Optimal discrete Morse functions for 2-manifolds

Morse theory is a powerful tool in its applications to computational topology, computer graphics and geometric modeling. It was originally formulated for smooth manifolds. Recently, Robin Forman formulated a version of this theory for discrete structures such as cell complexes. It opens up several categories of interesting objects (particularly meshes) to applications of Morse theory. Once a Morse function has been defined on a manifold, then information about its topology can be deduced from its critical elements. The main objective of this paper is to introduce a linear algorithm to define optimal discrete Morse functions on discrete 2-manifolds, where optimality entails having the least number of critical elements. The algorithm presented is also extended to general finite cell complexes of dimension at most 2, with no guarantee of optimality.     

The exact distribution of extremes of a non-gaussian process

The exact distribution of extremes of a non-gaussian stationary discrete process is obtained and their crossing intervals are studied in terms of the autocorrelation coefficients for any level of crossing. This process is an important model for some physical magnitudes.     

On removable singularities of locally solvable differential operators

We study removable sets of solutions of locally solvable partial differential operators with smooth coefficients and characterize them in terms of capacity in the sense of Harvey and Polking. For operators of order one we are able to give a geometric characterization of removable sets in terms of orbits in the sense of Sussmann. Oblatum 2-IX-1995 & 14-V-1996     

Optimization of the separation of flavonoids using solvent-modified micellar electrokinetic chromatography

In this work the separation of eighteen flavonoids was attempted using reduced-flow micellar elektrokinetic chromatography (RF-MEKC) electrolytes modified by selected solvents with differing properties: methanol (MeOH), acetonitrile (ACN) and tetrahydrofuran (THF). Structural aspects such as unsaturation of the C ring, number and position of OH groups, methylation and glycosylation as well as solvent effects and their impact on the electrophoretic behavior of flavonoids were addressed. By evaluating the electropherograms obtained from mixture-designed electrolytes and searching for changes in the critical pairs, a favorable separation condition was achieved using 20 mmol/L phosphate buffer at pH 2.5 containing 50 mmol/L sodium dodecyl sulfate (SDS), 15% ACN and 5% THF (one critical pair) in less than 12 min with 1.5% coefficient of variation (CV) for retention factor and 3% CV for peak area (n = 5). The applicability of the proposed separation condition was demonstrated by the inspection of flavonoids in herbal extracts of Neem.     

Proton radioactivity: The case for <Superscript>53m</Superscript>Co proton-emitter isomer

The partial proton emission half-life for ^53mCo unstable isomer is re-examined in the framework of a semiempirical model based on tunneling through a Coulomb-plus-centrifugal-plus-overlapping potential barrier within the spherical nucleus approximation. It is shown that the known measured half-life value of 17s is compatible with a large prolate shape for ^53mCo proton emitter and a high angular momentum ℓ = 11 assigned to the proton transition to the ground state of ⁵²Fe .     

Effect of salt identity on the phase diagram for a globular protein in aqueous electrolyte solution

Monte Carlo simulations are used to establish the potential of mean force between two globular proteins in an aqueous electrolyte solution. This potential includes nonelectrostatic contributions arising from dispersion forces first, between the globular proteins, and second, between ions in solution and between each ion and the globular protein. These latter contributions are missing from standard models. The potential of mean force, obtained from simulation, is fitted to an analytic equation. Using our analytic potential of mean force and Barker-Henderson perturbation theory, we obtain phase diagrams for lysozyme solutions that include stable and metastable fluid-fluid and solid-fluid phases when the electrolyte is 0.2 M NaSCN or NaI or NaCl. The nature of the electrolyte has a significant effect on the phase diagram.     

Identification of a set of genes showing regionally enriched expression in the mouse brain

Background

We have recorded responses from single neurons in murine visual cortex to determine the effectiveness of the input from the two murine cone photoreceptor mechanisms and whether there is any unique selectivity for cone inputs at this higher region of the visual system that would support the possibility of colour vision in mice. Each eye was stimulated by diffuse light, either 370 (strong stimulus for the ultra-violet (UV) cone opsin) or 505 nm (exclusively stimulating the middle wavelength sensitive (M) cone opsin), obtained from light emitting diodes (LEDs) in the presence of a strong adapting light that suppressed the responses of rods.

Results

Single cells responded to these diffuse stimuli in all areas of striate cortex. Two types of responsive cells were encountered. One type (135/323 – 42%) had little to no spontaneous activity and responded at either the on and/or the off phase of the light stimulus with a few impulses often of relatively large amplitude. A second type (166/323 – 51%) had spontaneous activity and responded tonically to light stimuli with impulses often of small amplitude. Most of the cells responded similarly to both spectral stimuli. A few (18/323 – 6%) responded strongly or exclusively to one or the other spectral stimulus and rarely in a spectrally opponent manner.

Conclusion

Most cells in murine striate cortex receive excitatory inputs from both UV- and M-cones. A small fraction shows either strong selectivity for one or the other cone mechanism and occasionally cone opponent responses. Cells that could underlie chromatic contrast detection are present but extremely rare in murine striate cortex.