Variant Monte Carlo algorithm for driven elastic strings in random media

We discuss the non-local Variant Monte Carlo algorithm which has been successfully employed in the study of driven elastic strings in disordered media at the depinning threshold. Here we prove two theorems, which establish that the algorithm satisfies the crucial no-passing rule and that, after some initial time, the string exclusively moves forward. The Variant Monte Carlo algorithm overcomes the shortcomings of local methods, as we show by analyzing the depinning threshold of a single-pin problem.Comment: 6 pages, 2 figures, proceedings of Conference on Computational Physics, CCP2004 (Genova, Italy

Origin of the roughness exponent in elastic strings at the depinning threshold

Within a recently developed framework of dynamical Monte Carlo algorithms, we compute the roughness exponent $\zeta$ of driven elastic strings at the depinning threshold in 1+1 dimensions for different functional forms of the (short-range) elastic energy. A purely harmonic elastic energy leads to an unphysical value for $\zeta$. We include supplementary terms in the elastic energy of at least quartic order in the local extension. We then find a roughness exponent of $\zeta \simeq 0.63$, which coincides with the one obtained for different cellular automaton models of directed percolation depinning. The quartic term translates into a nonlinear piece which changes the roughness exponent in the corresponding continuum equation of motion. We discuss the implications of our analysis for higher-dimensional elastic manifolds in disordered media.Comment: 4 pages, 2 figure

Creep dynamics of elastic manifolds via exact transition pathways

We study the steady state of driven elastic strings in disordered media below the depinning threshold. In the low-temperature limit, for a fixed sample, the steady state is dominated by a single configuration, which we determine exactly from the transition pathways between metastable states. We obtain the dynamical phase diagram in this limit. At variance with a thermodynamic phase transition, the depinning transition is not associated with a divergent length scale of the steady state below threshold, but only of the transient dynamics. We discuss the distribution of barrier heights, and check the validity of the dynamic phase diagram at small but finite temperatures using Langevin simulations. The phase diagram continues to hold for broken statistical tilt symmetry. We point out the relevance of our results for experiments of creep motion in elastic interfaces.Comment: 14 pages, 18 figure

Single DNA conformations and biological function

From a nanoscience perspective, cellular processes and their reduced in vitro imitations provide extraordinary examples for highly robust few or single molecule reaction pathways. A prime example are biochemical reactions involving DNA molecules, and the coupling of these reactions to the physical conformations of DNA. In this review, we summarise recent results on the following phenomena: We investigate the biophysical properties of DNA-looping and the equilibrium configurations of DNA-knots, whose relevance to biological processes are increasingly appreciated. We discuss how random DNA-looping may be related to the efficiency of the target search process of proteins for their specific binding site on the DNA molecule. And we dwell on the spontaneous formation of intermittent DNA nanobubbles and their importance for biological processes, such as transcription initiation. The physical properties of DNA may indeed turn out to be particularly suitable for the use of DNA in nanosensing applications.Comment: 53 pages, 45 figures. Slightly revised version of a review article, that is going to appear in the J. Comput. Theoret. Nanoscience; some typos correcte

Adaptive Feature Engineering Modeling for Ultrasound Image Classification for Decision Support

Ultrasonography is considered a relatively safe option for the diagnosis of benign and malignant cancer lesions due to the low-energy sound waves used. However, the visual interpretation of the ultrasound images is time-consuming and usually has high false alerts due to speckle noise. Improved methods of collection image-based data have been proposed to reduce noise in the images; however, this has proved not to solve the problem due to the complex nature of images and the exponential growth of biomedical datasets. Secondly, the target class in real-world biomedical datasets, that is the focus of interest of a biopsy, is usually significantly underrepresented compared to the non-target class. This makes it difficult to train standard classification models like Support Vector Machine (SVM), Decision Trees, and Nearest Neighbor techniques on biomedical datasets because they assume an equal class distribution or an equal misclassification cost. Resampling techniques by either oversampling the minority class or under-sampling the majority class have been proposed to mitigate the class imbalance problem but with minimal success. We propose a method of resolving the class imbalance problem with the design of a novel data-adaptive feature engineering model for extracting, selecting, and transforming textural features into a feature space that is inherently relevant to the application domain. We hypothesize that by maximizing the variance and preserving as much variability in well-engineered features prior to applying a classifier model will boost the differentiation of the thyroid nodules (benign or malignant) through effective model building. Our proposed a hybrid approach of applying Regression and Rule-Based techniques to build our Feature Engineering and a Bayesian Classifier respectively. In the Feature Engineering model, we transformed images pixel intensity values into a high dimensional structured dataset and fitting a regression analysis model to estimate relevant kernel parameters to be applied to the proposed filter method. We adopted an Elastic Net Regularization path to control the maximum log-likelihood estimation of the Regression model. Finally, we applied a Bayesian network inference to estimate a subset for the textural features with a significant conditional dependency in the classification of the thyroid lesion. This is performed to establish the conditional influence on the textural feature to the random factors generated through our feature engineering model and to evaluate the success criterion of our approach. The proposed approach was tested and evaluated on a public dataset obtained from thyroid cancer ultrasound diagnostic data. The analyses of the results showed that the classification performance had a significant improvement overall for accuracy and area under the curve when then proposed feature engineering model was applied to the data. We show that a high performance of 96.00% accuracy with a sensitivity and specificity of 99.64%) and 90.23% respectively was achieved for a filter size of 13 × 13

Morphologies of Semiflexible Polymers in Bulk and Spherical Confinement

Diese Dissertation befasst sich mit dem Verhalten eines generischen semiflexi- blen Polymermodells. Insbesondere untersucht es den Einfluss von Steifigkeit auf die unterschiedlichen thermodynamisch stabilen Konformationen. Es wird erläutert wie durch die Steifigkeit des Polymers verschiedene struk- turierte Phasen induziert werden. Insbesondere wird dabei auf die sta- bilen verknoteten Phasen eingegangen. Der zweite Teil der Dissertation beschäftigt sich dann mit dem Einfluss einer kugelförmigen Einsperrung auf das Phasendiagramm des selben Polymermodells. Es wird gezeigt wie in Abhängigkeit der Ordnung des Phasenüberganges die Einsperrung entweder zu einem stabilisierenden oder destabilisierenden Effekt führt. Im dritten Teil der Dissertation werden dann die komplexen Monte-Carlo Simulationen erläutert die für die Simulation der physikalischen Systeme genutzt wurde. Diese Algorithmen wurden in ein Framework integriert, so dass diese wieder verwendet werden können