A genus six cyclic tetragonal reduction of the Benney equations

A reduction of Benney’s equations is constructed corresponding to Schwartz–Christoffel maps associated with a family of genus six cyclic tetragonal curves. The mapping function, a second kind Abelian integral on the associated Riemann surface, is constructed explicitly as a rational expression in derivatives of the Kleinian σ-function of the curve

Morphological heterogeneity of HeLa cell mitochondria visualized by a modified diaminobenzidine staining technique

The diaminobenzidine (DAB) technique for the ultrastructural localization of sites of cytochrome c oxidase activity in animal tissues has been adapted to the visualization of mitochondria in animal cells growing in culture. The modified technique allows the staining of mitochondria in all cells in coverslip preparatins for light microscopy. Electron microscopy of thin sections of material treated by this method has revealed that all mitochondrial profiles within a cell (and only these) are stained and they exhibit a well preserved size and internal structure. Coverslip cultures of synchronized and unsynchronized HeLa (F-315) cells stained with the DAB reaction were examined under oil immersion. In the majority of the cells, mitochondria were recognized as discrete bodies in the thinner peripheral portion of the cytoplasm. This observation indicates that in a large proportion of HeLa F-315 cells, at least under the growth conditions used here, the mitochondrial complement is dividied into distinct organelles. This examination also revealed a considerable morphological heterogeneity of mitochondria, which exhibited an ovoid or short rod-like or, less frequently, long filamentous shape, with some evidence of branching. The variability in mitochondrial morphology appeared to be far more prounced between different cells than within individual cells; this cellular heterogeneity was not related in any obvious way to cell-cycle-dependent changes

Cylindrical Algebraic Sub-Decompositions

Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic geometry, used primarily for eliminating quantifiers over the reals and studying semi-algebraic sets. In this paper we introduce cylindrical algebraic sub-decompositions (sub-CADs), which are subsets of CADs containing all the information needed to specify a solution for a given problem. We define two new types of sub-CAD: variety sub-CADs which are those cells in a CAD lying on a designated variety; and layered sub-CADs which have only those cells of dimension higher than a specified value. We present algorithms to produce these and describe how the two approaches may be combined with each other and the recent theory of truth-table invariant CAD. We give a complexity analysis showing that these techniques can offer substantial theoretical savings, which is supported by experimentation using an implementation in Maple.Comment: 26 page

Toward quantum processing in molecules: A THz-bandwidth coherent memory for light

The unusual features of quantum mechanics are enabling the development of technologies not possible with classical physics. These devices utilize nonclassical phenomena in the states of atoms, ions, and solid-state media as the basis for many prototypes. Here we investigate molecular states as a distinct alternative. We demonstrate a memory for light based on storing photons in the vibrations of hydrogen molecules. The THz-bandwidth molecular memory is used to store 100-fs pulses for durations up to 1ns, enabling 10,000 operational time bins. The results demonstrate the promise of molecules for constructing compact ultrafast quantum photonic technologies.Comment: 5 pages, 3 figures, 1 tabl

The Effect of Vincristine Sulphate on the Axoplasmic Flow of Proteins in Cultured Sympathetic Neurons

The effect of vincristine sulphate on the axoplasmic flow of labelled proteins in neurites of chick embryo sympathetic neurons growing in tissue culture was studied by autoradiography. In control neurons most of the 3H-proteins synthesized during a 90-min pulse with a 3H-amino acid were localized in cell bodies. There was a diminishing gradient of labelled proteins in the neurites which was highest in portions adjacent to the cell bodies and lowest at the periphery. During a physiological chase there was a gradual increase in the amount of label in the neurites, so that after a 15-h chase even the most peripheral portions were well labelled. This indicates that a portion of the labelled proteins synthesized in the cell bodies are transported peripherally into the neurites. The centrifugal movement of labelled proteins in neurites was markedly decreased when cells were grown in medium containing 10 µg/ml vincristine sulphate. After a 15-h chase in the presence of drug only a small amount of label was in the peripheral portion of the neurites. Treatment with vincristine did not decrease the rate of amino acid incorporation or alter the rate of protein turnover during the course of the experiment. Thus an explanation of the results based on an altered rate of total cell protein synthesis or degradation is unlikely. The capacity of sympathetic neurons to take up and concentrate exogenous [3H]norepinephrine in their neurites was only slightly reduced by vincristine. This indicates that at least some cellular activities requiring metabolic energy are relatively unaffected by the interruption in axoplasmic flow caused by vincristine and that the mechanism by which vincristine interferes with axoplasmic flow does not involve general cellular toxicity. The major morphological differences between control and vincristine-treated neurons were the absence of microtubules and the presence of crystal-like structures within the cells. The relationship between the effect of vincristine on the axoplasmic flow of proteins and the arrangement of the microtubule system is discussed

Ultrafast slow-light: Raman-induced delay of THz-bandwidth pulses

We propose and experimentally demonstrate a scheme to generate optically-controlled delays based on off-resonant Raman absorption. Dispersion in a transparency window between two neighboring, optically-activated Raman absorption lines is used to reduce the group velocity of broadband 765 nm pulses. We implement this approach in a potassium titanyl phosphate (KTP) waveguide at room temperature, and demonstrate Raman-induced delays of up to 140 fs for a 650-fs duration, 1.8-THz bandwidth, signal pulse; the available delay-bandwidth product is $\approx1$. Our approach is applicable to single photon signals, offers wavelength tunability, and is a step toward processing ultrafast photons.Comment: 5+4 pages, 4+2 figure