Analysis of random curve and vortex filament topology

This thesis covers a range of topics through the analysis of random curves and vortex filaments in various contexts. We find that phase vortices in random wave model, which is a type of model for quantum and wave chaos, are closed random walks whose length distribution is of universal scaling relation. We analyze the phase vortex in two-plus-one dimensional random waves and find that they can be classified into three types based on length: small loops whose behaviour is model dependent, large loops that are closed random walks, and vortex lines that are long enough to penetrate through the space before getting closed. Since vortex loops are closed random walks, we investigate the knot probability of them by generating a very large amount of sampling of equilateral and non-equilateral closed random polygons and determining their knot type by the Alexander polynomial. Then with statistical analysis we confirm a general probability equation for knots in random polygons. We also investigate a series of problems regarding to the knot probability of random polygons. The vortex in three-plus-one-dimensional space-time is two-dimensional surface and we call them vortex worldsheet. We find that while the topology of the vortex worldsheet is relativistically invariant, the topology of the vortex in the timeslice of observers in different reference frame changes with the Lorentz boost. We discuss constructions we used for the scenario and the superluminal region on the vortex world sheet, which is where the speed of phase vortex exceeds the light speed

Chaotic Behavior of Lorenz-Based Chemical System under the Influence of Fractals

This research examines a chaotic chemical reaction system based on the variation of the Lorenz system. This study demonstrates that although the first phase portraits of the chemical models under consideration and the Lorenz models are comparable, they do not fully follow all the features of the Lorenz system. Questions about the existence of fractals in systems based on chemical reactions are addressed in the current work. Moreover, we have worked on the hidden information inside in each wings of a chaotic system generated through fractal process, for the first time, with the aid of basin for fractals. Additionally, we looked closely at the dynamics of the model across the basin, which revealed additional details regarding the existence of hidden and cyclic attractors inside each wing. We also produced multi-wings for system (1) in the current study, demonstrating in a general manner that the number of cyclic attractors increase in a direct relation to the number of wings. Moreover, Julia approach is used to accomplish the work of multi-wings whereas for searching cyclic attractors inside each extra wing, we have used fifteen million initial conditions and compiled them as a basin set. The data generated in this work is also provided within this paper for the ease of readers

Microscopic mechanisms of dephasing due to electron-electron interactions

We develop a non-perturbative numerical method to study tunneling of a single electron through an Aharonov-Bohm ring where several strongly interacting electrons are bound. Inelastic processes and spin-flip scattering are taken into account. The method is applied to study microscopic mechanisms of dephasing in a non-trivial model. We show that electron-electron interactions described by the Hubbard Hamiltonian lead to strong dephasing: the transmission probability at flux $\Phi=\pi$ is high even at small interaction strength. In addition to inelastic scattering, we identify two energy conserving mechanisms of dephasing: symmetry-changing and spin-flip scattering. The many-electron state on the ring determines which of these mechanisms will be at play: transmitted current can occur either in elastic or inelastic channels, with or without changing the spin of the scattering electron.Comment: 11 pages, 16 figures Submitted to Phys. Rev.

Shot noise in mesoscopic systems

This is a review of shot noise, the time-dependent fluctuations in the electrical current due to the discreteness of the electron charge, in small conductors. The shot-noise power can be smaller than that of a Poisson process as a result of correlations in the electron transmission imposed by the Pauli principle. This suppression takes on simple universal values in a symmetric double-barrier junction (suppression factor 1/2), a disordered metal (factor 1/3), and a chaotic cavity (factor 1/4). Loss of phase coherence has no effect on this shot-noise suppression, while thermalization of the electrons due to electron-electron scattering increases the shot noise slightly. Sub-Poissonian shot noise has been observed experimentally. So far unobserved phenomena involve the interplay of shot noise with the Aharonov-Bohm effect, Andreev reflection, and the fractional quantum Hall effect.Comment: 37 pages, Latex, 10 figures (eps). To be published in "Mesoscopic Electron Transport," edited by L. P. Kouwenhoven, G. Schoen, and L. L. Sohn, NATO ASI Series E (Kluwer Academic Publishing, Dordrecht

Shot Noise in Mesoscopic Conductors

Theoretical and experimental work concerned with dynamic fluctuations has developed into a very active and fascinating subfield of mesoscopic physics. We present a review of this development focusing on shot noise in small electric conductors. Shot noise is a consequence of the quantization of charge. It can be used to obtain information on a system which is not available through conductance measurements. In particular, shot noise experiments can determine the charge and statistics of the quasiparticles relevant for transport, and reveal information on the potential profile and internal energy scales of mesoscopic systems. Shot noise is generally more sensitive to the effects of electron-electron interactions than the average conductance. We present a discussion based on the conceptually transparent scattering approach and on the classical Langevin and Boltzmann-Langevin methods; in addition a discussion of results which cannot be obtained by these methods is provided. We conclude the review by pointing out a number of unsolved problems and an outlook on the likely future development of the field.Comment: 99 two-column pages; 38 .eps figures included. Submitted to Physics Reports. Many minor improvements; typos corrected; references added and update

Prognostic Value of Three Different Methods of MGMT Promoter Methylation Analysis in a Prospective Trial on Newly Diagnosed Glioblastoma

Hypermethylation in the promoter region of the MGMT gene encoding the DNA repair protein O6-methylguanine-DNA methyltransferase is among the most important prognostic factors for patients with glioblastoma and predicts response to treatment with alkylating agents like temozolomide. Hence, the MGMT status is widely determined in most clinical trials and frequently requested in routine diagnostics of glioblastoma. Since various different techniques are available for MGMT promoter methylation analysis, a generally accepted consensus as to the most suitable diagnostic method remains an unmet need. Here, we assessed methylation-specific polymerase chain reaction (MSP) as a qualitative and semi-quantitative method, pyrosequencing (PSQ) as a quantitative method, and methylation-specific multiplex ligation-dependent probe amplification (MS-MLPA) as a semi-quantitative method in a series of 35 formalin-fixed, paraffin-embedded glioblastoma tissues derived from patients treated in a prospective clinical phase II trial that tested up-front chemoradiotherapy with dose-intensified temozolomide (UKT-05). Our goal was to determine which of these three diagnostic methods provides the most accurate prediction of progression-free survival (PFS). The MGMT promoter methylation status was assessable by each method in almost all cases (n = 33/35 for MSP; n = 35/35 for PSQ; n = 34/35 for MS-MLPA). We were able to calculate significant cut-points for the continuous methylation signals at each CpG site analysed by PSQ (range, 11.5 to 44.9%) and at one CpG site assessed by MS-MLPA (3.6%) indicating that a dichotomisation of continuous methylation data as a prerequisite for comparative survival analyses is feasible. Our results show that, unlike MS-MLPA, MSP and PSQ provide a significant improvement of predicting PFS compared with established clinical prognostic factors alone (likelihood ratio tests: p<0.001). Conclusively, taking into consideration prognostic value, cost effectiveness and ease of use, we recommend pyrosequencing for analyses of MGMT promoter methylation in high-throughput settings and MSP for clinical routine diagnostics with low sample numbers

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead