Structural Studies of DNA–Cationic Lipid Complexes Confined in Lithographically Patterned Microchannel Arrays

We have used lithographically patterned microchannel arrays with channel widths ranging from 1 to 20 m, fabricated using electron beam lithography and reactive ion etching, in structural studies of DNA–cationic lipid complexes in confinement. Various techniques have been developed for loading these DNA–membrane complexes into the microchannels or to form the complexes in situ by sequentially depositing DNA and lipid solutions into the microchannels. Optical microscopy studies indicate that such complex formation is strongly influenced by the periodic channel structure even at channel widths much larger than the persistent length of the DNA molecules. Preliminary x-ray diffraction experiments conducted at Stanford Synchrotron Radiation Laboratory (SSRL) yielded only a weak signal from the lipid bilayers in the complexes. The use of a microfocused x-ray beam produced by the newly developed Bragg–Fresnel optics at a third-generation synchrotron facility may dramatically increase the signal-to-noise ratio and allow observation of orientational as well as positional ordering of DNA molecules induced by the microchannels. Structural control of the DNA–membrane complexes has a broad range of potential applications in gene probe technology and as mesoscopic biomolecular composites.     

Quasiconvolutional smoothing of polyhedra

This paper describes a method for rounding edges and corners of arbitrary polyhedra that uses a fast approximation to convolutional filtering. The approximation defines an implicit surface, which is rendered with a specialised ray-tracing algorithm. By varying the radius of the smoothing filter, a wide range of effects can be obtained, from perfect polyhedra to blobby models. Small rounding radii give polyhedra a softer, more natural look, with edges well delineated by shadows and highlights. The rounded surfaces are much easier to specify and compute than those obtained by traditional filleting and surface-blending techniques, and are far more economical in storage.     

An electron tomography algorithm for reconstructing 3D morphology using surface tangents of projected scattering interfaces

Upon discerning the mere shape of an imaged object, as portrayed by projected perimeters, the full three-dimensional scattering density may not be of particular interest. In this situation considerable simplifications to the reconstruction problem are possible, allowing calculations based upon geometric principles. Here we describe and provide an algorithm which reconstructs the three-dimensional morphology of specimens from tilt series of images for application to electron tomography. Our algorithm uses a differential approach to infer the intersection of projected tangent lines with surfaces which define boundaries between regions of different scattering densities within and around the perimeters of specimens. Details of the algorithm implementation are given and explained using reconstruction calculations from simulations, which are built into the code. An experimental application of the algorithm to a nano-sized Aluminium tip is also presented to demonstrate practical analysis for a real specimen.

Program summary

Program title: STOMO version 1.0Catalogue identifier: AEFS_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFS_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 2988No. of bytes in distributed program, including test data, etc.: 191 605Distribution format: tar.gzProgramming language: C/C++Computer: PCOperating system: Windows XPRAM: Depends upon the size of experimental data as input, ranging from 200 Mb to 1.5 GbSupplementary material: Sample output files, for the test run provided, are available.Classification: 7.4, 14External routines: Dev-C++ (http://www.bloodshed.net/devcpp.html)Nature of problem: Electron tomography of specimens for which conventional back projection may fail and/or data for which there is a limited angular range. The algorithm does not solve the tomographic back-projection problem but rather reconstructs the local 3D morphology of surfaces defined by varied scattering densities.Solution method: Reconstruction using differential geometry applied to image analysis computations.Restrictions: The code has only been tested with square images and has been developed for only single-axis tilting.Running time: For high quality reconstruction, 5-15 min     

Effect of micro-electrode geometry on NO2 gas-sensing characteristics of one-dimensional tin dioxide nanostructure microsensors

Electrodes with micro-gaps are fabricated by using dc-sputtering and FIB techniques. SnO₂ nanowires are deposited on the micro-gap (1-30 μm) by suspension dropping method to fabricate a micro-gas sensor. The sensing ability of various SnO₂ micro-gap sensors is measured. A comparison between sensors reveals that the short-gap electrode has numerous advantages in terms of reliability, high sensitivity and detection of low concentrations of NO₂, while the large-gap electrode is relatively sensitive for high concentrations. Conductance measurements are carried out at different surface temperatures and NO₂ concentrations in order to investigate the effects that the gap size has on the overall sensor conductance. The results suggest that the interface between the electrode and sensitive layer has a very important role for the sensing mechanism of tin dioxide gas sensors.     

