Robust self-assembly of graphs

Self-assembly is a process in which small building blocks interact autonomously to form larger structures. A recently studied model of self-assembly is the Accretive Graph Assembly Model whereby an edge-weighted graph is assembled one vertex at a time starting from a designated seed vertex. The weight of an edge specifies the magnitude of attraction (positive weight) or repulsion (negative weight) between adjacent vertices. It is feasible to add a vertex to the assembly if the total attraction minus repulsion of the already built neighbors exceeds a certain threshold, called the assembly temperature. This model naturally generalizes the extensively studied Tile Assembly Model. A natural question in graph self-assembly is to determine whether or not there exists a sequence of feasible vertex additions to realize the entire graph. However, even when it is feasible to realize the assembly, not much can be inferred about its likelihood of realization in practice due to the uncontrolled nature of the self-assembly process. Motivated by this, we introduce the robust self-assembly problem where the goal is to determine if every possible sequence of feasible vertex additions leads to the completion of the assembly. We show that the robust self-assembly problem is co-NP-complete even on planar graphs with two distinct edge weights. We then examine the tractability of the robust self-assembly problem on a natural subclass of planar graphs, namely grid graphs. We identify structural conditions that determine whether or not a grid graph can be robustly self-assembled, and give poly-time algorithms to determine this for several interesting cases of the problem. Finally, we also show that the problem of counting the number of feasible orderings that lead to the completion of an assembly is #P-complete.     

Growth of low dislocation density single crystals of nickel

Low dislocation density single crystals of nickel have been grown at high ambient pressure by the Czochralski method. X-ray Laue picture shows that the crystals are strain-free. The dislocation density was determined to be <10³/cm² by the etching procedure. It was found that the necking and cone regions are very critical in the dislocation introduction in the crystals. An increase in the ambient pressure used during the growth seems to aid the crystal quality.     

Novel technique for investigating high-power microwave pulses using Kerr effect

A novel method for the measurement of peak power of microwave pulses up to the few hundred kilowatts level based on the microwave-induced electro-optical Kerr effect in nonlossy dielectric liquids is described. This method provides additional information about the shape of the pulse, which is not usually given by the conventional methods.<>     

A Novel FRFT Beamformer for Rayleigh Faded Channels

A method of optimal beamforming for flat Rayleigh faded channels using the Fractional Fourier Transform (FRFT) is considered in this paper. It has been demonstrated through simulations that optimal beamforming with FRFT allows smaller mean-square errors in restoring signals degraded with linear time-or frequency variant distortions and Additive White Gaussian Noise. This is made possible by the additional flexibility that comes with free parameter ‘a’ of the fractional Fourier transform as oppose to the classical Fourier transform (FT). The method is especially useful in moving source problems, where Doppler Effect produces frequency shift when the source is moving, as in mobile and wireless communication where user produces the frequency shift while moving. In this paper it is shown through simulations that beamforming in fractional domain reduces BER as compared to time or frequency domain.     

Approximate Shortest Paths Avoiding a Failed Vertex: Near Optimal Data Structures for Undirected Unweighted Graphs

Let G=(V,E) be an undirected unweighted graph. A path between any two vertices u,v∈V is said to be t-approximate shortest path if its length is at most t times the length of the shortest path between u and v. We address the problem of building a compact data structure which can efficiently answer the following query for any u,v,x∈V and t>1: Report t-approximate shortest path between u and v when vertex x fails. We present data structures for the single source as well as all-pairs versions of this problem. The query time guaranteed by our data structures is optimal up to a constant factor. Moreover, the size of each of them nearly matches the size of the corresponding data structure with no failures.     

Effects of Doping Trivalent Ions in Bismuth Borate Glasses

Bismuth borate glasses from the system: 40Bi₂O₃–59B₂O₃–1Tv₂O₃ (where Tv=Al, Y, Nd, Sm, and Eu) and three glasses of composition: 40Bi₂O₃–60B₂O₃, 37.5Bi₂O₃–62.5B₂O₃ and 38Bi₂O₃–60B₂O₃–2Al₂O₃ were prepared by melt quenching and characterized by density, UV-visible absorption spectroscopy and differential thermal analysis (DTA) studies. Bismuth borate glasses exhibit a very strong optical absorption band just below their absorption edge. Glasses were devitrified by heat treatment at temperatures above their glass transition temperatures and the crystalline phases produced in them were characterized by Fourier transform infrared (FTIR) absorption spectroscopy and X-ray diffraction (XRD). Bi₃B₅O₁₂ was found to be the most abundant phase in all devitrified samples. DTA studies on glasses and FTIR and XRD analysis on crystallized samples revealed that very small amounts of trivalent ion doping causes significant changes in the devitrification properties of bismuth borate glasses; rare-earth ions promote the formation of metastable BiBO₃–I and BiBO₃–II phases during glass crystallization.     

Multiplex PCR/LDR for detection of K-ras mutations in primary colon tumors

The use of near-infrared spectroscopy to measure noninvasively changes in the redox state of cerebral cytochrome oxidase in vivo is controversial. We therefore tested these measurements using a multiwavelength detector in the neonatal pig brain. Exchange transfusion with perfluorocarbons revealed that the spectrum of cytochrome oxidase in the near-infrared was identical in the neonatal pig, the adult rat, and in the purified enzyme. Under normoxic conditions, the neonatal pig brain contained 15 micromol/L deoxyhemoglobin, 29 micromol/L oxyhemoglobin, and 1.2 micromol/L oxidized cytochrome oxidase. The mitochondrial inhibitor cyanide was used to determine whether redox changes in cytochrome oxidase could be detected in the presence of the larger cerebral hemoglobin concentration. Addition of cyanide induced full reduction of cytochrome oxidase in both blooded and bloodless animals. In the blooded animals, subsequent anoxia caused large changes in hemoglobin oxygenation and concentration but did not affect the cytochrome oxidase near-infrared signal. Simultaneous blood oxygenation level-dependent magnetic resonance imaging measurements showed a good correlation with near-infrared measurements of deoxyhemoglobin concentration. Possible interference in the near-infrared measurements from light scattering changes was discounted by simultaneous measurements of the optical pathlength using the cerebral water absorbance as a standard chromophore. We conclude that, under these conditions, near-infrared spectroscopy can accurately measure changes in the cerebral cytochrome oxidase redox state.