Ermakov Approach for Minisuperspace Oscillators

The Wheeler–DeWitt equation of arbitrary Hartle–Hawking factor ordering for several minisuperspace universe models, such as the pure gravity Friedmann–Robertson–Walker and Taub ones, is mapped onto the dynamics of corresponding classical oscillators. The latter ones are studied by the classical Ermakov invariant method, which is a natural approach in this context. For the more realistic case of a minimally coupled massive scalar field, one can study, within the same type of approach, the corresponding squeezing features as a possible means of describing cosmological evolution. Finally, we comment on the analogy with the accelerator physics.     

Acute Triangulations of the Regular Icosahedral Surface

We prove here that the surface of the regular icosahedron can be triangulated with 8 non-obtuse and with 12 acute triangles. We also show these numbers to be smallest possible.     

A virtual instrumentation based protocol for the automated implementation of the inner field compensation method

One influential parameter which mediates interactions between many types of molecules and biological membranes stems from the lumped contributions of the transmembrane potential, dipole potential and the difference in the surface potentials on both sides of a membrane. With relevance to cell physiology, such electrical features of a biomembrane are prone to undergoing changes as a result of interactions with the aqueous surrounding. Among the most useful tools devoted to exploring changes of electrical parameters of a lipid membrane induced by certain extracellular ions, lipid composition, and embedded membrane peptides and proteins, are spectroscopic imaging and the inner field compensation (IFC) method. In this work we layout the principles of a fully computerized version of the IFC method, which makes it more readily available to users. As a direct application, we deployed this improved version of the IFC method to time-resolve changes induced by alamethicin monomers upon membrane dipole potential, following their aggregation within an artificial lipid membrane. Intriguingly, even prior crossing the membrane core, the membrane-bound alamethicin monomers are shown to significantly increase the dipole potential of the monolayer they reside in. Such data further emphasize the yet less-explored interplay between membrane-based protein and peptides, and the membrane dipole potential.     

Supersymmetry of FRW Barotropic Cosmologies

Barotropic FRW cosmologies are presented from the standpoint of nonrelativistic supersymmetry. First, we reduce the barotropic FRW system of differential equations to simple harmonic oscillator differential equations. Employing the factorization procedure, the solutions of the latter equations are divided into the two classes of bosonic (nonsingular) and fermionic (singular) cosmological solutions. We next introduce a coupling parameter denoted by K between the two classes of solutions and obtain barotropic cosmologies with dissipative features acting on the scale factors and spatial curvature of the universe. The K-extended FRW equations in comoving time are presented in explicit form in the low coupling regime. The standard barotropic FRW cosmologies correspond to the dissipationless limit K = 0.     

Inferring mixed-culture growth from total biomass data in a wavelet approach

It is shown that the presence of mixed-culture growth in batch fermentation processes can be very accurately inferred from total biomass data by means of the wavelet analysis for singularity detection. This is accomplished by considering simple phenomenological models for the mixed growth and the more complicated case of mixed growth on a mixture of substrates. The main quantity provided by the wavelet analysis is the Hölder exponent of the singularity that we determine for our illustrative examples. The numerical results point to the possibility that Hölder exponents can be used to characterize the nature of the mixed-culture growth in batch fermentation processes with potential industrial applications. Moreover, the analysis of the same data affected by the common additive Gaussian noise still lead to the wavelet detection of the singularities although the Hölder exponent is no longer a useful parameter.     

Acute Triangulations of Flat Mobius Strips

In this paper we investigate the acute triangulations of flat Mobius strips. We find out that we can always triangulate a flat Mobius strip with at most nine acute triangles, and sometimes (but not always) that many triangles are really needed.     

Optimal control for semilinear stochastic evolution equations

Existence, uniqueness, continuous dependence with respect to controls and convergence in the probability of finite differences for controlled semilinear stochastic evolution equations, driven by continuous semimartingales, are considered under Lipschitz and monotone coefficients. The existence of discrete-optimal feedback controls for an associated optimization problem is proved.     

