Subexponential Parameterized Odd Cycle Transversal on Planar Graphs

In the Odd Cycle Transversal (OCT) problem we are given a graph G on n vertices and an integer k, the objective is to determine whether there exists a vertex set O in G of size at most k such that G - O is bipartite. Reed, Smith and Vetta [Oper. Res. Lett., 2004] gave an algorithm for OCT with running time 3^kn^{O(1)}. Assuming the exponential time hypothesis of Impagliazzo, Paturi and Zane, the running time can not be improved to 2^{o(k)}n^{O(1)}. We show that OCT admits a randomized algorithm running in O(n^{O(1)} + 2^{O(sqrt{k} log k)}n) time when the input graph is planar. As a byproduct we also obtain a linear time algorithm for OCT on planar graphs with running time O(n^O(1) + 2O( sqrt(k) log k) n) time. This improves over an algorithm of Fiorini et al. [Disc. Appl. Math., 2008]

Exponentially-improved asymptotics of single and multidimensional integrals

Two different approaches for finding the exponentially improved asymptotic behaviour of integrals with saddlepoints are presented. Both rely on the deformation of the contours of integration and can be applied to single and multidimensional integrals alike. The class of integrals studied is of the form J J g(z1, ,zp)e-f{zu 'Zp,X)dz1 dz

Electron beam generation and structure of defects in carbon and boron nitride nanotubes

The nature and role of defects is of primary importance to understand the physical properties of C and BN single walled nanotubes. Transmission electron microscopy (TEM) is a well known powerful tool to study the structure of defects in materials. However, in the case of SWNTs, the electron irradiation of the TEM may knock out atoms. This effect may alter the native structure of the tube, and has also been proposed as a potential tool for nanoengineering of nanotubular structures. Here we develop a theoretical description of the irradiation mechanism. First, the anisotropy of the emission energy threshold is obtained via density functional based calculations. Then, we numerically derive the total Mott cross section for different emission sites of carbon and boron nitride nanotubes with different chiralities. Using a dedicated STEM microscope with experimental conditions optimised on the basis of derived cross-sections, we are able to control the generation of defects in nanotubular systems. Either point or line defects can be obtained with a spatial resolution of a few nanometers. The structure, energetics and electronics of point and line defects in BN systems have been investigated. Stability of mono- and di- vacancy defects in hexagonal boron nitride layers is investigated, and their activation energies and reaction paths for diffusion have been derived using the nudged elastic band method (NEB) combined with density functional based techniques. We demonstrate that the appearance of extended linear defects under electron irradiation is more favorable than a random distribution of point defects and this is due to the existence of preferential sites for atom emission in the presence of pre-existing defects, rather than thermal vacancy nucleation and migration

Rapid-Scan EPR and Imaging

EPR imaging at low frequency is a powerful tool to obtain important biological information in vivo in a non-invasive way. Properties of nitroxide and trityl radical imaging reagents have been studied. Developments in rapid scan imaging techniques are reported that improve efficiency of experiments and user-friendliness of software. Relaxation and signal-to-noise ratio (S/N) in pulse experiments on trityl radicals were measured at frequencies between 400 MHz and 1.5 GHz. Relaxation time increases as the frequency increases and the radical concentration decreases. Since relaxation time is a sensitive and accurate measure of oxygen pressure, this study provides criteria for the selection of the frequencies for in vivo applications. Rapid-scan EPR of irradiated solids at L-band was studied. The results show that for the same data acquisition time, S/N for rapid-scans was significantly higher than for conventional continuous wave spectra. Rapid scan EPR imaging of nitroxide was performed at 250 MHz. Experimental parameters for the sinusoidal single-sweep method were varied to get better image quality. The results show that larger gradient strength provides higher spatial resolution while smaller gradient step size provides finer texture. Another method based on field-stepped linear-scans was developed; field step size, rapid-scan segment width, rapid-scan frequencies and some other parameters were varied. The field-stepped linear-scan method was compared with the sinusoidal single-sweep method using criteria including linewidth and S/N, and the former turned out to be a less effective alternative to the latter. New developments have been made to expand what can be achieved with EPR imaging, such as reduced data acquisition time, quantification of image features, efficient use of instrument time, and simplified experimental procedures from data acquisition to spectral analysis. The Python programming language was used successfully as a new and comprehensive approach to run EPR imaging experiments compared to the prior method that used multiple software packages. These developments will make EPR imaging more accessible for a much wider user group

Eleventh International Conference on the Bearing Capacity of Roads, Railways and Airfields

Innovations in Road, Railway and Airfield Bearing Capacity – Volume 3 comprises the third part of contributions to the 11th International Conference on Bearing Capacity of Roads, Railways and Airfields (2022). In anticipation of the event, it unveils state-of-the-art information and research on the latest policies, traffic loading measurements, in-situ measurements and condition surveys, functional testing, deflection measurement evaluation, structural performance prediction for pavements and tracks, new construction and rehabilitation design systems, frost affected areas, drainage and environmental effects, reinforcement, traditional and recycled materials, full scale testing and on case histories of road, railways and airfields. This edited work is intended for a global audience of road, railway and airfield engineers, researchers and consultants, as well as building and maintenance companies looking to further upgrade their practices in the field

Geometry of moduli spaces of spin and prym curves of small genus

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