Finding the Homology of Submanifolds with High Confidence from Random Samples

Recently there has been a lot of interest in geometrically motivated approaches to data analysis in high-dimensional spaces. We consider the case where data are drawn from sampling a probability distribution that has support on or near a submanifold of Euclidean space. We show how to “learn” the homology of the submanifold with high confidence. We discuss an algorithm to do this and provide learning-theoretic complexity bounds. Our bounds are obtained in terms of a condition number that limits the curvature and nearness to self-intersection of the submanifold. We are also able to treat the situation where the data are “noisy” and lie near rather than on the submanifold in question. The main results of this paper were first presented at a conference in honor of John Franks and Clark Robinson at Northwestern University in April 2003. These results were formally written as Technical Report No. TR-2004-08, Department of Computer Science, University of Chicago.     

Numerical study of magnetohydrodynamic laminar flow separation in a channel with smooth expansion

The flow of an electrically conducting incompressible viscous fluid in a plane channel with smooth expansion in the presence of a uniform transverse magnetic field has been analysed. A solution technique for the governing magnetohydrodynamic equations in primitive variable formulation has been developed. A co‐ordinate transformation has been employed to map the infinite irregular domain into a finite regular computational domain. The governing equations are discretized using finite‐difference approximations in staggered grid. Pressure Poisson equation and pressure correction formulae are derived and solved numerically. It is found that with increase in the magnetic field, the size of the flow separation zone diminishes and for sufficiently large magnetic field, the separation zone disappears completely. The peak u‐velocity decreases with increase in the magnetic field. It is also found that the asymmetric flow in a symmetric geometry, which occurs at moderate Reynolds numbers, becomes symmetric with sufficient increase in the transverse magnetic field. Thus, a transverse magnetic field of suitable strength has a stabilizing effect in controlling flow separation, as also in delaying the transition to turbulence. Copyright © 2008 John Wiley & Sons, Ltd.     

Anti-inflammatory chromone alkaloids and glycoside from Dysoxylum binectariferum

Herein we report isolation of a new chromone alkaloid chrotacumine K (12) from fruits and a chromone glycoside schumaniofioside A (13) from leaves of Dysoxylum binectariferum Hook f. Schumaniofioside A is reported for the first time from Meliaceae family. Other known alkaloids isolated include rohitukine (1) and chrotacumine E (6). The structure of new alkaloid 12 was elucidated on the basis of extensive 1D and 2D NMR analysis, synthesis and chemical hydrolysis. Chemically, chrotacumine K (12) is a 3′-O-acetyl rohitukine which on chemical or enzymatic hydrolysis produces rohitukine. The new alkaloid 12 is also present in seeds and stem-barks of this plant. The glycoside schumaniofioside A (13) is present only in leaves, and in abundance (～1% w/w of dried leaves). The isolated compounds and extracts were evaluated for in vitro effect on the proinflammatory cytokines (TNF-α and IL-6) in human monocytic THP-1 cells. The alkaloid 12 displayed potent inhibition (57%) of TNF-α at 0.3 µM, and was non-toxic to THP-1 cells up to 40 µM, indicating its excellent therapeutic window. Furthermore, a nitrobenzoyl ester analog 15e showed better inhibition of IL-6 than parent natural product chrotacumine K.     

Two-body T-matrix continued off the energy shell

A generalized parametrization scheme, which treats both half-shell and off-shell scattering on equal footing, is derived for the two-particle transition operator. The appropriate theory in respect of this is developed by using a wave function approach to off-shell scattering and the computational procedure to be followed is demonstrated by means of a model calculation.     

BOUNDARY TREATMENT AND AN EFFICIENT PRESSURE ALGORITHM FOR INTERNAL TURBULENT FLOWS USING THE PDF METHOD

The generalized Langevin model, which is used to model the motion of stochastic particles in the velocity–composition joint probability density function (PDF) method for reacting turbulent flows, has been extended to incorporate solid wall effects. Anisotropy of Reynolds stresses in the near-wall region has been addressed. Numerical experiments have been performed to demonstrate that the forces in the near-wall region of a turbulent flow cause the stochastic particles approachi ng a solid wall to reverse their direction of motion normal to the wall and thereby, leave the near-wall layer. This new boundary treatment has subsequently been implemented in a full-scale problem to prove its validity. The test problem considered here is that of an isothermal, non-reacting turbulent flow in a two-dimensional channel with plug inflow and a fixed back-pressure. An efficient pressure correction method, developed in the spirit of the PISO algorithm, has been implemented. The pressure correction strategy is easy to implement and is completely consistent with the time- marching scheme used for the solution of the Lagrangian momentum equations. The results show remarkable agreement with both k–ϵ and algebraic Reynolds stress model calculations for the primary velocity. The secondary flow velocity and the turbulent moments are in better agreement with the algebraic Reynolds stress model predictions than the k– ϵ predictions. © 1997 by John Wiley & Sons, Ltd.     

Gram level synthesis of lead-free solder in the nanometer length scale obtained from tin and silver compounds using silicone oil

A straightforward route to gram level synthesis of a pure phase of the Sn-Ag nanoalloy in an eutectic composition (Sn/Ag 96.5:3.5) in silicone oil is reported. The composition, morphology, and microstructure of the alloy were fully characterized. In a mixture of ethylene glycol and silicone oil, direct reduction of Sn(II) acetate and Ag(I) nitrate gave the Sn-Ag nanoalloy. The nanoalloy disintegrates by sonication and reforms by heating, leading to smaller particles with a melting point as low as 128 degrees C.     

Galactic neutrino communication

We examine the possibility to employ neutrinos to communicate within the galaxy. We discuss various issues associated with transmission and reception, and suggest that the resonant neutrino energy near 6.3 PeV may be most appropriate. In one scheme we propose to make Zo$Z^o$ particles in an overtaking e⁺−e⁻$e^{+}-e^{-}$ collider such that the resulting decay neutrinos are near the W⁻$W^{-}$ resonance on electrons in the laboratory. Information is encoded via time structure of the beam. In another scheme we propose to use a 30 PeV pion accelerator to create neutrino or anti-neutrino beams. The latter encodes information via the beam CP state as well as timing. Moreover the latter beam requires far less power, and can be accomplished with presently foreseeable technology. Such signals from an advanced civilization, should they exist, will be eminently detectable in existing neutrino detectors.     

Electroosmotic flow in a rectangular channel with variable wall zeta-potential: comparison of numerical simulation with asymptotic theory

Electroosmotic flow in a straight micro-channel of rectangular cross-section is computed numerically for several situations where the wall zeta-potential is not constant but has a specified spatial variation. The results of the computation are compared with an earlier published asymptotic theory based on the lubrication approximation: the assumption that any axial variations take place on a long length scale compared to a characteristic channel width. The computational results are found to be in excellent agreement with the theory even when the scale of axial variations is comparable to the channel width. In the opposite limit when the wavelength of fluctuations is much shorter than the channel width, the lubrication theory fails to describe the solution either qualitatively or quantitatively. In this short wave limit the solution is well described by Ajdari's theory for electroosmotic flow between infinite parallel plates (Ajdari, A., Phys. Rev. E 1996, 53, 4996-5005.) The infinitely thin electric double layer limit is assumed in the theory as well as in the simulation.