Influence of response factors on determining equilibrium association constants of non-covalent complexes by electrospray ionization mass spectrometry

A method for determining the equilibrium association constant of a complexation reaction A + B left harpoon over right harpoon AB by electrospray ionization mass spectrometry is described. The method consists in measuring the relative intensities of the peaks corresponding to A and to AB in equimolar A-B solutions at different concentrations C(0). The results are fitted by a non-linear least-squares procedure, with the two variable parameters being the equilibrium association constant K(a) and a factor R, defined by I(AB)/I(A) = R x [AB]/[A]. The factor R is the ratio between the response factors of AB and A, and corrects for the relative electrospray responses of the complex and the free substrate A, mass discrimination of instrumental origin and/or moderate in-source dissociation. The method is illustrated with the following two systems: complexes between a double-stranded 12-base pair oligonucleotide and minor groove binders, and cyclodextrin complexes with alpha,omega-dicarboxylic acids. For the oligonucleotide complexes, it is found that the response of the complex is not dramatically different to the response of the free oligonucleotide duplex, as the double helix conformation is disturbed by the drug only to a minor extent. In the case of cyclodextrin complexes, these complexes were found to have a much higher response than free cyclodextrin. This may be due to the fact that cyclodextrin is neutral in solution, whereas the complex is charged, but it can also stem from the fact that a significant proportion of the complex is in a non-inclusion geometry. The present method requires the exact determination of the concentrations of the reactants and is applicable to 1 : 1 complexes.     

Triplex and quadruplex DNA structures studied by electrospray mass spectrometry

DNA triplex and quadruplex structures have been successfully detected by electrospray ionization mass spectrometry (ESI-MS). Circular dichroism and UV-melting experiments show that these structures are stable in 150 mM ammonium acetate at pH 7 for the quadruplexes and pH 5.5 for the triplexes. The studied quadruplexes were the tetramer [d(TGGGGT)](4), the dimer [d(GGGGTTTTGGGG)](2), and the intramolecular folded strand dGGG(TTAGGG)(3), which is an analog of the human telomeric sequence. The absence of sodium contamination allowed demonstration of the specific inclusion of n - 1 ammonium cations in the quadruplex structures, where n is the number of consecutive G-tetrads. We also detected the complexes between the quadruplexes and the quadruplex-specific drug mesoporphyrin IX. MS/MS spectra of [d(TGGGGT)](4) and the complex with the drug are also reported. As the drug does not displace the ammonium cations, one can conclude that the drug binds at the exterior of the tetrads, and not between them. For the triplex structure the ESI-MS spectra show the detection of the specific triplex, at m/z values typically higher than those typically observed for duplex species. Upon MS/MS the antigene strand, which is bound into the major groove of the duplex, separates from the triplex. This is the same dissociation pathway as in solution. To our knowledge this is the first report of a triplex DNA structure by electrospray mass spectrometry.     

Three-dimensional quantitative structure-activity relationships of steroid aromatase inhibitors

Summary Inhibition of aromatase, a cytochrome P450 that converts androgens to estrogens, is relevant in the therapeutic control of breast cancer. We investigate this inhibition using a three-dimensional quantitative structure-activity relationship (3D QSAR) method known as Comparative Molecular Field Analysis, CoMFA [Cramer III, R.D. et al., J. Am. Chem. Soc., 110 (1988) 5959]. We analyzed the data for 50 steroid inhibitors [Numazawa, M. et al., J. Med. Chem., 37 (1994) 2198, and references cited therein] assayed against androstenedione on human placental microsomes. An initial CoMFA resulted in a three-component model for log(1/K_i), with an explained variance r² of 0.885, and a cross-validated q² of 0.673. Chemometric studies were performed using GOLPE [Baroni, M. et al., Quant. Struct.-Act. Relatsh., 12 (1993) 9]. The CoMFA/GOLPE model is discussed in terms of robustness, predictivity, explanatory power and simplicity. After randomized exclusion of 25 or 10 compounds (repeated 25 times), the q² for one component was 0.62 and 0.61, respectively, while r² was 0.674. We demonstrate that the predictive r² based on the mean activity (Y_m) of the training set is misleading, while the test set Y_m-based predictive r² index gives a more accurate estimate of external predictivity. Using CoMFA, the observed differences in aromatase inhibition among C6-substituted steroids are rationalized at the atomic level. The CoMFA fields are consistent with known, potent inhibitors of aromatase, not included in the model. When positioned in the same alignment, these compounds have distinct features that overlap with the steric and electrostatic fields obtained in the CoMFA model. The presence of two hydrophobic binding pockets near the aromatase active site is discussed: a steric bulk tolerant one, common for C4, C6-alpha and C7-alpha substitutents, and a smaller one at the C6-beta region.