shown to be consistent with the presence of a high ionic contribution (79%) and a dispersion type (van der Waals) interaction (21%).     

Live-cell-permeant thiophene fluorophores and cell-mediated formation of fluorescent fibrils

In our search for thiophene fluorophores that can overcome the limits of currently available organic dyes in live-cell staining, we synthesized biocompatible dithienothiophene-S,S-dioxide derivatives (DTTOs) that were spontaneously taken up by live mouse embryonic fibroblasts and HeLa cells. Upon treatment with DTTOs, the cells secreted nanostructured fluorescent fibrils, while cell viability remained unaltered. Comparison with the behavior of other cell-permeant, newly synthesized thiophene fluorophores showed that the formation of fluorescent fibrils was peculiar to DTTO dyes. Laser scanning confocal microscopy of the fluorescent fibrils showed that most of them were characterized by helical supramolecular organization. Electrophoretic analysis and theoretical calculations suggested that the DTTOs were selectively recognized by the HyPro component of procollagen polypeptide chains and incorporated through the formation of multiple H-bondings.