On the possible patterns of inputs for block sorting in the Burrows-Wheeler transformation

Block sorting in the Burrows-Wheeler transformation is to sort all of the n circular shifts of a string of length n lexicographically. We introduce a notion called the width of a sequence of n strings of length n and show that the values of widths are very different between the two types of sequences of strings; (1) a sequence of n randomly generated strings of length n, and (2) the sequence of n circular shifts of a randomly generated string of length n.     

The Other Mathematical Bridge

This paper contextualises, describes and discusses a student project which takes a particular exploratory approach to using mathematical surface definition as a language and vehicle for co-rational design co-authorship for architecture and engineering. The project has two authors, one from an architectural and one from an engineering educational background. It investigates the metaphorical and operational role of mathematics in the design process and outcomes.     

Interplay Between Wetting and Phase Behavior in Binary Polymer Films and Wedges: Monte Carlo Simulations and Mean Field Calculations

Confining a binary mixture, one can profoundly alter its miscibility behavior. The qualitative features of miscibility in confined geometry are ratheruniversal and shared by polymer mixtures as well as small molecules, but the unmixing transition in the bulk and the wetting transition are typically well separated in polymer blends. The interplay between wetting and miscibility of a symmetric polymer mixture via large-scale Monte Carlo simulations in the framework of the bond fluctuation model and via numerical self–consistent field calculations is studied. The film surfaces interact with the monomers via short ranged potentials, and the wetting transition of the semi–infinite system is of first order. It can be accurately located in the simulations by measuring the surface and interface tensions and using Young’s equation. If both surfaces in a film attract the same component, capillary condensation occurs and the critical point is close to the critical point of the bulk. If surfaces attract different components, an interface localization/delocalization occurs which gives rise to phase diagrams with two critical points in the vicinity of the pre-wetting critical point of the semi–infinite system. The crossover between these two types of phase diagrams as a function of the surface field asymmetry is studied. The dependence of the phase diagram on the film thickness Δ for antisymmetric surface fields is investigated. Upon decreasing the film thickness, the two critical points approach the symmetry axis of the phase diagram, and below a certain thickness Δ_tri, there remains only a single critical point at the symmetric composition. This corresponds to a second-order interface localization/delocalization transition even though the wetting transition is of first order. At a specific film thickness, Δ_tri, tricritical behavior is found. The behavior of antisymmetric films is compared with the phase behavior in an antisymmetric double wedge. While the former is the analog of the wetting transition of a planar surface, the latter is related to the filling behavior of a single wedge. Evidence for a second-order interface localization/delocalization transition in an antisymmetric double wedge is presented, and its unconventional critical behavior is related to the predictions of Parry et al. (Phys. Rev. Lett. 83:5535 (1999)) for wedge filling. The critical behavior differs from the Ising universality class and is characterized by strong anisotropic fluctuations.Invited paper presented at the Fifteenth Symposium on Thermophysical Properties, June 022–27, 2003, Boulder, Colorado, U.S.A.     

A Unified Theory of Uncalibrated Stereo for Both Perspective and Affine Cameras

This paper addresses the recovery of structure and motion from uncalibrated images of a scene under full perspective or under affine projection. Particular emphasis is placed on the configuration of two views, while the extension to $N$ views is given in Appendix. A unified expression of the fundamental matrix is derived which is valid for any projection model without lens distortion (including full perspective and affine camera). Affine reconstruction is considered as a special projective reconstruction. The theory is elaborated in a way such that everyone having knowledge of linear algebra can understand the discussion without difficulty. A new technique for affine reconstruction is developed, which consists in first estimating the affine epipolar geometry and then performing a triangulation for each point match with respect to an implicit common affine basis.